Average Error: 0.0 → 0.0
Time: 2.8s
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 r54573 = re;
        double r54574 = r54573 * r54573;
        double r54575 = im;
        double r54576 = r54575 * r54575;
        double r54577 = r54574 - r54576;
        return r54577;
}
↓
double f(double re, double im) {
        double r54578 = re;
        double r54579 = r54578 * r54578;
        double r54580 = im;
        double r54581 = r54580 * r54580;
        double r54582 = r54579 - r54581;
        return r54582;
}

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 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))