(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) cp) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) cn)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) cp) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) cn)))

Average Error: 3.3 → 3.3

Time: 57.1s

Precision: binary64

• could not determine a ground truth for program body

  1. s = -2.5100131778205086e-56
  2. cp = 7.283753147485352e-195
  3. cn = -1.1279046134271384e-162
  4. t = 1.1716375684399015e+125

Math

\[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{cn}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{cn}}\]

↓

\[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{cn}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{cn}}\]

Error

Bits error versus s

Bits error versus cp

Bits error versus cn

Bits error versus t

Derivation

1. Initial program 3.3

   \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{cn}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{cn}}\]

2. Final simplification 3.3

   \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{cn}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{cp} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{cn}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (s cp cn t)
  :name "(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) cp) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) cn)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) cp) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) cn)))"
  :precision binary64
  (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) cp) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) cn)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) cp) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) cn))))