Average Error: 0.0 → 0.0

Time: 1.4s

Precision: 64

\[re \cdot im + im \cdot re\]

↓

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

re \cdot im + im \cdot re

↓

im \cdot \left(re + re\right)

double f(double re, double im) {
        double r8131 = re;
        double r8132 = im;
        double r8133 = r8131 * r8132;
        double r8134 = r8132 * r8131;
        double r8135 = r8133 + r8134;
        return r8135;
}

↓

double f(double re, double im) {
        double r8136 = im;
        double r8137 = re;
        double r8138 = r8137 + r8137;
        double r8139 = r8136 * r8138;
        return r8139;
}

Error

The X axis uses an exponential scale — Bits error versus `re`

Try it out

In
Out

Enter valid numbers for all inputs

Derivation

Initial program 0.0
\[re \cdot im + im \cdot re\]
Simplified0.0
\[\leadsto \color{blue}{im \cdot \left(re + re\right)}\]
Final simplification0.0
\[\leadsto im \cdot \left(re + re\right)\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))