Average Error: 30.6 → 0.0
Time: 8.3s
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 r1394960 = re;
        double r1394961 = r1394960 * r1394960;
        double r1394962 = im;
        double r1394963 = r1394962 * r1394962;
        double r1394964 = r1394961 + r1394963;
        double r1394965 = sqrt(r1394964);
        double r1394966 = log(r1394965);
        return r1394966;
}
↓
double f(double re, double im) {
        double r1394967 = re;
        double r1394968 = im;
        double r1394969 = hypot(r1394967, r1394968);
        double r1394970 = log(r1394969);
        return r1394970;
}

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 30.6

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

  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 2019151 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))