Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[re \cdot im + im \cdot re\]
re \cdot im + im \cdot re
↓
re \cdot im + im \cdot re
double f(double re, double im) {
        double r2000 = re;
        double r2001 = im;
        double r2002 = r2000 * r2001;
        double r2003 = r2001 * r2000;
        double r2004 = r2002 + r2003;
        return r2004;
}
↓
double f(double re, double im) {
        double r2005 = re;
        double r2006 = im;
        double r2007 = r2005 * r2006;
        double r2008 = r2006 * r2005;
        double r2009 = r2007 + r2008;
        return r2009;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))