Average Error: 0.1 → 0.1
Time: 14.7s
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 r45493 = 1.0;
        double r45494 = x;
        double r45495 = 0.253;
        double r45496 = 0.12;
        double r45497 = r45494 * r45496;
        double r45498 = r45495 + r45497;
        double r45499 = r45494 * r45498;
        double r45500 = r45493 - r45499;
        return r45500;
}
↓
double f(double x) {
        double r45501 = 1.0;
        double r45502 = 0.253;
        double r45503 = x;
        double r45504 = r45502 * r45503;
        double r45505 = 0.12;
        double r45506 = 2.0;
        double r45507 = pow(r45503, r45506);
        double r45508 = r45505 * r45507;
        double r45509 = r45504 + r45508;
        double r45510 = r45501 - r45509;
        return r45510;
}

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 2019326 +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)))))