Average Error: 30.5 → 0
Time: 1.0s
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 r1267402 = re;
        double r1267403 = r1267402 * r1267402;
        double r1267404 = im;
        double r1267405 = r1267404 * r1267404;
        double r1267406 = r1267403 + r1267405;
        double r1267407 = sqrt(r1267406);
        double r1267408 = log(r1267407);
        return r1267408;
}
↓
double f(double re, double im) {
        double r1267409 = re;
        double r1267410 = im;
        double r1267411 = hypot(r1267409, r1267410);
        double r1267412 = log(r1267411);
        return r1267412;
}

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 30.5

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

  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 2019164 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))