Average Error: 31.1 → 0
Time: 7.3s
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 r827965 = re;
        double r827966 = r827965 * r827965;
        double r827967 = im;
        double r827968 = r827967 * r827967;
        double r827969 = r827966 + r827968;
        double r827970 = sqrt(r827969);
        double r827971 = log(r827970);
        return r827971;
}
↓
double f(double re, double im) {
        double r827972 = re;
        double r827973 = im;
        double r827974 = hypot(r827972, r827973);
        double r827975 = log(r827974);
        return r827975;
}

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

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))