Average Error: 0.0 → 0.0
Time: 8.9s
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 r335264 = re;
        double r335265 = r335264 * r335264;
        double r335266 = im;
        double r335267 = r335266 * r335266;
        double r335268 = r335265 - r335267;
        return r335268;
}
↓
double f(double re, double im) {
        double r335269 = im;
        double r335270 = re;
        double r335271 = r335269 + r335270;
        double r335272 = r335270 - r335269;
        double r335273 = r335271 * r335272;
        return r335273;
}

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 2019152 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))