Average Error: 0.0 → 0.0
Time: 14.4s
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 r8164 = re;
        double r8165 = r8164 * r8164;
        double r8166 = im;
        double r8167 = r8166 * r8166;
        double r8168 = r8165 - r8167;
        return r8168;
}
↓
double f(double re, double im) {
        double r8169 = re;
        double r8170 = r8169 * r8169;
        double r8171 = im;
        double r8172 = r8171 * r8171;
        double r8173 = r8170 - r8172;
        return r8173;
}

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)))