Average Error: 0.0 → 0.0
Time: 710.0ms
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 r993 = re;
        double r994 = im;
        double r995 = r993 * r994;
        double r996 = r994 * r993;
        double r997 = r995 + r996;
        return r997;
}
↓
double f(double re, double im) {
        double r998 = re;
        double r999 = im;
        double r1000 = r998 * r999;
        double r1001 = r999 * r998;
        double r1002 = r1000 + r1001;
        return r1002;
}

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 2020089 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))