Average Error: 0.0 → 0
Time: 1.2s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot \left(im + im\right)\]
re \cdot im + im \cdot re
↓
re \cdot \left(im + im\right)
double f(double re, double im) {
        double r8132 = re;
        double r8133 = im;
        double r8134 = r8132 * r8133;
        double r8135 = r8133 * r8132;
        double r8136 = r8134 + r8135;
        return r8136;
}
↓
double f(double re, double im) {
        double r8137 = re;
        double r8138 = im;
        double r8139 = r8138 + r8138;
        double r8140 = r8137 * r8139;
        return r8140;
}

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. Simplified0

    \[\leadsto \color{blue}{re \cdot \left(im + im\right)}\]

  3. Final simplification0

    \[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))