Average Error: 32.5 → 0.0
Time: 2.2s
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 r58571 = re;
        double r58572 = r58571 * r58571;
        double r58573 = im;
        double r58574 = r58573 * r58573;
        double r58575 = r58572 + r58574;
        double r58576 = sqrt(r58575);
        double r58577 = log(r58576);
        return r58577;
}
↓
double f(double re, double im) {
        double r58578 = re;
        double r58579 = im;
        double r58580 = hypot(r58578, r58579);
        double r58581 = log(r58580);
        return r58581;
}

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