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

Average Error: 0.1 → 0.1

Time: 21.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r4525805 = 1.0;
        double r4525806 = x;
        double r4525807 = 0.253;
        double r4525808 = 0.12;
        double r4525809 = r4525806 * r4525808;
        double r4525810 = r4525807 + r4525809;
        double r4525811 = r4525806 * r4525810;
        double r4525812 = r4525805 - r4525811;
        return r4525812;
}

↓

double f(double x) {
        double r4525813 = 1.0;
        double r4525814 = 0.12;
        double r4525815 = x;
        double r4525816 = r4525814 * r4525815;
        double r4525817 = 0.253;
        double r4525818 = r4525816 + r4525817;
        double r4525819 = r4525818 * r4525815;
        double r4525820 = r4525813 - r4525819;
        return r4525820;
}

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 +-commutative 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))