Average Error: 0.0 → 0.0
Time: 12.5s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[re \cdot re - im \cdot im\]
re \cdot re - im \cdot im
↓
re \cdot re - im \cdot im
double f(double re, double im) {
        double r889619 = re;
        double r889620 = r889619 * r889619;
        double r889621 = im;
        double r889622 = r889621 * r889621;
        double r889623 = r889620 - r889622;
        return r889623;
}
↓
double f(double re, double im) {
        double r889624 = re;
        double r889625 = r889624 * r889624;
        double r889626 = im;
        double r889627 = r889626 * r889626;
        double r889628 = r889625 - r889627;
        return r889628;
}

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. Final simplification0.0

    \[\leadsto re \cdot re - im \cdot im\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))