Average Error: 0.0 → 0.0
Time: 5.6s
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 r91466 = re;
        double r91467 = r91466 * r91466;
        double r91468 = im;
        double r91469 = r91468 * r91468;
        double r91470 = r91467 - r91469;
        return r91470;
}
↓
double f(double re, double im) {
        double r91471 = re;
        double r91472 = r91471 * r91471;
        double r91473 = im;
        double r91474 = r91473 * r91473;
        double r91475 = r91472 - r91474;
        return r91475;
}

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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))