Average Error: 31.7 → 0.0
Time: 3.0s
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 r41542 = re;
        double r41543 = r41542 * r41542;
        double r41544 = im;
        double r41545 = r41544 * r41544;
        double r41546 = r41543 + r41545;
        double r41547 = sqrt(r41546);
        return r41547;
}
↓
double f(double re, double im) {
        double r41548 = re;
        double r41549 = im;
        double r41550 = hypot(r41548, r41549);
        return r41550;
}

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

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

  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 2020043 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))