Average Error: 0.1 → 0.2
Time: 2.2s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(0.253 \cdot x + 0.12 \cdot {x}^{2}\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(0.253 \cdot x + 0.12 \cdot {x}^{2}\right)
(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))
↓
(FPCore (x) :precision binary64 (- 1.0 (+ (* 0.253 x) (* 0.12 (pow x 2.0)))))
double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}
↓
double code(double x) {
	return 1.0 - ((0.253 * x) + (0.12 * pow(x, 2.0)));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]

  2. Taylor expanded around 0 0.2

    \[\leadsto 1 - \color{blue}{\left(0.253 \cdot x + 0.12 \cdot {x}^{2}\right)}\]

  3. Final simplification0.2

    \[\leadsto 1 - \left(0.253 \cdot x + 0.12 \cdot {x}^{2}\right)\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))