Average Error: 31.7 → 0
Time: 3.0s
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 r41569 = re;
        double r41570 = r41569 * r41569;
        double r41571 = im;
        double r41572 = r41571 * r41571;
        double r41573 = r41570 + r41572;
        double r41574 = sqrt(r41573);
        double r41575 = log(r41574);
        return r41575;
}
↓
double f(double re, double im) {
        double r41576 = re;
        double r41577 = im;
        double r41578 = hypot(r41576, r41577);
        double r41579 = log(r41578);
        return r41579;
}

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 31.7

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

  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 2019208 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))