Average Error: 0.0 → 0.0
Time: 1.2s
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 r557 = re;
        double r558 = r557 * r557;
        double r559 = im;
        double r560 = r559 * r559;
        double r561 = r558 - r560;
        return r561;
}
↓
double f(double re, double im) {
        double r562 = re;
        double r563 = im;
        double r564 = r562 + r563;
        double r565 = r562 - r563;
        double r566 = r564 * r565;
        return r566;
}

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 2019353 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))