Average Error: 0.0 → 0.0
Time: 6.4s
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 r407597 = re;
        double r407598 = im;
        double r407599 = r407597 * r407598;
        double r407600 = r407598 * r407597;
        double r407601 = r407599 + r407600;
        return r407601;
}
↓
double f(double re, double im) {
        double r407602 = re;
        double r407603 = im;
        double r407604 = r407603 + r407603;
        double r407605 = r407602 * r407604;
        return r407605;
}

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

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

  4. Applied distribute-lft-out0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))