Average Error: 0.0 → 0.0
Time: 998.0ms
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 r546 = re;
        double r547 = r546 * r546;
        double r548 = im;
        double r549 = r548 * r548;
        double r550 = r547 - r549;
        return r550;
}
↓
double f(double re, double im) {
        double r551 = re;
        double r552 = im;
        double r553 = r551 + r552;
        double r554 = r551 - r552;
        double r555 = r553 * r554;
        return r555;
}

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 2020024 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))