Average Error: 32.5 → 0.0
Time: 851.0ms
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 r78088 = re;
        double r78089 = r78088 * r78088;
        double r78090 = im;
        double r78091 = r78090 * r78090;
        double r78092 = r78089 + r78091;
        double r78093 = sqrt(r78092);
        double r78094 = log(r78093);
        return r78094;
}
↓
double f(double re, double im) {
        double r78095 = re;
        double r78096 = im;
        double r78097 = hypot(r78095, r78096);
        double r78098 = log(r78097);
        return r78098;
}

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 32.5

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0.0

    \[\leadsto \log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))