math.log/1 on complex, real part

Average Error: 31.2 → 0.0

Time: 1.6s

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 r14742 = re;
        double r14743 = r14742 * r14742;
        double r14744 = im;
        double r14745 = r14744 * r14744;
        double r14746 = r14743 + r14745;
        double r14747 = sqrt(r14746);
        double r14748 = log(r14747);
        return r14748;
}

↓

double f(double re, double im) {
        double r14749 = re;
        double r14750 = im;
        double r14751 = hypot(r14749, r14750);
        double r14752 = log(r14751);
        return r14752;
}

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)))))