Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[\left(im + im\right) \cdot re\]
re \cdot im + im \cdot re
↓
\left(im + im\right) \cdot re
double f(double re, double im) {
        double r662 = re;
        double r663 = im;
        double r664 = r662 * r663;
        double r665 = r663 * r662;
        double r666 = r664 + r665;
        return r666;
}
↓
double f(double re, double im) {
        double r667 = im;
        double r668 = r667 + r667;
        double r669 = re;
        double r670 = r668 * r669;
        return r670;
}

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

    \[\leadsto \color{blue}{2 \cdot \left(im \cdot re\right)}\]
  3. Using strategy rm

  4. Applied associate-*r*0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))