Average Error: 0.0 → 0.0
Time: 9.9s
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 r8137 = re;
        double r8138 = im;
        double r8139 = r8137 * r8138;
        double r8140 = r8138 * r8137;
        double r8141 = r8139 + r8140;
        return r8141;
}
↓
double f(double re, double im) {
        double r8142 = re;
        double r8143 = im;
        double r8144 = r8142 * r8143;
        double r8145 = r8143 * r8142;
        double r8146 = r8144 + r8145;
        return r8146;
}

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 2019202 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))