Average Error: 0.0 → 0.0
Time: 2.9s
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 r56452 = re;
        double r56453 = im;
        double r56454 = r56452 * r56453;
        double r56455 = r56453 * r56452;
        double r56456 = r56454 + r56455;
        return r56456;
}
↓
double f(double re, double im) {
        double r56457 = re;
        double r56458 = im;
        double r56459 = r56458 + r56458;
        double r56460 = r56457 * r56459;
        return r56460;
}

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 2019142 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))