Average Error: 30.6 → 0.0
Time: 1.8s
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 r558823 = re;
        double r558824 = r558823 * r558823;
        double r558825 = im;
        double r558826 = r558825 * r558825;
        double r558827 = r558824 + r558826;
        double r558828 = sqrt(r558827);
        double r558829 = log(r558828);
        return r558829;
}
↓
double f(double re, double im) {
        double r558830 = re;
        double r558831 = im;
        double r558832 = hypot(r558830, r558831);
        double r558833 = log(r558832);
        return r558833;
}

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 30.6

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

  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 2019130 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))