Average Error: 0.0 → 0
Time: 8.9s
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 r142065 = re;
        double r142066 = im;
        double r142067 = r142065 * r142066;
        double r142068 = r142066 * r142065;
        double r142069 = r142067 + r142068;
        return r142069;
}
↓
double f(double re, double im) {
        double r142070 = re;
        double r142071 = im;
        double r142072 = r142071 + r142071;
        double r142073 = r142070 * r142072;
        return r142073;
}

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. Simplified0.0

    \[\leadsto \color{blue}{im \cdot re + im \cdot re}\]
  3. Using strategy rm

  4. Applied distribute-rgt-out0

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

  5. Final simplification0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))