Average Error: 0.0 → 0.0
Time: 14.3s
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 r8140 = re;
        double r8141 = r8140 * r8140;
        double r8142 = im;
        double r8143 = r8142 * r8142;
        double r8144 = r8141 - r8143;
        return r8144;
}
↓
double f(double re, double im) {
        double r8145 = re;
        double r8146 = r8145 * r8145;
        double r8147 = im;
        double r8148 = r8147 * r8147;
        double r8149 = r8146 - r8148;
        return r8149;
}

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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))