Average Error: 0.0 → 0.0
Time: 5.3s
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 r196131 = re;
        double r196132 = im;
        double r196133 = r196131 * r196132;
        double r196134 = r196132 * r196131;
        double r196135 = r196133 + r196134;
        return r196135;
}
↓
double f(double re, double im) {
        double r196136 = re;
        double r196137 = im;
        double r196138 = r196137 + r196137;
        double r196139 = r196136 * r196138;
        return r196139;
}

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 2019163 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))