Average Error: 0.1 → 0.1
Time: 16.2s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(0.2530000000000000026645352591003756970167 \cdot x + 0.1199999999999999955591079014993738383055 \cdot {x}^{2}\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(0.2530000000000000026645352591003756970167 \cdot x + 0.1199999999999999955591079014993738383055 \cdot {x}^{2}\right)
double f(double x) {
        double r47490 = 1.0;
        double r47491 = x;
        double r47492 = 0.253;
        double r47493 = 0.12;
        double r47494 = r47491 * r47493;
        double r47495 = r47492 + r47494;
        double r47496 = r47491 * r47495;
        double r47497 = r47490 - r47496;
        return r47497;
}
↓
double f(double x) {
        double r47498 = 1.0;
        double r47499 = 0.253;
        double r47500 = x;
        double r47501 = r47499 * r47500;
        double r47502 = 0.12;
        double r47503 = 2.0;
        double r47504 = pow(r47500, r47503);
        double r47505 = r47502 * r47504;
        double r47506 = r47501 + r47505;
        double r47507 = r47498 - r47506;
        return r47507;
}

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

    \[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto 1 - \color{blue}{\left(x \cdot 0.2530000000000000026645352591003756970167 + x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\right)}\]

  4. Simplified0.1

    \[\leadsto 1 - \left(\color{blue}{0.2530000000000000026645352591003756970167 \cdot x} + x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\right)\]

  5. Simplified0.1

    \[\leadsto 1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \color{blue}{0.1199999999999999955591079014993738383055 \cdot {x}^{2}}\right)\]

  6. Final simplification0.1

    \[\leadsto 1 - \left(0.2530000000000000026645352591003756970167 \cdot x + 0.1199999999999999955591079014993738383055 \cdot {x}^{2}\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))