Average Error: 0.1 → 0.1
Time: 13.9s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)\right)\]
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)
double f(double x) {
        double r46312 = 1.0;
        double r46313 = x;
        double r46314 = 0.253;
        double r46315 = 0.12;
        double r46316 = r46313 * r46315;
        double r46317 = r46314 + r46316;
        double r46318 = r46313 * r46317;
        double r46319 = r46312 - r46318;
        return r46319;
}
↓
double f(double x) {
        double r46320 = 1.0;
        double r46321 = x;
        double r46322 = 0.253;
        double r46323 = r46321 * r46322;
        double r46324 = 0.12;
        double r46325 = r46321 * r46324;
        double r46326 = r46321 * r46325;
        double r46327 = r46323 + r46326;
        double r46328 = r46320 - r46327;
        return r46328;
}

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. Final simplification0.1

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

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)))))