Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re + im\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r2728 = re;
        double r2729 = r2728 * r2728;
        double r2730 = im;
        double r2731 = r2730 * r2730;
        double r2732 = r2729 - r2731;
        return r2732;
}
↓
double f(double re, double im) {
        double r2733 = re;
        double r2734 = im;
        double r2735 = r2733 + r2734;
        double r2736 = r2733 - r2734;
        double r2737 = r2735 * r2736;
        return r2737;
}

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

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

Reproduce

herbie shell --seed 2020083 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))