Average Error: 0.0 → 0.0
Time: 11.4s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re - im\right) \cdot re + im \cdot \left(re - im\right)\]
re \cdot re - im \cdot im
↓
\left(re - im\right) \cdot re + im \cdot \left(re - im\right)
double f(double re, double im) {
        double r10115 = re;
        double r10116 = r10115 * r10115;
        double r10117 = im;
        double r10118 = r10117 * r10117;
        double r10119 = r10116 - r10118;
        return r10119;
}
↓
double f(double re, double im) {
        double r10120 = re;
        double r10121 = im;
        double r10122 = r10120 - r10121;
        double r10123 = r10122 * r10120;
        double r10124 = r10121 * r10122;
        double r10125 = r10123 + r10124;
        return r10125;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(re - im\right) \cdot \left(re + im\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))