Average Error: 0.0 → 0.0
Time: 634.0ms
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 r1091 = re;
        double r1092 = im;
        double r1093 = r1091 * r1092;
        double r1094 = r1092 * r1091;
        double r1095 = r1093 + r1094;
        return r1095;
}
↓
double f(double re, double im) {
        double r1096 = re;
        double r1097 = im;
        double r1098 = r1097 * r1096;
        double r1099 = fma(r1096, r1097, r1098);
        return r1099;
}

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 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))