Average Error: 0.0 → 0.0
Time: 9.0s
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 r9344 = re;
        double r9345 = r9344 * r9344;
        double r9346 = im;
        double r9347 = r9346 * r9346;
        double r9348 = r9345 - r9347;
        return r9348;
}
↓
double f(double re, double im) {
        double r9349 = re;
        double r9350 = r9349 * r9349;
        double r9351 = im;
        double r9352 = r9351 * r9351;
        double r9353 = r9350 - r9352;
        return r9353;
}

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 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))