Average Error: 0.1 → 0.1
Time: 15.2s
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 r48493 = 1.0;
        double r48494 = x;
        double r48495 = 0.253;
        double r48496 = 0.12;
        double r48497 = r48494 * r48496;
        double r48498 = r48495 + r48497;
        double r48499 = r48494 * r48498;
        double r48500 = r48493 - r48499;
        return r48500;
}
↓
double f(double x) {
        double r48501 = 1.0;
        double r48502 = 0.253;
        double r48503 = x;
        double r48504 = r48502 * r48503;
        double r48505 = 0.12;
        double r48506 = 2.0;
        double r48507 = pow(r48503, r48506);
        double r48508 = r48505 * r48507;
        double r48509 = r48504 + r48508;
        double r48510 = r48501 - r48509;
        return r48510;
}

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)))))