Average Error: 0.0 → 0.0
Time: 8.1s
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 r2101 = re;
        double r2102 = im;
        double r2103 = r2101 * r2102;
        double r2104 = r2102 * r2101;
        double r2105 = r2103 + r2104;
        return r2105;
}
↓
double f(double re, double im) {
        double r2106 = re;
        double r2107 = im;
        double r2108 = r2107 + r2107;
        double r2109 = r2106 * r2108;
        return r2109;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot \left(re \cdot im\right)}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

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