# Example 949 — The fifth dose was the same as the first and the level was double `the_fifth_dose_was_the_same_as_the_first_and_the_level_was_double.eml` - A patient takes one 160 mg tablet a day of a drug whose half-life is one day, the label is right, every tablet is taken, and the patient reasons that one tablet a day means one tablet's worth in the blood. What yesterday's half adds to today's tablet is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A patient takes # one 160 mg tablet a day of a drug whose half-life is one day, the label is # right, every tablet is taken, and the patient reasons that one tablet a day # means one tablet's worth in the blood. What yesterday's half adds to today's # tablet is computed below. # # The reasoning is careful. The dose is exactly 160 mg; the interval is exactly # one day; no dose is missed or doubled; and the intent is exactly 'how much of # this drug is in me'. # # Each tablet is the same, but a day later half of it is still there, and the # new tablet lands on top of it - so the peak climbs 160, 240, 280, 300, 310 # and levels off at 320, double the dose, while every tablet stayed 160. 160 => dose_mg 1 => half_life_days 1 => dosing_interval_days dose_mg => peak_after_dose_one_mg dose_mg + int(peak_after_dose_one_mg / 2) => peak_after_dose_two_mg dose_mg + int(peak_after_dose_two_mg / 2) => peak_after_dose_three_mg dose_mg + int(peak_after_dose_three_mg / 2) => peak_after_dose_four_mg dose_mg + int(peak_after_dose_four_mg / 2) => peak_after_dose_five_mg dose_mg * 2 => steady_state_peak_mg int(steady_state_peak_mg / 2) => steady_state_trough_mg int(peak_after_dose_five_mg * 10000 / steady_state_peak_mg) => share_of_plateau_reached_by_dose_five_per_myriad int(peak_after_dose_five_mg * 10000 / peak_after_dose_one_mg) => dose_five_peak_as_a_share_of_dose_one_per_myriad peak_after_dose_five_mg - dose_mg => carried_over_from_earlier_doses_mg "tablet : " + str(dose_mg) + " mg, once a day" ^0 "half-life : " + str(half_life_days) + " day" ^0 "interval : " + str(dosing_interval_days) + " day" ^0 "" ^0 "peak after dose one : " + str(peak_after_dose_one_mg) + " mg" ^0 "peak after dose two : " + str(peak_after_dose_two_mg) + " mg" ^0 "peak after dose three : " + str(peak_after_dose_three_mg) + " mg" ^0 "peak after dose four : " + str(peak_after_dose_four_mg) + " mg" ^0 "peak after dose five : " + str(peak_after_dose_five_mg) + " mg" ^0 "steady-state peak : " + str(steady_state_peak_mg) + " mg" ^0 "steady-state trough : " + str(steady_state_trough_mg) + " mg" ^0 "plateau reached by dose five : " + str(share_of_plateau_reached_by_dose_five_per_myriad) + " per ten thousand" ^0 "dose five peak vs dose one peak : " + str(dose_five_peak_as_a_share_of_dose_one_per_myriad) + " per ten thousand" ^0 "carried over from earlier doses : " + str(carried_over_from_earlier_doses_mg) + " mg" ^0 "" ^0 # ---- what the patient verified ---- "the one-tablet reasoning" ^0 " dose : exactly " + str(dose_mg) + " mg, as labelled" ^0 " interval : exactly one day, never missed, never doubled" ^0 " tablets : identical, every one" ^0 " intent : how much of this drug is in me" ^0 " facts wrong : 0" ^0 " verdict : ONE TABLET A DAY IS ONE TABLET'S WORTH IN THE BLOOD" ^0 "" ^0 " taking the labelled dose at the labelled interval is the" ^0 " part done right here, and it is why every peak in the" ^0 " table above contains exactly one fresh tablet" ^0 "" ^0 # ---- what yesterday's half adds ---- "accumulation" ^0 " day one : " + str(dose_mg) + " mg, one tablet, nothing before it" ^0 " day two : one tablet plus half of day one, " + str(peak_after_dose_two_mg) + " mg" ^0 " day three : one tablet plus half of day two, " + str(peak_after_dose_three_mg) + " mg" ^0 " where it levels off : when the half that is lost in a day" ^0 " equals the tablet that is added, at " + str(steady_state_peak_mg) + " mg" ^0 " what one tablet a day means : one tablet added, half of" ^0 " everything removed, and the balance sits at two tablets" ^0 "" ^0 # ---- what the patient got ---- "the level" ^0 " believed : " + str(dose_mg) + " mg after every tablet" ^0 " actual by dose five : " + str(peak_after_dose_five_mg) + " mg, and still rising toward " + str(steady_state_peak_mg) ^0 " is the label wrong : no; the tablet is " + str(dose_mg) + " mg" ^0 " is the level one tablet : no; it is one tablet plus " + str(carried_over_from_earlier_doses_mg) + " mg of" ^0 " earlier tablets that have not yet been cleared" ^0 "" ^0 # ---- null control ---- # The same schedule read with the carry-over included instead of by # equating the level with the tablet. 160 => nc_level_read_as_one_tablet_mg 310 => nc_level_read_with_carry_over_by_dose_five_mg 150 => nc_carry_over_the_reading_reveals_mg "null control - read the level with yesterday's half included" ^0 " level, read as one tablet : " + str(nc_level_read_as_one_tablet_mg) + " mg" ^0 " level, read with carry-over, dose five : " + str(nc_level_read_with_carry_over_by_dose_five_mg) + " mg" ^0 " carry-over the reading reveals : " + str(nc_carry_over_the_reading_reveals_mg) + " mg" ^0 " no tablet and no interval changed; the level stopped being" ^0 " read as the dose" ^0 "" ^0 # ---- the rule ---- "what a correct label and a perfect schedule guarantee" ^0 " each tablet delivers " + str(dose_mg) + " mg : exactly, every day" ^0 " the level in the blood is " + str(dose_mg) + " mg : not addressed;" ^0 " with a one-day half-life and a one-day interval, half of" ^0 " every earlier tablet is still present, and the peaks climb" ^0 " to " + str(steady_state_peak_mg) + " mg, double the dose" ^0 "" ^0 "a dose is what goes in; a level is what has not yet gone out; the second is" ^0 "a running balance, and a balance fed the same deposit every day while it loses" ^0 "half of itself settles at two deposits, not one" ^0 "" ^0 "Every tablet is " + str(dose_mg) + " mg - the label is right. But the level is a balance:" ^0 "by dose five the peak is " + str(peak_after_dose_five_mg) + " mg, " + str(share_of_plateau_reached_by_dose_five_per_myriad) + " per ten thousand of a plateau at" ^0 "" + str(steady_state_peak_mg) + " mg, because " + str(carried_over_from_earlier_doses_mg) + " mg of earlier tablets is still there when each new one" ^0 "lands, until the level is read as a balance and not as the dose." ^0 ``` ## Python (deterministic transpilation) ```python dose_mg = 160 half_life_days = 1 dosing_interval_days = 1 peak_after_dose_one_mg = dose_mg peak_after_dose_two_mg = dose_mg + int(peak_after_dose_one_mg / 2) peak_after_dose_three_mg = dose_mg + int(peak_after_dose_two_mg / 2) peak_after_dose_four_mg = dose_mg + int(peak_after_dose_three_mg / 2) peak_after_dose_five_mg = dose_mg + int(peak_after_dose_four_mg / 2) steady_state_peak_mg = dose_mg * 2 steady_state_trough_mg = int(steady_state_peak_mg / 2) share_of_plateau_reached_by_dose_five_per_myriad = int(peak_after_dose_five_mg * 10000 / steady_state_peak_mg) dose_five_peak_as_a_share_of_dose_one_per_myriad = int(peak_after_dose_five_mg * 10000 / peak_after_dose_one_mg) carried_over_from_earlier_doses_mg = peak_after_dose_five_mg - dose_mg print("tablet : " + str(dose_mg) + " mg, once a day") print("half-life : " + str(half_life_days) + " day") print("interval : " + str(dosing_interval_days) + " day") print("") print("peak after dose one : " + str(peak_after_dose_one_mg) + " mg") print("peak after dose two : " + str(peak_after_dose_two_mg) + " mg") print("peak after dose three : " + str(peak_after_dose_three_mg) + " mg") print("peak after dose four : " + str(peak_after_dose_four_mg) + " mg") print("peak after dose five : " + str(peak_after_dose_five_mg) + " mg") print("steady-state peak : " + str(steady_state_peak_mg) + " mg") print("steady-state trough : " + str(steady_state_trough_mg) + " mg") print("plateau reached by dose five : " + str(share_of_plateau_reached_by_dose_five_per_myriad) + " per ten thousand") print("dose five peak vs dose one peak : " + str(dose_five_peak_as_a_share_of_dose_one_per_myriad) + " per ten thousand") print("carried over from earlier doses : " + str(carried_over_from_earlier_doses_mg) + " mg") print("") print("the one-tablet reasoning") print(" dose : exactly " + str(dose_mg) + " mg, as labelled") print(" interval : exactly one day, never missed, never doubled") print(" tablets : identical, every one") print(" intent : how much of this drug is in me") print(" facts wrong : 0") print(" verdict : ONE TABLET A DAY IS ONE TABLET'S WORTH IN THE BLOOD") print("") print(" taking the labelled dose at the labelled interval is the") print(" part done right here, and it is why every peak in the") print(" table above contains exactly one fresh tablet") print("") print("accumulation") print(" day one : " + str(dose_mg) + " mg, one tablet, nothing before it") print(" day two : one tablet plus half of day one, " + str(peak_after_dose_two_mg) + " mg") print(" day three : one tablet plus half of day two, " + str(peak_after_dose_three_mg) + " mg") print(" where it levels off : when the half that is lost in a day") print(" equals the tablet that is added, at " + str(steady_state_peak_mg) + " mg") print(" what one tablet a day means : one tablet added, half of") print(" everything removed, and the balance sits at two tablets") print("") print("the level") print(" believed : " + str(dose_mg) + " mg after every tablet") print(" actual by dose five : " + str(peak_after_dose_five_mg) + " mg, and still rising toward " + str(steady_state_peak_mg)) print(" is the label wrong : no; the tablet is " + str(dose_mg) + " mg") print(" is the level one tablet : no; it is one tablet plus " + str(carried_over_from_earlier_doses_mg) + " mg of") print(" earlier tablets that have not yet been cleared") print("") nc_level_read_as_one_tablet_mg = 160 nc_level_read_with_carry_over_by_dose_five_mg = 310 nc_carry_over_the_reading_reveals_mg = 150 print("null control - read the level with yesterday's half included") print(" level, read as one tablet : " + str(nc_level_read_as_one_tablet_mg) + " mg") print(" level, read with carry-over, dose five : " + str(nc_level_read_with_carry_over_by_dose_five_mg) + " mg") print(" carry-over the reading reveals : " + str(nc_carry_over_the_reading_reveals_mg) + " mg") print(" no tablet and no interval changed; the level stopped being") print(" read as the dose") print("") print("what a correct label and a perfect schedule guarantee") print(" each tablet delivers " + str(dose_mg) + " mg : exactly, every day") print(" the level in the blood is " + str(dose_mg) + " mg : not addressed;") print(" with a one-day half-life and a one-day interval, half of") print(" every earlier tablet is still present, and the peaks climb") print(" to " + str(steady_state_peak_mg) + " mg, double the dose") print("") print("a dose is what goes in; a level is what has not yet gone out; the second is") print("a running balance, and a balance fed the same deposit every day while it loses") print("half of itself settles at two deposits, not one") print("") print("Every tablet is " + str(dose_mg) + " mg - the label is right. But the level is a balance:") print("by dose five the peak is " + str(peak_after_dose_five_mg) + " mg, " + str(share_of_plateau_reached_by_dose_five_per_myriad) + " per ten thousand of a plateau at") print("" + str(steady_state_peak_mg) + " mg, because " + str(carried_over_from_earlier_doses_mg) + " mg of earlier tablets is still there when each new one") print("lands, until the level is read as a balance and not as the dose.") ``` ## stdout (executed) ```text tablet : 160 mg, once a day half-life : 1 day interval : 1 day peak after dose one : 160 mg peak after dose two : 240 mg peak after dose three : 280 mg peak after dose four : 300 mg peak after dose five : 310 mg steady-state peak : 320 mg steady-state trough : 160 mg plateau reached by dose five : 9687 per ten thousand dose five peak vs dose one peak : 19375 per ten thousand carried over from earlier doses : 150 mg the one-tablet reasoning dose : exactly 160 mg, as labelled interval : exactly one day, never missed, never doubled tablets : identical, every one intent : how much of this drug is in me facts wrong : 0 verdict : ONE TABLET A DAY IS ONE TABLET'S WORTH IN THE BLOOD taking the labelled dose at the labelled interval is the part done right here, and it is why every peak in the table above contains exactly one fresh tablet accumulation day one : 160 mg, one tablet, nothing before it day two : one tablet plus half of day one, 240 mg day three : one tablet plus half of day two, 280 mg where it levels off : when the half that is lost in a day equals the tablet that is added, at 320 mg what one tablet a day means : one tablet added, half of everything removed, and the balance sits at two tablets the level believed : 160 mg after every tablet actual by dose five : 310 mg, and still rising toward 320 is the label wrong : no; the tablet is 160 mg is the level one tablet : no; it is one tablet plus 150 mg of earlier tablets that have not yet been cleared null control - read the level with yesterday's half included level, read as one tablet : 160 mg level, read with carry-over, dose five : 310 mg carry-over the reading reveals : 150 mg no tablet and no interval changed; the level stopped being read as the dose what a correct label and a perfect schedule guarantee each tablet delivers 160 mg : exactly, every day the level in the blood is 160 mg : not addressed; with a one-day half-life and a one-day interval, half of every earlier tablet is still present, and the peaks climb to 320 mg, double the dose a dose is what goes in; a level is what has not yet gone out; the second is a running balance, and a balance fed the same deposit every day while it loses half of itself settles at two deposits, not one Every tablet is 160 mg - the label is right. But the level is a balance: by dose five the peak is 310 mg, 9687 per ten thousand of a plateau at 320 mg, because 150 mg of earlier tablets is still there when each new one lands, until the level is read as a balance and not as the dose. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done