Average Error: 0.0 → 0.0
Time: 4.1s
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 r8326 = re;
        double r8327 = r8326 * r8326;
        double r8328 = im;
        double r8329 = r8328 * r8328;
        double r8330 = r8327 - r8329;
        return r8330;
}
↓
double f(double re, double im) {
        double r8331 = re;
        double r8332 = r8331 * r8331;
        double r8333 = im;
        double r8334 = r8333 * r8333;
        double r8335 = r8332 - r8334;
        return r8335;
}

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 2019298 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))