Average Error: 0.0 → 0.0
Time: 1.4s
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 r1246 = re;
        double r1247 = r1246 * r1246;
        double r1248 = im;
        double r1249 = r1248 * r1248;
        double r1250 = r1247 - r1249;
        return r1250;
}
↓
double f(double re, double im) {
        double r1251 = re;
        double r1252 = r1251 * r1251;
        double r1253 = im;
        double r1254 = r1253 * r1253;
        double r1255 = r1252 - r1254;
        return r1255;
}

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 2020001 
(FPCore (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))