Average Error: 31.5 → 0
Time: 4.0s
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 r24969 = re;
        double r24970 = r24969 * r24969;
        double r24971 = im;
        double r24972 = r24971 * r24971;
        double r24973 = r24970 + r24972;
        double r24974 = sqrt(r24973);
        double r24975 = log(r24974);
        return r24975;
}
↓
double f(double re, double im) {
        double r24976 = re;
        double r24977 = im;
        double r24978 = hypot(r24976, r24977);
        double r24979 = log(r24978);
        return r24979;
}

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 31.5

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

  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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))