Average Error: 3.8 → 3.8
Time: 1.3s
Precision: binary64
\[z + \alpha \cdot \left(\left(R + \gamma \cdot z\right) - z\right)\]
↓
\[z + \alpha \cdot \left(\left(R + \gamma \cdot z\right) - z\right)\]
z + \alpha \cdot \left(\left(R + \gamma \cdot z\right) - z\right)
↓
z + \alpha \cdot \left(\left(R + \gamma \cdot z\right) - z\right)
double code(double z, double alpha, double R, double gamma) {
	return ((double) (z + ((double) (alpha * ((double) (((double) (R + ((double) (gamma * z)))) - z))))));
}
↓
double code(double z, double alpha, double R, double gamma) {
	return ((double) (z + ((double) (alpha * ((double) (((double) (R + ((double) (gamma * z)))) - z))))));
}

Error

Bits error versus z

Bits error versus alpha

Bits error versus R

Bits error versus gamma

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.8

    \[z + \alpha \cdot \left(\left(R + \gamma \cdot z\right) - z\right)\]

  2. Final simplification3.8

    \[\leadsto z + \alpha \cdot \left(\left(R + \gamma \cdot z\right) - z\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (z alpha R gamma)
  :name "(+ z (* alpha (- (+ R (* gamma z)) z)))"
  :precision binary64
  (+ z (* alpha (- (+ R (* gamma z)) z))))