Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A

Average Error: 0.1 → 0.1

Time: 14.2s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r54561 = 1.0;
        double r54562 = x;
        double r54563 = 0.253;
        double r54564 = 0.12;
        double r54565 = r54562 * r54564;
        double r54566 = r54563 + r54565;
        double r54567 = r54562 * r54566;
        double r54568 = r54561 - r54567;
        return r54568;
}

↓

double f(double x) {
        double r54569 = 1.0;
        double r54570 = x;
        double r54571 = 0.253;
        double r54572 = r54570 * r54571;
        double r54573 = 0.12;
        double r54574 = r54570 * r54573;
        double r54575 = r54570 * r54574;
        double r54576 = r54572 + r54575;
        double r54577 = r54569 - r54576;
        return r54577;
}

Error

Bits error versus x

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-in 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))