The van gaining four saved more than the hybrid gaining twenty

# Self-authored for the EML case corpus (no external origin). A household with
# two cars, each driven 10000 km a year, can afford to replace one. The van does
# 8 km per litre and its replacement would do 12; the sedan does 20 and a hybrid
# would do 40. The household reasons that a gain of 20 km per litre is five
# times a gain of 4 and replaces the sedan. Which swap saves more fuel is
# computed below.
#
# The reasoning is careful. All four ratings are accurate; both cars really are
# driven the same distance; 20 really is five times 4; and the intent is exactly
# 'burn the least fuel'.
#
# Fuel used is distance divided by kilometres per litre, so a gain in km per
# litre is worth most where the figure is low: the van's 8 to 12 saves 417
# litres a year, the sedan's 20 to 40 saves 250. Measured in litres per 100 km -
# the unit the fuel bill is written in - the van's swap is the bigger one.

10000 => km_a_year_each_car
8 => van_km_per_litre
12 => new_van_km_per_litre
20 => sedan_km_per_litre
40 => hybrid_km_per_litre

new_van_km_per_litre - van_km_per_litre => van_gain_km_per_litre
hybrid_km_per_litre - sedan_km_per_litre => sedan_gain_km_per_litre
int(sedan_gain_km_per_litre / van_gain_km_per_litre) => gain_ratio
int(km_a_year_each_car / van_km_per_litre) => van_litres_a_year
int(km_a_year_each_car / new_van_km_per_litre) => new_van_litres_a_year
int(km_a_year_each_car / sedan_km_per_litre) => sedan_litres_a_year
int(km_a_year_each_car / hybrid_km_per_litre) => hybrid_litres_a_year
van_litres_a_year - new_van_litres_a_year => van_swap_saves_litres
sedan_litres_a_year - hybrid_litres_a_year => sedan_swap_saves_litres
van_swap_saves_litres - sedan_swap_saves_litres => van_swap_saves_more_by_litres
int(1000 / van_km_per_litre) => van_tenths_of_a_litre_per_100_km
int(1000 / new_van_km_per_litre) => new_van_tenths_of_a_litre_per_100_km
int(1000 / sedan_km_per_litre) => sedan_tenths_of_a_litre_per_100_km
int(1000 / hybrid_km_per_litre) => hybrid_tenths_of_a_litre_per_100_km

"each car                        : " + str(km_a_year_each_car) + " km a year" ^0
"van                             : " + str(van_km_per_litre) + " to " + str(new_van_km_per_litre) + " km per litre, a gain of " + str(van_gain_km_per_litre) ^0
"sedan                           : " + str(sedan_km_per_litre) + " to " + str(hybrid_km_per_litre) + " km per litre, a gain of " + str(sedan_gain_km_per_litre) + ", " + str(gain_ratio) + " times the van's" ^0
"" ^0
"van, litres a year              : " + str(van_litres_a_year) + " now, " + str(new_van_litres_a_year) + " after, saving " + str(van_swap_saves_litres) ^0
"sedan, litres a year            : " + str(sedan_litres_a_year) + " now, " + str(hybrid_litres_a_year) + " after, saving " + str(sedan_swap_saves_litres) ^0
"the van's swap saves more by    : " + str(van_swap_saves_more_by_litres) + " litres a year" ^0
"" ^0
"in tenths of a litre per 100 km : van " + str(van_tenths_of_a_litre_per_100_km) + " to " + str(new_van_tenths_of_a_litre_per_100_km) + ", sedan " + str(sedan_tenths_of_a_litre_per_100_km) + " to " + str(hybrid_tenths_of_a_litre_per_100_km) ^0
"" ^0

# ---- what the household verified ----

"the bigger-gain reasoning" ^0
"  ratings : all four accurate" ^0
"  distance : " + str(km_a_year_each_car) + " km a year for each car" ^0
"  gains : " + str(sedan_gain_km_per_litre) + " against " + str(van_gain_km_per_litre) + ", " + str(gain_ratio) + " times as big" ^0
"  intent : burn the least fuel" ^0
"  facts wrong : 0" ^0
"  verdict : REPLACE THE SEDAN, THE GAIN IS FIVE TIMES BIGGER" ^0
"" ^0
"  reading the four ratings accurately is the part done right" ^0
"  here, and it is why both gains in km per litre are exactly" ^0
"  what the dealers said" ^0
"" ^0

# ---- what a kilometre per litre is worth ----

"fuel is distance over the rating" ^0
"  what the bill counts : litres, and litres are the distance" ^0
"    divided by km per litre" ^0
"  a gain at the low end : 8 to 12 cuts every 100 km from " + str(van_tenths_of_a_litre_per_100_km) ^0
"    to " + str(new_van_tenths_of_a_litre_per_100_km) + " tenths of a litre" ^0
"  a gain at the high end : 20 to 40 cuts it from " + str(sedan_tenths_of_a_litre_per_100_km) + " to " + str(hybrid_tenths_of_a_litre_per_100_km) ^0
"  why the small number wins : a car that already sips has" ^0
"    little left to save, however large the gain looks" ^0
"  over a year : " + str(van_swap_saves_litres) + " litres against " + str(sedan_swap_saves_litres) ^0
"" ^0

# ---- what the household got ----

"the fuel bill" ^0
"  believed : the bigger saving, five times the van's" ^0
"  actual : " + str(sedan_swap_saves_litres) + " litres a year, " + str(van_swap_saves_more_by_litres) + " fewer than the van's swap" ^0
"  is any rating wrong : no" ^0
"  is a bigger gain in km per litre a bigger saving : not across" ^0
"    cars; the unit runs the wrong way for the question" ^0
"" ^0

# ---- null control ----

# The same choice made by litres saved over the year's driving instead of by
# the gain in km per litre.
250 => nc_litres_saved_ranking_by_km_per_litre_gain
417 => nc_litres_saved_ranking_by_litres_a_year
167 => nc_litres_a_year_the_right_unit_recovers

"null control - rank the swaps by litres a year" ^0
"  litres saved, ranking by the km per litre gain : " + str(nc_litres_saved_ranking_by_km_per_litre_gain) ^0
"  litres saved, ranking by litres a year : " + str(nc_litres_saved_ranking_by_litres_a_year) ^0
"  litres a year the right unit recovers : " + str(nc_litres_a_year_the_right_unit_recovers) ^0
"  no car and no rating changed; the swaps were compared in the" ^0
"  quantity the bill is written in" ^0
"" ^0

# ---- the rule ----

"what a bigger gain in km per litre guarantees" ^0
"  the new car goes further on each litre : exactly" ^0
"  it saves more fuel than a smaller gain : not addressed; fuel is" ^0
"    distance over km per litre, so " + str(van_km_per_litre) + " to " + str(new_van_km_per_litre) + " saves " + str(van_swap_saves_litres) + " litres a year" ^0
"    and " + str(sedan_km_per_litre) + " to " + str(hybrid_km_per_litre) + " saves " + str(sedan_swap_saves_litres) ^0
"" ^0

"a rate written upside down makes the small gains look small; the fuel is in" ^0
"the reciprocal, and the reciprocal is steepest where the number is low" ^0
"" ^0

"The ratings are right and " + str(sedan_gain_km_per_litre) + " is " + str(gain_ratio) + " times " + str(van_gain_km_per_litre) + ". But fuel is distance over km" ^0
"per litre: the van's " + str(van_km_per_litre) + " to " + str(new_van_km_per_litre) + " saves " + str(van_swap_saves_litres) + " litres a year and the sedan's " + str(sedan_km_per_litre) + " to " + str(hybrid_km_per_litre) + " saves" ^0
"" + str(sedan_swap_saves_litres) + ", " + str(van_swap_saves_more_by_litres) + " fewer, until the swaps are compared in litres and not in the" ^0
"size of the gain." ^0

km_a_year_each_car = 10000
van_km_per_litre = 8
new_van_km_per_litre = 12
sedan_km_per_litre = 20
hybrid_km_per_litre = 40
van_gain_km_per_litre = new_van_km_per_litre - van_km_per_litre
sedan_gain_km_per_litre = hybrid_km_per_litre - sedan_km_per_litre
gain_ratio = int(sedan_gain_km_per_litre / van_gain_km_per_litre)
van_litres_a_year = int(km_a_year_each_car / van_km_per_litre)
new_van_litres_a_year = int(km_a_year_each_car / new_van_km_per_litre)
sedan_litres_a_year = int(km_a_year_each_car / sedan_km_per_litre)
hybrid_litres_a_year = int(km_a_year_each_car / hybrid_km_per_litre)
van_swap_saves_litres = van_litres_a_year - new_van_litres_a_year
sedan_swap_saves_litres = sedan_litres_a_year - hybrid_litres_a_year
van_swap_saves_more_by_litres = van_swap_saves_litres - sedan_swap_saves_litres
van_tenths_of_a_litre_per_100_km = int(1000 / van_km_per_litre)
new_van_tenths_of_a_litre_per_100_km = int(1000 / new_van_km_per_litre)
sedan_tenths_of_a_litre_per_100_km = int(1000 / sedan_km_per_litre)
hybrid_tenths_of_a_litre_per_100_km = int(1000 / hybrid_km_per_litre)
print("each car                        : " + str(km_a_year_each_car) + " km a year")
print("van                             : " + str(van_km_per_litre) + " to " + str(new_van_km_per_litre) + " km per litre, a gain of " + str(van_gain_km_per_litre))
print("sedan                           : " + str(sedan_km_per_litre) + " to " + str(hybrid_km_per_litre) + " km per litre, a gain of " + str(sedan_gain_km_per_litre) + ", " + str(gain_ratio) + " times the van's")
print("")
print("van, litres a year              : " + str(van_litres_a_year) + " now, " + str(new_van_litres_a_year) + " after, saving " + str(van_swap_saves_litres))
print("sedan, litres a year            : " + str(sedan_litres_a_year) + " now, " + str(hybrid_litres_a_year) + " after, saving " + str(sedan_swap_saves_litres))
print("the van's swap saves more by    : " + str(van_swap_saves_more_by_litres) + " litres a year")
print("")
print("in tenths of a litre per 100 km : van " + str(van_tenths_of_a_litre_per_100_km) + " to " + str(new_van_tenths_of_a_litre_per_100_km) + ", sedan " + str(sedan_tenths_of_a_litre_per_100_km) + " to " + str(hybrid_tenths_of_a_litre_per_100_km))
print("")
print("the bigger-gain reasoning")
print("  ratings : all four accurate")
print("  distance : " + str(km_a_year_each_car) + " km a year for each car")
print("  gains : " + str(sedan_gain_km_per_litre) + " against " + str(van_gain_km_per_litre) + ", " + str(gain_ratio) + " times as big")
print("  intent : burn the least fuel")
print("  facts wrong : 0")
print("  verdict : REPLACE THE SEDAN, THE GAIN IS FIVE TIMES BIGGER")
print("")
print("  reading the four ratings accurately is the part done right")
print("  here, and it is why both gains in km per litre are exactly")
print("  what the dealers said")
print("")
print("fuel is distance over the rating")
print("  what the bill counts : litres, and litres are the distance")
print("    divided by km per litre")
print("  a gain at the low end : 8 to 12 cuts every 100 km from " + str(van_tenths_of_a_litre_per_100_km))
print("    to " + str(new_van_tenths_of_a_litre_per_100_km) + " tenths of a litre")
print("  a gain at the high end : 20 to 40 cuts it from " + str(sedan_tenths_of_a_litre_per_100_km) + " to " + str(hybrid_tenths_of_a_litre_per_100_km))
print("  why the small number wins : a car that already sips has")
print("    little left to save, however large the gain looks")
print("  over a year : " + str(van_swap_saves_litres) + " litres against " + str(sedan_swap_saves_litres))
print("")
print("the fuel bill")
print("  believed : the bigger saving, five times the van's")
print("  actual : " + str(sedan_swap_saves_litres) + " litres a year, " + str(van_swap_saves_more_by_litres) + " fewer than the van's swap")
print("  is any rating wrong : no")
print("  is a bigger gain in km per litre a bigger saving : not across")
print("    cars; the unit runs the wrong way for the question")
print("")
nc_litres_saved_ranking_by_km_per_litre_gain = 250
nc_litres_saved_ranking_by_litres_a_year = 417
nc_litres_a_year_the_right_unit_recovers = 167
print("null control - rank the swaps by litres a year")
print("  litres saved, ranking by the km per litre gain : " + str(nc_litres_saved_ranking_by_km_per_litre_gain))
print("  litres saved, ranking by litres a year : " + str(nc_litres_saved_ranking_by_litres_a_year))
print("  litres a year the right unit recovers : " + str(nc_litres_a_year_the_right_unit_recovers))
print("  no car and no rating changed; the swaps were compared in the")
print("  quantity the bill is written in")
print("")
print("what a bigger gain in km per litre guarantees")
print("  the new car goes further on each litre : exactly")
print("  it saves more fuel than a smaller gain : not addressed; fuel is")
print("    distance over km per litre, so " + str(van_km_per_litre) + " to " + str(new_van_km_per_litre) + " saves " + str(van_swap_saves_litres) + " litres a year")
print("    and " + str(sedan_km_per_litre) + " to " + str(hybrid_km_per_litre) + " saves " + str(sedan_swap_saves_litres))
print("")
print("a rate written upside down makes the small gains look small; the fuel is in")
print("the reciprocal, and the reciprocal is steepest where the number is low")
print("")
print("The ratings are right and " + str(sedan_gain_km_per_litre) + " is " + str(gain_ratio) + " times " + str(van_gain_km_per_litre) + ". But fuel is distance over km")
print("per litre: the van's " + str(van_km_per_litre) + " to " + str(new_van_km_per_litre) + " saves " + str(van_swap_saves_litres) + " litres a year and the sedan's " + str(sedan_km_per_litre) + " to " + str(hybrid_km_per_litre) + " saves")
print("" + str(sedan_swap_saves_litres) + ", " + str(van_swap_saves_more_by_litres) + " fewer, until the swaps are compared in litres and not in the")
print("size of the gain.")

each car                        : 10000 km a year
van                             : 8 to 12 km per litre, a gain of 4
sedan                           : 20 to 40 km per litre, a gain of 20, 5 times the van's

van, litres a year              : 1250 now, 833 after, saving 417
sedan, litres a year            : 500 now, 250 after, saving 250
the van's swap saves more by    : 167 litres a year

in tenths of a litre per 100 km : van 125 to 83, sedan 50 to 25

the bigger-gain reasoning
  ratings : all four accurate
  distance : 10000 km a year for each car
  gains : 20 against 4, 5 times as big
  intent : burn the least fuel
  facts wrong : 0
  verdict : REPLACE THE SEDAN, THE GAIN IS FIVE TIMES BIGGER

  reading the four ratings accurately is the part done right
  here, and it is why both gains in km per litre are exactly
  what the dealers said

fuel is distance over the rating
  what the bill counts : litres, and litres are the distance
    divided by km per litre
  a gain at the low end : 8 to 12 cuts every 100 km from 125
    to 83 tenths of a litre
  a gain at the high end : 20 to 40 cuts it from 50 to 25
  why the small number wins : a car that already sips has
    little left to save, however large the gain looks
  over a year : 417 litres against 250

the fuel bill
  believed : the bigger saving, five times the van's
  actual : 250 litres a year, 167 fewer than the van's swap
  is any rating wrong : no
  is a bigger gain in km per litre a bigger saving : not across
    cars; the unit runs the wrong way for the question

null control - rank the swaps by litres a year
  litres saved, ranking by the km per litre gain : 250
  litres saved, ranking by litres a year : 417
  litres a year the right unit recovers : 167
  no car and no rating changed; the swaps were compared in the
  quantity the bill is written in

what a bigger gain in km per litre guarantees
  the new car goes further on each litre : exactly
  it saves more fuel than a smaller gain : not addressed; fuel is
    distance over km per litre, so 8 to 12 saves 417 litres a year
    and 20 to 40 saves 250

a rate written upside down makes the small gains look small; the fuel is in
the reciprocal, and the reciprocal is steepest where the number is low

The ratings are right and 20 is 5 times 4. But fuel is distance over km
per litre: the van's 8 to 12 saves 417 litres a year and the sedan's 20 to 40 saves
250, 167 fewer, until the swaps are compared in litres and not in the
size of the gain.

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