Average Error: 31.9 → 0.0
Time: 973.0ms
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 r1892019 = re;
        double r1892020 = r1892019 * r1892019;
        double r1892021 = im;
        double r1892022 = r1892021 * r1892021;
        double r1892023 = r1892020 + r1892022;
        double r1892024 = sqrt(r1892023);
        return r1892024;
}
↓
double f(double re, double im) {
        double r1892025 = re;
        double r1892026 = im;
        double r1892027 = hypot(r1892025, r1892026);
        return r1892027;
}

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 31.9

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

  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 2019170 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))