Average Error: 0.1 → 0.1
Time: 2.4s
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 r69450 = 1.0;
        double r69451 = x;
        double r69452 = 0.253;
        double r69453 = 0.12;
        double r69454 = r69451 * r69453;
        double r69455 = r69452 + r69454;
        double r69456 = r69451 * r69455;
        double r69457 = r69450 - r69456;
        return r69457;
}
↓
double f(double x) {
        double r69458 = 1.0;
        double r69459 = x;
        double r69460 = 0.253;
        double r69461 = r69459 * r69460;
        double r69462 = 0.12;
        double r69463 = r69459 * r69462;
        double r69464 = r69459 * r69463;
        double r69465 = r69461 + r69464;
        double r69466 = r69458 - r69465;
        return r69466;
}

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 2019353 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))