math.log/1 on complex, real part

Average Error: 31.2 → 0.0

Time: 2.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double re, double im) {
        double r52553 = re;
        double r52554 = r52553 * r52553;
        double r52555 = im;
        double r52556 = r52555 * r52555;
        double r52557 = r52554 + r52556;
        double r52558 = sqrt(r52557);
        double r52559 = log(r52558);
        return r52559;
}

↓

double f(double re, double im) {
        double r52560 = re;
        double r52561 = im;
        double r52562 = hypot(r52560, r52561);
        double r52563 = log(r52562);
        return r52563;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 31.2

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

2. Simplified 0.0

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

3. Final simplification 0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))