Average Error: 0.1 → 0.1
Time: 20.6s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right) + x \cdot 0.2530000000000000026645352591003756970167\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right) + x \cdot 0.2530000000000000026645352591003756970167\right)
double f(double x) {
        double r55315 = 1.0;
        double r55316 = x;
        double r55317 = 0.253;
        double r55318 = 0.12;
        double r55319 = r55316 * r55318;
        double r55320 = r55317 + r55319;
        double r55321 = r55316 * r55320;
        double r55322 = r55315 - r55321;
        return r55322;
}
↓
double f(double x) {
        double r55323 = 1.0;
        double r55324 = x;
        double r55325 = 0.12;
        double r55326 = r55324 * r55325;
        double r55327 = r55324 * r55326;
        double r55328 = 0.253;
        double r55329 = r55324 * r55328;
        double r55330 = r55327 + r55329;
        double r55331 = r55323 - r55330;
        return r55331;
}

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. Simplified0.1

    \[\leadsto \color{blue}{1 - x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

    \[\leadsto 1 - \left(x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right) + x \cdot 0.2530000000000000026645352591003756970167\right)\]

Reproduce

herbie shell --seed 2019209 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))