Average Error: 0.1 → 0.1
Time: 2.1s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(0.12 \cdot {x}^{2} + 0.253 \cdot x\right)
double code(double x) {
	return ((double) (1.0 - ((double) (x * ((double) (0.253 + ((double) (x * 0.12))))))));
}
↓
double code(double x) {
	return ((double) (1.0 - ((double) (((double) (0.12 * ((double) pow(x, 2.0)))) + ((double) (0.253 * x))))));
}

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. Using strategy rm

  3. Applied flip-+0.1

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

  4. Taylor expanded around 0 0.2

    \[\leadsto 1 - x \cdot \frac{0.253 \cdot 0.253 - \color{blue}{0.0144 \cdot {x}^{2}}}{0.253 - x \cdot 0.12}\]

  5. Taylor expanded around 0 0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020171 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))