Average Error: 30.7 → 0.0
Time: 2.0s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{re^2 + im^2}^*\right)\]
double f(double re, double im) {
        double r798062 = re;
        double r798063 = r798062 * r798062;
        double r798064 = im;
        double r798065 = r798064 * r798064;
        double r798066 = r798063 + r798065;
        double r798067 = sqrt(r798066);
        double r798068 = log(r798067);
        return r798068;
}
↓
double f(double re, double im) {
        double r798069 = re;
        double r798070 = im;
        double r798071 = hypot(r798069, r798070);
        double r798072 = log(r798071);
        return r798072;
}


\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\sqrt{re^2 + im^2}^*\right)

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 30.7

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right)}\]

  3. Final simplification0.0

    \[\leadsto \log \left(\sqrt{re^2 + im^2}^*\right)\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))