Average Error: 0.1 → 0.1
Time: 12.9s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(0.1199999999999999955591079014993738383055 \cdot {x}^{2} + 0.2530000000000000026645352591003756970167 \cdot x\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(0.1199999999999999955591079014993738383055 \cdot {x}^{2} + 0.2530000000000000026645352591003756970167 \cdot x\right)
double f(double x) {
        double r84607 = 1.0;
        double r84608 = x;
        double r84609 = 0.253;
        double r84610 = 0.12;
        double r84611 = r84608 * r84610;
        double r84612 = r84609 + r84611;
        double r84613 = r84608 * r84612;
        double r84614 = r84607 - r84613;
        return r84614;
}
↓
double f(double x) {
        double r84615 = 1.0;
        double r84616 = 0.12;
        double r84617 = x;
        double r84618 = 2.0;
        double r84619 = pow(r84617, r84618);
        double r84620 = r84616 * r84619;
        double r84621 = 0.253;
        double r84622 = r84621 * r84617;
        double r84623 = r84620 + r84622;
        double r84624 = r84615 - r84623;
        return r84624;
}

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 flip-+0.1

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

  4. Taylor expanded around 0 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))