Average Error: 30.8 → 0.0
Time: 1.6s
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 r1084152 = re;
        double r1084153 = r1084152 * r1084152;
        double r1084154 = im;
        double r1084155 = r1084154 * r1084154;
        double r1084156 = r1084153 + r1084155;
        double r1084157 = sqrt(r1084156);
        double r1084158 = log(r1084157);
        return r1084158;
}
↓
double f(double re, double im) {
        double r1084159 = re;
        double r1084160 = im;
        double r1084161 = hypot(r1084159, r1084160);
        double r1084162 = log(r1084161);
        return r1084162;
}

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 30.8

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

  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 2019144 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))