Average Error: 0.0 → 0.0
Time: 19.1s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r366462 = re;
        double r366463 = r366462 * r366462;
        double r366464 = im;
        double r366465 = r366464 * r366464;
        double r366466 = r366463 - r366465;
        return r366466;
}
↓
double f(double re, double im) {
        double r366467 = im;
        double r366468 = re;
        double r366469 = r366467 + r366468;
        double r366470 = r366468 - r366467;
        double r366471 = r366469 * r366470;
        return r366471;
}

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

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))