Average Error: 32.5 → 0.0
Time: 2.1s
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 r36205 = re;
        double r36206 = r36205 * r36205;
        double r36207 = im;
        double r36208 = r36207 * r36207;
        double r36209 = r36206 + r36208;
        double r36210 = sqrt(r36209);
        double r36211 = log(r36210);
        return r36211;
}
↓
double f(double re, double im) {
        double r36212 = re;
        double r36213 = im;
        double r36214 = hypot(r36212, r36213);
        double r36215 = log(r36214);
        return r36215;
}

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 32.5

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

  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 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))