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 r79079 = 1.0;
        double r79080 = x;
        double r79081 = 0.253;
        double r79082 = 0.12;
        double r79083 = r79080 * r79082;
        double r79084 = r79081 + r79083;
        double r79085 = r79080 * r79084;
        double r79086 = r79079 - r79085;
        return r79086;
}
↓
double f(double x) {
        double r79087 = 1.0;
        double r79088 = x;
        double r79089 = 0.253;
        double r79090 = r79088 * r79089;
        double r79091 = 0.12;
        double r79092 = r79088 * r79091;
        double r79093 = r79088 * r79092;
        double r79094 = r79090 + r79093;
        double r79095 = r79087 - r79094;
        return r79095;
}

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 2019354 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))