Average Error: 32.1 → 0
Time: 1.0s
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 r713302 = re;
        double r713303 = r713302 * r713302;
        double r713304 = im;
        double r713305 = r713304 * r713304;
        double r713306 = r713303 + r713305;
        double r713307 = sqrt(r713306);
        double r713308 = log(r713307);
        return r713308;
}
↓
double f(double re, double im) {
        double r713309 = re;
        double r713310 = im;
        double r713311 = hypot(r713309, r713310);
        double r713312 = log(r713311);
        return r713312;
}

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 32.1

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))