Average Error: 32.4 → 0.6
Time: 2.8s
Precision: 64
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
↓
\[\frac{\log \left(\mathsf{hypot}\left(im, re\right)\right)}{\log 10}\]
\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}
↓
\frac{\log \left(\mathsf{hypot}\left(im, re\right)\right)}{\log 10}
double code(double re, double im) {
	return (log(sqrt(((re * re) + (im * im)))) / log(10.0));
}
↓
double code(double re, double im) {
	return (log(hypot(im, re)) / log(10.0));
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 32.4

    \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
  2. Using strategy rm

  3. Applied +-commutative32.4

    \[\leadsto \frac{\log \left(\sqrt{\color{blue}{im \cdot im + re \cdot re}}\right)}{\log 10}\]

  4. Applied hypot-def0.6

    \[\leadsto \frac{\log \color{blue}{\left(\mathsf{hypot}\left(im, re\right)\right)}}{\log 10}\]

  5. Final simplification0.6

    \[\leadsto \frac{\log \left(\mathsf{hypot}\left(im, re\right)\right)}{\log 10}\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (re im)
  :name "math.log10 on complex, real part"
  :precision binary64
  (/ (log (sqrt (+ (* re re) (* im im)))) (log 10)))