Average Error: 0.1 → 0.1
Time: 3.0s
Precision: binary64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(x \cdot 0.253 + \left(x \cdot x\right) \cdot 0.12\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(x \cdot 0.253 + \left(x \cdot x\right) \cdot 0.12\right)
(FPCore (x) :precision binary64 (- 1.0 (* x (+ 0.253 (* x 0.12)))))
↓
(FPCore (x) :precision binary64 (- 1.0 (+ (* x 0.253) (* (* x x) 0.12))))
double code(double x) {
	return 1.0 - (x * (0.253 + (x * 0.12)));
}
↓
double code(double x) {
	return 1.0 - ((x * 0.253) + ((x * x) * 0.12));
}

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 distribute-rgt-in_binary64_19010.1

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

  4. Simplified0.1

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

  5. Simplified0.1

    \[\leadsto 1 - \left(x \cdot 0.253 + \color{blue}{x \cdot \left(x \cdot 0.12\right)}\right)\]
  6. Using strategy rm

  7. Applied associate-*r*_binary64_19170.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020231 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))