Average Error: 0.0 → 0.0
Time: 2.4s
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 r9405 = re;
        double r9406 = r9405 * r9405;
        double r9407 = im;
        double r9408 = r9407 * r9407;
        double r9409 = r9406 - r9408;
        return r9409;
}
↓
double f(double re, double im) {
        double r9410 = re;
        double r9411 = im;
        double r9412 = r9410 + r9411;
        double r9413 = r9410 - r9411;
        double r9414 = r9412 * r9413;
        return r9414;
}

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 2019304 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))