Average Error: 30.8 → 0.0
Time: 1.4s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{re^2 + im^2}^*\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\sqrt{re^2 + im^2}^*\right)
double f(double re, double im) {
        double r1287406 = re;
        double r1287407 = r1287406 * r1287406;
        double r1287408 = im;
        double r1287409 = r1287408 * r1287408;
        double r1287410 = r1287407 + r1287409;
        double r1287411 = sqrt(r1287410);
        double r1287412 = log(r1287411);
        return r1287412;
}
↓
double f(double re, double im) {
        double r1287413 = re;
        double r1287414 = im;
        double r1287415 = hypot(r1287413, r1287414);
        double r1287416 = log(r1287415);
        return r1287416;
}

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 30.8

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right)}\]

  3. Final simplification0.0

    \[\leadsto \log \left(\sqrt{re^2 + im^2}^*\right)\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))