Average Error: 0.8 → 0.7
Time: 13.6s
Precision: 64
Internal Precision: 576
\[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
↓
\[\log_* (1 + (e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*)\]

Error

Bits error versus re

Bits error versus im

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.8

    \[\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]

  2. Initial simplification0.8

    \[\leadsto \frac{\tan^{-1}_* \frac{im}{re}}{\log 10}\]
  3. Using strategy rm

  4. Applied log1p-expm1-u0.7

    \[\leadsto \color{blue}{\log_* (1 + (e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*)}\]

  5. Final simplification0.7

    \[\leadsto \log_* (1 + (e^{\frac{\tan^{-1}_* \frac{im}{re}}{\log 10}} - 1)^*)\]

Runtime

Time bar (total: 13.6s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.70.70.00.70%
herbie shell --seed 2018263 +o rules:numerics
(FPCore (re im)
  :name "math.log10 on complex, imaginary part"
  (/ (atan2 im re) (log 10)))