Average Error: 0.0 → 0.0
Time: 12.6s
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 r8127 = re;
        double r8128 = r8127 * r8127;
        double r8129 = im;
        double r8130 = r8129 * r8129;
        double r8131 = r8128 - r8130;
        return r8131;
}
↓
double f(double re, double im) {
        double r8132 = re;
        double r8133 = r8132 * r8132;
        double r8134 = im;
        double r8135 = r8134 * r8134;
        double r8136 = r8133 - r8135;
        return r8136;
}

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 2019323 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))