Average Error: 0.0 → 0.0
Time: 1.3s
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 r8406 = re;
        double r8407 = im;
        double r8408 = r8406 * r8407;
        double r8409 = r8407 * r8406;
        double r8410 = r8408 + r8409;
        return r8410;
}
↓
double f(double re, double im) {
        double r8411 = re;
        double r8412 = im;
        double r8413 = r8412 + r8412;
        double r8414 = r8411 * r8413;
        return r8414;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))