Average Error: 0.0 → 0.0
Time: 7.6s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(im + re\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r9224 = re;
        double r9225 = r9224 * r9224;
        double r9226 = im;
        double r9227 = r9226 * r9226;
        double r9228 = r9225 - r9227;
        return r9228;
}
↓
double f(double re, double im) {
        double r9229 = im;
        double r9230 = re;
        double r9231 = r9229 + r9230;
        double r9232 = r9230 - r9229;
        double r9233 = r9231 * r9232;
        return r9233;
}

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

    \[\leadsto \left(im + re\right) \cdot \left(re - im\right)\]

Reproduce

herbie shell --seed 2019179 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))