Average Error: 0.0 → 0.0
Time: 10.8s
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 r311605 = re;
        double r311606 = r311605 * r311605;
        double r311607 = im;
        double r311608 = r311607 * r311607;
        double r311609 = r311606 - r311608;
        return r311609;
}
↓
double f(double re, double im) {
        double r311610 = im;
        double r311611 = re;
        double r311612 = r311610 + r311611;
        double r311613 = r311611 - r311610;
        double r311614 = r311612 * r311613;
        return r311614;
}

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 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))