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 r581 = re;
        double r582 = r581 * r581;
        double r583 = im;
        double r584 = r583 * r583;
        double r585 = r582 - r584;
        return r585;
}
↓
double f(double re, double im) {
        double r586 = re;
        double r587 = im;
        double r588 = r586 + r587;
        double r589 = r586 - r587;
        double r590 = r588 * r589;
        return r590;
}

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 2019354 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))