Average Error: 0.0 → 0.0
Time: 2.1s
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 r34133 = re;
        double r34134 = r34133 * r34133;
        double r34135 = im;
        double r34136 = r34135 * r34135;
        double r34137 = r34134 - r34136;
        return r34137;
}
↓
double f(double re, double im) {
        double r34138 = im;
        double r34139 = re;
        double r34140 = r34138 + r34139;
        double r34141 = r34139 - r34138;
        double r34142 = r34140 * r34141;
        return r34142;
}

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 2019107 
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))