Average Error: 0.0 → 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 r167482 = re;
        double r167483 = im;
        double r167484 = r167482 * r167483;
        double r167485 = r167483 * r167482;
        double r167486 = r167484 + r167485;
        return r167486;
}
↓
double f(double re, double im) {
        double r167487 = re;
        double r167488 = im;
        double r167489 = r167488 + r167488;
        double r167490 = r167487 * r167489;
        return r167490;
}

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 2019168 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))