Average Error: 2.8 → 0.1
Time: 12.8s
Precision: binary64
\[\left(x \cdot x + \left(x + y\right) \cdot \left(x + y\right)\right) - \left(\left(2 \cdot x\right) \cdot \left(x + y\right)\right) \cdot cos_psi\]
↓
\[\left(x + y\right) \cdot \left(\left(x + y\right) - \left(2 \cdot x\right) \cdot cos_psi\right) + x \cdot x\]
\left(x \cdot x + \left(x + y\right) \cdot \left(x + y\right)\right) - \left(\left(2 \cdot x\right) \cdot \left(x + y\right)\right) \cdot cos_psi
↓
\left(x + y\right) \cdot \left(\left(x + y\right) - \left(2 \cdot x\right) \cdot cos_psi\right) + x \cdot x
double code(double x, double y, double cos_psi) {
	return ((double) (((double) (((double) (x * x)) + ((double) (((double) (x + y)) * ((double) (x + y)))))) - ((double) (((double) (((double) (2.0 * x)) * ((double) (x + y)))) * cos_psi))));
}
↓
double code(double x, double y, double cos_psi) {
	return ((double) (((double) (((double) (x + y)) * ((double) (((double) (x + y)) - ((double) (((double) (2.0 * x)) * cos_psi)))))) + ((double) (x * x))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus cos_psi

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.8

    \[\left(x \cdot x + \left(x + y\right) \cdot \left(x + y\right)\right) - \left(\left(2 \cdot x\right) \cdot \left(x + y\right)\right) \cdot cos_psi\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(\left(x + y\right) - \left(2 \cdot x\right) \cdot cos_psi\right) + x \cdot x}\]

  3. Final simplification0.1

    \[\leadsto \left(x + y\right) \cdot \left(\left(x + y\right) - \left(2 \cdot x\right) \cdot cos_psi\right) + x \cdot x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y cos_psi)
  :name "(- (+ (* x x) (* (+ x y) (+ x y))) (* (* (* 2 x) (+ x y)) cos_psi))"
  :precision binary64
  (- (+ (* x x) (* (+ x y) (+ x y))) (* (* (* 2.0 x) (+ x y)) cos_psi)))