Average Error: 0.0 → 0.0
Time: 569.0ms
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot im + im \cdot re\]
re \cdot im + im \cdot re
↓
re \cdot im + im \cdot re
double f(double re, double im) {
        double r705 = re;
        double r706 = im;
        double r707 = r705 * r706;
        double r708 = r706 * r705;
        double r709 = r707 + r708;
        return r709;
}
↓
double f(double re, double im) {
        double r710 = re;
        double r711 = im;
        double r712 = r710 * r711;
        double r713 = r711 * r710;
        double r714 = r712 + r713;
        return r714;
}

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 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))