Average Error: 31.8 → 0
Time: 1.2s
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 r1376013 = re;
        double r1376014 = r1376013 * r1376013;
        double r1376015 = im;
        double r1376016 = r1376015 * r1376015;
        double r1376017 = r1376014 + r1376016;
        double r1376018 = sqrt(r1376017);
        double r1376019 = log(r1376018);
        return r1376019;
}
↓
double f(double re, double im) {
        double r1376020 = re;
        double r1376021 = im;
        double r1376022 = hypot(r1376020, r1376021);
        double r1376023 = log(r1376022);
        return r1376023;
}

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 31.8

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

  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 2019171 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))