Average Error: 0.0 → 0.0
Time: 583.0ms
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 r1004 = re;
        double r1005 = im;
        double r1006 = r1004 * r1005;
        double r1007 = r1005 * r1004;
        double r1008 = r1006 + r1007;
        return r1008;
}
↓
double f(double re, double im) {
        double r1009 = re;
        double r1010 = im;
        double r1011 = r1009 * r1010;
        double r1012 = r1010 * r1009;
        double r1013 = r1011 + r1012;
        return r1013;
}

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