Average Error: 0.0 → 0.0
Time: 14.5s
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 r8175 = re;
        double r8176 = r8175 * r8175;
        double r8177 = im;
        double r8178 = r8177 * r8177;
        double r8179 = r8176 - r8178;
        return r8179;
}
↓
double f(double re, double im) {
        double r8180 = re;
        double r8181 = r8180 * r8180;
        double r8182 = im;
        double r8183 = r8182 * r8182;
        double r8184 = r8181 - r8183;
        return r8184;
}

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)))