# Example 984 — The taller tyres made every kilometre read short `the_taller_tyres_made_every_kilometre_read_short.eml` - A driver replaces 205/55 R16 tyres with taller 225/60 R16 ones on the same rims, keeps the needle at the 100 km/h limit on the motorway, and reasons that the speedometer shows the car's speed and reads a little high anyway. What the needle means on the new tyres is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A driver replaces # 205/55 R16 tyres with taller 225/60 R16 ones on the same rims, keeps the # needle at the 100 km/h limit on the motorway, and reasons that the # speedometer shows the car's speed and reads a little high anyway. What the # needle means on the new tyres is computed below. # # The reasoning is careful. The needle really does sit at 100; nothing in the # car's electronics was changed; the speedometer really did read high before, # 100 on the needle at a true 96; and the intent is exactly 'stay at the limit'. # # A speedometer does not see the road; it counts turns of the wheels and was # calibrated for the old tyre's circumference. The taller tyre covers 10704 per # ten thousand of the old distance in each turn, so the needle's 100 is now a # true 102: the factory's four-kilometre margin has become two over. The # odometer, accurate before, now shows 18684 of every 20000 km driven. 16 => rim_inches 254 => tenths_of_a_mm_per_inch 205 => old_tyre_width_mm 55 => old_sidewall_percent 225 => new_tyre_width_mm 60 => new_sidewall_percent 100 => indicated_kmh 96 => true_kmh_at_the_needle_100_on_the_old_tyres 20000 => km_driven_in_a_year rim_inches * tenths_of_a_mm_per_inch => rim_tenths_of_a_mm rim_tenths_of_a_mm + int(2 * old_tyre_width_mm * old_sidewall_percent * 10 / 100) => old_diameter_tenths_of_a_mm rim_tenths_of_a_mm + int(2 * new_tyre_width_mm * new_sidewall_percent * 10 / 100) => new_diameter_tenths_of_a_mm int(new_diameter_tenths_of_a_mm * 10000 / old_diameter_tenths_of_a_mm) => road_per_turn_vs_old_per_myriad int(true_kmh_at_the_needle_100_on_the_old_tyres * new_diameter_tenths_of_a_mm / old_diameter_tenths_of_a_mm) => true_kmh_at_the_needle_100_now indicated_kmh - true_kmh_at_the_needle_100_on_the_old_tyres => old_margin_kmh true_kmh_at_the_needle_100_now - indicated_kmh => now_over_the_needle_kmh int(km_driven_in_a_year * old_diameter_tenths_of_a_mm / new_diameter_tenths_of_a_mm) => odometer_shows_km km_driven_in_a_year - odometer_shows_km => odometer_short_by_km "rim : " + str(rim_inches) + " inches, " + str(rim_tenths_of_a_mm) + " tenths of a mm" ^0 "old tyre, 205/55 : " + str(old_diameter_tenths_of_a_mm) + " tenths of a mm across" ^0 "new tyre, 225/60 : " + str(new_diameter_tenths_of_a_mm) + " tenths of a mm across" ^0 "road per wheel turn vs old : " + str(road_per_turn_vs_old_per_myriad) + " per ten thousand" ^0 "" ^0 "needle at " + str(indicated_kmh) + ", old tyres : true " + str(true_kmh_at_the_needle_100_on_the_old_tyres) + " km/h, " + str(old_margin_kmh) + " under the needle" ^0 "needle at " + str(indicated_kmh) + ", new tyres : true " + str(true_kmh_at_the_needle_100_now) + " km/h, " + str(now_over_the_needle_kmh) + " over the needle" ^0 "odometer after " + str(km_driven_in_a_year) + " km driven : " + str(odometer_shows_km) + " km, short by " + str(odometer_short_by_km) ^0 "" ^0 # ---- what the driver verified ---- "the needle-is-the-speed reasoning" ^0 " needle : exactly at " + str(indicated_kmh) ^0 " electronics : unchanged" ^0 " known margin : the needle read " + str(old_margin_kmh) + " high on the old tyres" ^0 " intent : stay at the limit" ^0 " facts wrong : 0" ^0 " verdict : AT 100 ON THE NEEDLE I AM AT OR UNDER THE LIMIT" ^0 "" ^0 " holding the needle exactly at " + str(indicated_kmh) + " is the part done right here," ^0 " and it is why the wheels turn at exactly the rate that" ^0 " meant " + str(true_kmh_at_the_needle_100_on_the_old_tyres) + " km/h on the old tyres" ^0 "" ^0 # ---- what the needle counts ---- "a speedometer counts turns" ^0 " what it measures : how fast the wheels turn" ^0 " what it assumes : how much road one turn covers, the old" ^0 " tyre's circumference" ^0 " the new tyre : " + str(new_diameter_tenths_of_a_mm) + " tenths of a mm across instead of " + str(old_diameter_tenths_of_a_mm) + "," ^0 " so each turn covers " + str(road_per_turn_vs_old_per_myriad) + " per ten thousand of the old distance" ^0 " the same turning rate : now a true " + str(true_kmh_at_the_needle_100_now) + " km/h; the margin" ^0 " of " + str(old_margin_kmh) + " under has become " + str(now_over_the_needle_kmh) + " over" ^0 " the odometer : counts the same turns, and loses " + str(odometer_short_by_km) + " km a year" ^0 "" ^0 # ---- what the driver got ---- "the motorway" ^0 " believed : at or under the limit, with room to spare" ^0 " actual : " + str(true_kmh_at_the_needle_100_now) + " km/h at a needle of " + str(indicated_kmh) ^0 " is the speedometer broken : no; it counts turns exactly as before" ^0 " does the needle show the car's speed : only for the tyre it" ^0 " was calibrated on" ^0 "" ^0 # ---- null control ---- # The same needle recalibrated for the new tyre's circumference instead of left # on the old one. 102 => nc_true_kmh_at_the_needle_100_uncalibrated 96 => nc_true_kmh_at_the_needle_100_recalibrated 6 => nc_kmh_the_recalibration_returns "null control - recalibrate for the new tyre" ^0 " true speed at a needle of 100, uncalibrated : " + str(nc_true_kmh_at_the_needle_100_uncalibrated) + " km/h" ^0 " true speed at a needle of 100, recalibrated : " + str(nc_true_kmh_at_the_needle_100_recalibrated) + " km/h" ^0 " km/h the recalibration returns : " + str(nc_kmh_the_recalibration_returns) ^0 " no tyre and no road changed; the instrument was told how much" ^0 " road one turn now covers" ^0 "" ^0 # ---- the rule ---- "what an unchanged speedometer guarantees" ^0 " it counts wheel turns exactly as before : exactly" ^0 " its needle shows the car's speed : not addressed; a turn of the" ^0 " taller tyre covers " + str(road_per_turn_vs_old_per_myriad) + " per ten thousand of the old distance," ^0 " so the needle's " + str(indicated_kmh) + " is a true " + str(true_kmh_at_the_needle_100_now) + " and the year's " + str(km_driven_in_a_year) + " km" ^0 " show as " + str(odometer_shows_km) ^0 "" ^0 "an instrument that counts something else and converts is only as right as" ^0 "its conversion; change what one count is worth and every reading drifts by" ^0 "the same share, silently" ^0 "" ^0 "The needle sits at " + str(indicated_kmh) + " and the electronics are untouched - both true. But the" ^0 "speedometer counts turns, and a turn of the taller tyre covers " + str(road_per_turn_vs_old_per_myriad) + " per ten" ^0 "thousand of the old one's road, so the needle's " + str(indicated_kmh) + " is a true " + str(true_kmh_at_the_needle_100_now) + " and " + str(km_driven_in_a_year) + " km" ^0 "read as " + str(odometer_shows_km) + ", until the speedometer is told what one turn is now worth." ^0 ``` ## Python (deterministic transpilation) ```python rim_inches = 16 tenths_of_a_mm_per_inch = 254 old_tyre_width_mm = 205 old_sidewall_percent = 55 new_tyre_width_mm = 225 new_sidewall_percent = 60 indicated_kmh = 100 true_kmh_at_the_needle_100_on_the_old_tyres = 96 km_driven_in_a_year = 20000 rim_tenths_of_a_mm = rim_inches * tenths_of_a_mm_per_inch old_diameter_tenths_of_a_mm = rim_tenths_of_a_mm + int(2 * old_tyre_width_mm * old_sidewall_percent * 10 / 100) new_diameter_tenths_of_a_mm = rim_tenths_of_a_mm + int(2 * new_tyre_width_mm * new_sidewall_percent * 10 / 100) road_per_turn_vs_old_per_myriad = int(new_diameter_tenths_of_a_mm * 10000 / old_diameter_tenths_of_a_mm) true_kmh_at_the_needle_100_now = int(true_kmh_at_the_needle_100_on_the_old_tyres * new_diameter_tenths_of_a_mm / old_diameter_tenths_of_a_mm) old_margin_kmh = indicated_kmh - true_kmh_at_the_needle_100_on_the_old_tyres now_over_the_needle_kmh = true_kmh_at_the_needle_100_now - indicated_kmh odometer_shows_km = int(km_driven_in_a_year * old_diameter_tenths_of_a_mm / new_diameter_tenths_of_a_mm) odometer_short_by_km = km_driven_in_a_year - odometer_shows_km print("rim : " + str(rim_inches) + " inches, " + str(rim_tenths_of_a_mm) + " tenths of a mm") print("old tyre, 205/55 : " + str(old_diameter_tenths_of_a_mm) + " tenths of a mm across") print("new tyre, 225/60 : " + str(new_diameter_tenths_of_a_mm) + " tenths of a mm across") print("road per wheel turn vs old : " + str(road_per_turn_vs_old_per_myriad) + " per ten thousand") print("") print("needle at " + str(indicated_kmh) + ", old tyres : true " + str(true_kmh_at_the_needle_100_on_the_old_tyres) + " km/h, " + str(old_margin_kmh) + " under the needle") print("needle at " + str(indicated_kmh) + ", new tyres : true " + str(true_kmh_at_the_needle_100_now) + " km/h, " + str(now_over_the_needle_kmh) + " over the needle") print("odometer after " + str(km_driven_in_a_year) + " km driven : " + str(odometer_shows_km) + " km, short by " + str(odometer_short_by_km)) print("") print("the needle-is-the-speed reasoning") print(" needle : exactly at " + str(indicated_kmh)) print(" electronics : unchanged") print(" known margin : the needle read " + str(old_margin_kmh) + " high on the old tyres") print(" intent : stay at the limit") print(" facts wrong : 0") print(" verdict : AT 100 ON THE NEEDLE I AM AT OR UNDER THE LIMIT") print("") print(" holding the needle exactly at " + str(indicated_kmh) + " is the part done right here,") print(" and it is why the wheels turn at exactly the rate that") print(" meant " + str(true_kmh_at_the_needle_100_on_the_old_tyres) + " km/h on the old tyres") print("") print("a speedometer counts turns") print(" what it measures : how fast the wheels turn") print(" what it assumes : how much road one turn covers, the old") print(" tyre's circumference") print(" the new tyre : " + str(new_diameter_tenths_of_a_mm) + " tenths of a mm across instead of " + str(old_diameter_tenths_of_a_mm) + ",") print(" so each turn covers " + str(road_per_turn_vs_old_per_myriad) + " per ten thousand of the old distance") print(" the same turning rate : now a true " + str(true_kmh_at_the_needle_100_now) + " km/h; the margin") print(" of " + str(old_margin_kmh) + " under has become " + str(now_over_the_needle_kmh) + " over") print(" the odometer : counts the same turns, and loses " + str(odometer_short_by_km) + " km a year") print("") print("the motorway") print(" believed : at or under the limit, with room to spare") print(" actual : " + str(true_kmh_at_the_needle_100_now) + " km/h at a needle of " + str(indicated_kmh)) print(" is the speedometer broken : no; it counts turns exactly as before") print(" does the needle show the car's speed : only for the tyre it") print(" was calibrated on") print("") nc_true_kmh_at_the_needle_100_uncalibrated = 102 nc_true_kmh_at_the_needle_100_recalibrated = 96 nc_kmh_the_recalibration_returns = 6 print("null control - recalibrate for the new tyre") print(" true speed at a needle of 100, uncalibrated : " + str(nc_true_kmh_at_the_needle_100_uncalibrated) + " km/h") print(" true speed at a needle of 100, recalibrated : " + str(nc_true_kmh_at_the_needle_100_recalibrated) + " km/h") print(" km/h the recalibration returns : " + str(nc_kmh_the_recalibration_returns)) print(" no tyre and no road changed; the instrument was told how much") print(" road one turn now covers") print("") print("what an unchanged speedometer guarantees") print(" it counts wheel turns exactly as before : exactly") print(" its needle shows the car's speed : not addressed; a turn of the") print(" taller tyre covers " + str(road_per_turn_vs_old_per_myriad) + " per ten thousand of the old distance,") print(" so the needle's " + str(indicated_kmh) + " is a true " + str(true_kmh_at_the_needle_100_now) + " and the year's " + str(km_driven_in_a_year) + " km") print(" show as " + str(odometer_shows_km)) print("") print("an instrument that counts something else and converts is only as right as") print("its conversion; change what one count is worth and every reading drifts by") print("the same share, silently") print("") print("The needle sits at " + str(indicated_kmh) + " and the electronics are untouched - both true. But the") print("speedometer counts turns, and a turn of the taller tyre covers " + str(road_per_turn_vs_old_per_myriad) + " per ten") print("thousand of the old one's road, so the needle's " + str(indicated_kmh) + " is a true " + str(true_kmh_at_the_needle_100_now) + " and " + str(km_driven_in_a_year) + " km") print("read as " + str(odometer_shows_km) + ", until the speedometer is told what one turn is now worth.") ``` ## stdout (executed) ```text rim : 16 inches, 4064 tenths of a mm old tyre, 205/55 : 6319 tenths of a mm across new tyre, 225/60 : 6764 tenths of a mm across road per wheel turn vs old : 10704 per ten thousand needle at 100, old tyres : true 96 km/h, 4 under the needle needle at 100, new tyres : true 102 km/h, 2 over the needle odometer after 20000 km driven : 18684 km, short by 1316 the needle-is-the-speed reasoning needle : exactly at 100 electronics : unchanged known margin : the needle read 4 high on the old tyres intent : stay at the limit facts wrong : 0 verdict : AT 100 ON THE NEEDLE I AM AT OR UNDER THE LIMIT holding the needle exactly at 100 is the part done right here, and it is why the wheels turn at exactly the rate that meant 96 km/h on the old tyres a speedometer counts turns what it measures : how fast the wheels turn what it assumes : how much road one turn covers, the old tyre's circumference the new tyre : 6764 tenths of a mm across instead of 6319, so each turn covers 10704 per ten thousand of the old distance the same turning rate : now a true 102 km/h; the margin of 4 under has become 2 over the odometer : counts the same turns, and loses 1316 km a year the motorway believed : at or under the limit, with room to spare actual : 102 km/h at a needle of 100 is the speedometer broken : no; it counts turns exactly as before does the needle show the car's speed : only for the tyre it was calibrated on null control - recalibrate for the new tyre true speed at a needle of 100, uncalibrated : 102 km/h true speed at a needle of 100, recalibrated : 96 km/h km/h the recalibration returns : 6 no tyre and no road changed; the instrument was told how much road one turn now covers what an unchanged speedometer guarantees it counts wheel turns exactly as before : exactly its needle shows the car's speed : not addressed; a turn of the taller tyre covers 10704 per ten thousand of the old distance, so the needle's 100 is a true 102 and the year's 20000 km show as 18684 an instrument that counts something else and converts is only as right as its conversion; change what one count is worth and every reading drifts by the same share, silently The needle sits at 100 and the electronics are untouched - both true. But the speedometer counts turns, and a turn of the taller tyre covers 10704 per ten thousand of the old one's road, so the needle's 100 is a true 102 and 20000 km read as 18684, until the speedometer is told what one turn is now worth. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done