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 r8265 = re;
        double r8266 = im;
        double r8267 = r8265 * r8266;
        double r8268 = r8266 * r8265;
        double r8269 = r8267 + r8268;
        return r8269;
}

↓

double f(double re, double im) {
        double r8270 = im;
        double r8271 = re;
        double r8272 = r8271 + r8271;
        double r8273 = r8270 * r8272;
        return r8273;
}

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 2019132 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))