Average Error: 31.2 → 0
Time: 2.0s
Precision: 64
Internal Precision: 576
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{re^2 + im^2}^*\right)\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 31.2

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Applied simplify0

    \[\leadsto \color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right)}\]

Runtime

Time bar (total: 2.0s)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))