Average Error: 0.0 → 0.0
Time: 903.0ms
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[\mathsf{fma}\left(re, im, im \cdot re\right)\]
re \cdot im + im \cdot re
↓
\mathsf{fma}\left(re, im, im \cdot re\right)
double f(double re, double im) {
        double r98 = re;
        double r99 = im;
        double r100 = r98 * r99;
        double r101 = r99 * r98;
        double r102 = r100 + r101;
        return r102;
}
↓
double f(double re, double im) {
        double r103 = re;
        double r104 = im;
        double r105 = r104 * r103;
        double r106 = fma(r103, r104, r105);
        return r106;
}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

    \[re \cdot im + im \cdot re\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))