(- (log (+ (- (exp (- T)) (exp (- Z))) (exp (- G)))))

Average Error: 45.9 → 45.9

Time: 5.0s

Precision: binary64

• could not determine a ground truth for program body

  1. T = 7.960518986233747e+131
  2. Z = 6.554615620151916e+77
  3. G = 3.93074659044643e+159

Math

\[-\log \left(\left(e^{-T} - e^{-Z}\right) + e^{-G}\right)\]

↓

\[-\log \left(\left(e^{-T} - e^{-Z}\right) + e^{-G}\right)\]

Error

Bits error versus T

Bits error versus Z

Bits error versus G

Derivation

1. Initial program 45.9

   \[-\log \left(\left(e^{-T} - e^{-Z}\right) + e^{-G}\right)\]

2. Final simplification 45.9

   \[\leadsto -\log \left(\left(e^{-T} - e^{-Z}\right) + e^{-G}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (T Z G)
  :name "(- (log (+ (- (exp (- T)) (exp (- Z))) (exp (- G)))))"
  :precision binary64
  (neg (log (+ (- (exp (neg T)) (exp (neg Z))) (exp (neg G))))))