(log (- (* a (exp (* (- (sqrt s)) x))) (- a 1)))

Average Error: 42.3 → 42.3

Time: 5.8s

Precision: binary64

Math

\[\log \left(a \cdot e^{\left(-\sqrt{s}\right) \cdot x} - \left(a - 1\right)\right)\]

↓

\[\log \left(a \cdot e^{\left(-\sqrt{s}\right) \cdot x} - \left(a - 1\right)\right)\]

Error

Bits error versus a

Bits error versus s

Bits error versus x

Derivation

1. Initial program 42.3

   \[\log \left(a \cdot e^{\left(-\sqrt{s}\right) \cdot x} - \left(a - 1\right)\right)\]

2. Final simplification 42.3

   \[\leadsto \log \left(a \cdot e^{\left(-\sqrt{s}\right) \cdot x} - \left(a - 1\right)\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (a s x)
  :name "(log (- (* a (exp (* (- (sqrt s)) x))) (- a 1)))"
  :precision binary64
  (log (- (* a (exp (* (neg (sqrt s)) x))) (- a 1.0))))