Average Error: 0.1 → 0.2
Time: 2.0s
Precision: 64
\[1 - x \cdot \left(0.253 + x \cdot 0.12\right)\]
↓
\[1 - \left(x \cdot 0.253 + {x}^{2} \cdot 0.12\right)\]
1 - x \cdot \left(0.253 + x \cdot 0.12\right)
↓
1 - \left(x \cdot 0.253 + {x}^{2} \cdot 0.12\right)
double code(double x) {
	return (1.0 - (x * (0.253 + (x * 0.12))));
}
↓
double code(double x) {
	return (1.0 - ((x * 0.253) + (pow(x, 2.0) * 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-lft-in0.1

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

  5. Applied associate-*r*0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))