Average Error: 0.1 → 0.1
Time: 795.0ms
Precision: binary64
\[\left(\left(\frac{5}{4} \cdot b\right) \cdot b + 2 \cdot b\right) + 1\]
↓
\[1 + b \cdot \left(\frac{5}{4} \cdot b + 2\right)\]
\left(\left(\frac{5}{4} \cdot b\right) \cdot b + 2 \cdot b\right) + 1
↓
1 + b \cdot \left(\frac{5}{4} \cdot b + 2\right)
double code(double b) {
	return ((double) (((double) (((double) (((double) (((double) (5.0 / 4.0)) * b)) * b)) + ((double) (2.0 * b)))) + 1.0));
}
↓
double code(double b) {
	return ((double) (1.0 + ((double) (b * ((double) (((double) (((double) (5.0 / 4.0)) * b)) + 2.0))))));
}

Error

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\frac{5}{4} \cdot b\right) \cdot b + 2 \cdot b\right) + 1\]

  2. Simplified0.1

    \[\leadsto \color{blue}{1 + b \cdot \left(\frac{5}{4} \cdot b + 2\right)}\]

  3. Final simplification0.1

    \[\leadsto 1 + b \cdot \left(\frac{5}{4} \cdot b + 2\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (b)
  :name "(+ (+ (* (* (/ 5.0 4.0) b) b) (* 2.0 b)) 1.0)"
  :precision binary64
  (+ (+ (* (* (/ 5.0 4.0) b) b) (* 2.0 b)) 1.0))