Average Error: 31.4 → 0.0
Time: 3.1s
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 r462173 = re;
        double r462174 = r462173 * r462173;
        double r462175 = im;
        double r462176 = r462175 * r462175;
        double r462177 = r462174 + r462176;
        double r462178 = sqrt(r462177);
        double r462179 = log(r462178);
        return r462179;
}
↓
double f(double re, double im) {
        double r462180 = re;
        double r462181 = im;
        double r462182 = hypot(r462180, r462181);
        double r462183 = log(r462182);
        return r462183;
}

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 31.4

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

  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 2019133 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))