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 r64 = re;
        double r65 = r64 * r64;
        double r66 = im;
        double r67 = r66 * r66;
        double r68 = r65 - r67;
        return r68;
}
↓
double f(double re, double im) {
        double r69 = re;
        double r70 = im;
        double r71 = r69 + r70;
        double r72 = r69 - r70;
        double r73 = r71 * r72;
        return r73;
}

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 2020025 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))