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 r221171 = re;
        double r221172 = r221171 * r221171;
        double r221173 = im;
        double r221174 = r221173 * r221173;
        double r221175 = r221172 - r221174;
        return r221175;
}
↓
double f(double re, double im) {
        double r221176 = im;
        double r221177 = re;
        double r221178 = r221176 + r221177;
        double r221179 = r221177 - r221176;
        double r221180 = r221178 * r221179;
        return r221180;
}

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 2019134 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))