Average Error: 0.0 → 0.0

Time: 1.7s

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 r8942 = re;
        double r8943 = im;
        double r8944 = r8942 * r8943;
        double r8945 = r8943 * r8942;
        double r8946 = r8944 + r8945;
        return r8946;
}

↓

double f(double re, double im) {
        double r8947 = im;
        double r8948 = re;
        double r8949 = r8948 + r8948;
        double r8950 = r8947 * r8949;
        return r8950;
}

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

Reproduce

herbie shell --seed 2019308 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))