Average Error: 0.0 → 0.0
Time: 8.1s
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 r514071 = re;
        double r514072 = r514071 * r514071;
        double r514073 = im;
        double r514074 = r514073 * r514073;
        double r514075 = r514072 - r514074;
        return r514075;
}
↓
double f(double re, double im) {
        double r514076 = im;
        double r514077 = re;
        double r514078 = r514076 + r514077;
        double r514079 = r514077 - r514076;
        double r514080 = r514078 * r514079;
        return r514080;
}

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)))