Average Error: 0.1 → 0.2
Time: 10.3s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + \left(x \cdot x\right) \cdot 0.1199999999999999955591079014993738383055\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + \left(x \cdot x\right) \cdot 0.1199999999999999955591079014993738383055\right)
double f(double x) {
        double r3614956 = 1.0;
        double r3614957 = x;
        double r3614958 = 0.253;
        double r3614959 = 0.12;
        double r3614960 = r3614957 * r3614959;
        double r3614961 = r3614958 + r3614960;
        double r3614962 = r3614957 * r3614961;
        double r3614963 = r3614956 - r3614962;
        return r3614963;
}
↓
double f(double x) {
        double r3614964 = 1.0;
        double r3614965 = x;
        double r3614966 = 0.253;
        double r3614967 = r3614965 * r3614966;
        double r3614968 = r3614965 * r3614965;
        double r3614969 = 0.12;
        double r3614970 = r3614968 * r3614969;
        double r3614971 = r3614967 + r3614970;
        double r3614972 = r3614964 - r3614971;
        return r3614972;
}

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 flip-+0.1

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

  4. Taylor expanded around 0 0.2

    \[\leadsto 1 - \color{blue}{\left(0.2530000000000000026645352591003756970167 \cdot x + 0.1199999999999999955591079014993738383055 \cdot {x}^{2}\right)}\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))