Average Error: 0.0 → 0.0

Time: 1.3s

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 r8276 = re;
        double r8277 = im;
        double r8278 = r8276 * r8277;
        double r8279 = r8277 * r8276;
        double r8280 = r8278 + r8279;
        return r8280;
}

↓

double f(double re, double im) {
        double r8281 = im;
        double r8282 = re;
        double r8283 = r8282 + r8282;
        double r8284 = r8281 * r8283;
        return r8284;
}

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 2019133 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))