Average Error: 0.0 → 0.0

Time: 1.3s

Precision: 64

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

↓

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

re \cdot im + im \cdot re

↓

re \cdot im + re \cdot im

double f(double re, double im) {
        double r8405 = re;
        double r8406 = im;
        double r8407 = r8405 * r8406;
        double r8408 = r8406 * r8405;
        double r8409 = r8407 + r8408;
        return r8409;
}

↓

double f(double re, double im) {
        double r8410 = re;
        double r8411 = im;
        double r8412 = r8410 * r8411;
        double r8413 = r8412 + r8412;
        return r8413;
}

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

Reproduce

herbie shell --seed 2019162 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))