Average Error: 0.0 → 0.0
Time: 1.0s
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 r570 = re;
        double r571 = r570 * r570;
        double r572 = im;
        double r573 = r572 * r572;
        double r574 = r571 - r573;
        return r574;
}
↓
double f(double re, double im) {
        double r575 = re;
        double r576 = im;
        double r577 = r575 + r576;
        double r578 = r575 - r576;
        double r579 = r577 * r578;
        return r579;
}

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 2020049 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))