Average Error: 0.0 → 0.0

Time: 617.0ms

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 r8496 = re;
        double r8497 = im;
        double r8498 = r8496 * r8497;
        double r8499 = r8497 * r8496;
        double r8500 = r8498 + r8499;
        return r8500;
}

↓

double f(double re, double im) {
        double r8501 = im;
        double r8502 = re;
        double r8503 = r8502 + r8502;
        double r8504 = r8501 * r8503;
        return r8504;
}

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 2019318 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))