Average Error: 32.4 → 0.0
Time: 509.0ms
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 r34049 = re;
        double r34050 = r34049 * r34049;
        double r34051 = im;
        double r34052 = r34051 * r34051;
        double r34053 = r34050 + r34052;
        double r34054 = sqrt(r34053);
        double r34055 = log(r34054);
        return r34055;
}
↓
double f(double re, double im) {
        double r34056 = re;
        double r34057 = im;
        double r34058 = hypot(r34056, r34057);
        double r34059 = log(r34058);
        return r34059;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))