Average Error: 0.0 → 0.0
Time: 1.1s
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 r8383 = re;
        double r8384 = r8383 * r8383;
        double r8385 = im;
        double r8386 = r8385 * r8385;
        double r8387 = r8384 - r8386;
        return r8387;
}
↓
double f(double re, double im) {
        double r8388 = re;
        double r8389 = r8388 * r8388;
        double r8390 = im;
        double r8391 = r8390 * r8390;
        double r8392 = r8389 - r8391;
        return r8392;
}

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 2019318 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))