Average Error: 0.0 → 0.0
Time: 14.9s
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 r8144 = re;
        double r8145 = r8144 * r8144;
        double r8146 = im;
        double r8147 = r8146 * r8146;
        double r8148 = r8145 - r8147;
        return r8148;
}
↓
double f(double re, double im) {
        double r8149 = re;
        double r8150 = r8149 * r8149;
        double r8151 = im;
        double r8152 = r8151 * r8151;
        double r8153 = r8150 - r8152;
        return r8153;
}

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