Average Error: 0.0 → 0.0
Time: 626.0ms
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 r2244 = re;
        double r2245 = im;
        double r2246 = r2244 * r2245;
        double r2247 = r2245 * r2244;
        double r2248 = r2246 + r2247;
        return r2248;
}
↓
double f(double re, double im) {
        double r2249 = re;
        double r2250 = im;
        double r2251 = r2250 * r2249;
        double r2252 = fma(r2249, r2250, r2251);
        return r2252;
}

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 2019346 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))