(log (- (* 100 (exp (* (- (sqrt 1e-11)) x))) 99))

Average Error: 58.5 → 58.5

Time: 3.7s

Precision: binary64

Math

\[\log \left(100 \cdot e^{\left(-\sqrt{9.99999999999999939 \cdot 10^{-12}}\right) \cdot x} - 99\right)\]

↓

\[\log \left(100 \cdot e^{\left(-\sqrt{9.99999999999999939 \cdot 10^{-12}}\right) \cdot x} - 99\right)\]

Error

Bits error versus x

Derivation

1. Initial program 58.5

   \[\log \left(100 \cdot e^{\left(-\sqrt{9.99999999999999939 \cdot 10^{-12}}\right) \cdot x} - 99\right)\]

2. Final simplification 58.5

   \[\leadsto \log \left(100 \cdot e^{\left(-\sqrt{9.99999999999999939 \cdot 10^{-12}}\right) \cdot x} - 99\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(log (- (* 100 (exp (* (- (sqrt 1e-11)) x))) 99))"
  :precision binary64
  (log (- (* 100.0 (exp (* (neg (sqrt 1e-11)) x))) 99.0)))