Average Error: 31.8 → 0.0
Time: 675.0ms
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\mathsf{hypot}\left(re, im\right)\]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)
double f(double re, double im) {
        double r94603 = re;
        double r94604 = r94603 * r94603;
        double r94605 = im;
        double r94606 = r94605 * r94605;
        double r94607 = r94604 + r94606;
        double r94608 = sqrt(r94607);
        return r94608;
}
↓
double f(double re, double im) {
        double r94609 = re;
        double r94610 = im;
        double r94611 = hypot(r94609, r94610);
        return r94611;
}

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

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))