Average Error: 31.1 → 0.0
Time: 1.4s
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 r573016 = re;
        double r573017 = r573016 * r573016;
        double r573018 = im;
        double r573019 = r573018 * r573018;
        double r573020 = r573017 + r573019;
        double r573021 = sqrt(r573020);
        double r573022 = log(r573021);
        return r573022;
}
↓
double f(double re, double im) {
        double r573023 = re;
        double r573024 = im;
        double r573025 = hypot(r573023, r573024);
        double r573026 = log(r573025);
        return r573026;
}

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 31.1

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

  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 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))