Average Error: 0.0 → 0.0

Time: 1.3s

Precision: 64

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

↓

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

double f(double re, double im) {
        double r8444 = re;
        double r8445 = im;
        double r8446 = r8444 * r8445;
        double r8447 = r8445 * r8444;
        double r8448 = r8446 + r8447;
        return r8448;
}

↓

double f(double re, double im) {
        double r8449 = re;
        double r8450 = im;
        double r8451 = r8450 + r8450;
        double r8452 = r8449 * r8451;
        return r8452;
}

re \cdot im + im \cdot re

↓

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

Error

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

Derivation

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))