(- (/ (* e (- (exp (* (+ a b) e)) 1)) (* (- (exp (* a e)) 1) (- (exp (* b e)) 1))) (- 1000000000000000))

Average Error: 47.5 → 47.5

Time: 5.2s

Precision: binary64

• could not determine a ground truth for program body

  1. e = -3.875288692549204e+20
  2. a = 7.3053867032941905e+106
  3. b = 1.9191905532794926e+46

Math

\[\frac{e \cdot \left(e^{\left(a + b\right) \cdot e} - 1\right)}{\left(e^{a \cdot e} - 1\right) \cdot \left(e^{b \cdot e} - 1\right)} - \left(-10^{15}\right)\]

↓

\[10^{15} + \frac{e \cdot \left(e^{\left(a + b\right) \cdot e} - 1\right)}{\left(e^{a \cdot e} - 1\right) \cdot \left(e^{b \cdot e} - 1\right)}\]

Error

Bits error versus e

Bits error versus a

Bits error versus b

Derivation

1. Initial program 47.5

   \[\frac{e \cdot \left(e^{\left(a + b\right) \cdot e} - 1\right)}{\left(e^{a \cdot e} - 1\right) \cdot \left(e^{b \cdot e} - 1\right)} - \left(-10^{15}\right)\]

2. Simplified 47.5

   \[\leadsto \color{blue}{10^{15} + \frac{e \cdot \left(e^{\left(a + b\right) \cdot e} - 1\right)}{\left(e^{a \cdot e} - 1\right) \cdot \left(e^{b \cdot e} - 1\right)}}\]

3. Final simplification 47.5

   \[\leadsto 10^{15} + \frac{e \cdot \left(e^{\left(a + b\right) \cdot e} - 1\right)}{\left(e^{a \cdot e} - 1\right) \cdot \left(e^{b \cdot e} - 1\right)}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (e a b)
  :name "(- (/ (* e (- (exp (* (+ a b) e)) 1)) (* (- (exp (* a e)) 1) (- (exp (* b e)) 1))) (- 1000000000000000))"
  :precision binary64
  (- (/ (* e (- (exp (* (+ a b) e)) 1.0)) (* (- (exp (* a e)) 1.0) (- (exp (* b e)) 1.0))) (neg 1e+15)))