Average Error: 0.0 → 0.0
Time: 16.4s
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 r8187 = re;
        double r8188 = r8187 * r8187;
        double r8189 = im;
        double r8190 = r8189 * r8189;
        double r8191 = r8188 - r8190;
        return r8191;
}
↓
double f(double re, double im) {
        double r8192 = re;
        double r8193 = r8192 * r8192;
        double r8194 = im;
        double r8195 = r8194 * r8194;
        double r8196 = r8193 - r8195;
        return r8196;
}

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)))