Average Error: 31.8 → 0
Time: 1.5s
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 r1035241 = re;
        double r1035242 = r1035241 * r1035241;
        double r1035243 = im;
        double r1035244 = r1035243 * r1035243;
        double r1035245 = r1035242 + r1035244;
        double r1035246 = sqrt(r1035245);
        double r1035247 = log(r1035246);
        return r1035247;
}
↓
double f(double re, double im) {
        double r1035248 = re;
        double r1035249 = im;
        double r1035250 = hypot(r1035248, r1035249);
        double r1035251 = log(r1035250);
        return r1035251;
}

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 31.8

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

  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 2019171 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))