Average Error: 31.0 → 0
Time: 2.9s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r16156 = re;
        double r16157 = r16156 * r16156;
        double r16158 = im;
        double r16159 = r16158 * r16158;
        double r16160 = r16157 + r16159;
        double r16161 = sqrt(r16160);
        double r16162 = log(r16161);
        return r16162;
}
↓
double f(double re, double im) {
        double r16163 = re;
        double r16164 = im;
        double r16165 = hypot(r16163, r16164);
        double r16166 = log(r16165);
        return r16166;
}

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 31.0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))