Average Error: 0.0 → 0.0
Time: 586.0ms
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 r1080 = re;
        double r1081 = im;
        double r1082 = r1080 * r1081;
        double r1083 = r1081 * r1080;
        double r1084 = r1082 + r1083;
        return r1084;
}
↓
double f(double re, double im) {
        double r1085 = re;
        double r1086 = im;
        double r1087 = r1086 * r1085;
        double r1088 = fma(r1085, r1086, r1087);
        return r1088;
}

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 2020049 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))