Average Error: 0.0 → 0.0
Time: 4.2s
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 r8323 = re;
        double r8324 = r8323 * r8323;
        double r8325 = im;
        double r8326 = r8325 * r8325;
        double r8327 = r8324 - r8326;
        return r8327;
}
↓
double f(double re, double im) {
        double r8328 = re;
        double r8329 = r8328 * r8328;
        double r8330 = im;
        double r8331 = r8330 * r8330;
        double r8332 = r8329 - r8331;
        return r8332;
}

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 2019291 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))