Average Error: 0.0 → 0.0
Time: 1.7s
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 r672 = re;
        double r673 = im;
        double r674 = r672 * r673;
        double r675 = r673 * r672;
        double r676 = r674 + r675;
        return r676;
}
↓
double f(double re, double im) {
        double r677 = re;
        double r678 = im;
        double r679 = r677 * r678;
        double r680 = r678 * r677;
        double r681 = r679 + r680;
        return r681;
}

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 2020045 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))