Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re + im\right) \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re + im\right) \cdot \left(re - im\right)
double f(double re, double im) {
        double r103878 = re;
        double r103879 = r103878 * r103878;
        double r103880 = im;
        double r103881 = r103880 * r103880;
        double r103882 = r103879 - r103881;
        return r103882;
}
↓
double f(double re, double im) {
        double r103883 = re;
        double r103884 = im;
        double r103885 = r103883 + r103884;
        double r103886 = r103883 - r103884;
        double r103887 = r103885 * r103886;
        return r103887;
}

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. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{{re}^{2} - {im}^{2}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\left(im + re\right) \cdot \left(re - im\right)}\]

  4. Final simplification0.0

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

Reproduce

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