Average Error: 0.0 → 0.0

Time: 1.3s

Precision: 64

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

↓

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

re \cdot im + im \cdot re

↓

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

double f(double re, double im) {
        double r8259 = re;
        double r8260 = im;
        double r8261 = r8259 * r8260;
        double r8262 = r8260 * r8259;
        double r8263 = r8261 + r8262;
        return r8263;
}

↓

double f(double re, double im) {
        double r8264 = re;
        double r8265 = im;
        double r8266 = r8265 + r8265;
        double r8267 = r8264 * r8266;
        return r8267;
}

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))