Average Error: 0.0 → 0.0
Time: 11.0s
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 r102549 = re;
        double r102550 = r102549 * r102549;
        double r102551 = im;
        double r102552 = r102551 * r102551;
        double r102553 = r102550 - r102552;
        return r102553;
}
↓
double f(double re, double im) {
        double r102554 = re;
        double r102555 = r102554 * r102554;
        double r102556 = im;
        double r102557 = r102556 * r102556;
        double r102558 = r102555 - r102557;
        return r102558;
}

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 2019170 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))