Average Error: 0.1 → 0.1
Time: 7.3s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \left(x \cdot x\right) \cdot 0.1199999999999999955591079014993738383055\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(0.2530000000000000026645352591003756970167 \cdot x + \left(x \cdot x\right) \cdot 0.1199999999999999955591079014993738383055\right)
double f(double x) {
        double r60776 = 1.0;
        double r60777 = x;
        double r60778 = 0.253;
        double r60779 = 0.12;
        double r60780 = r60777 * r60779;
        double r60781 = r60778 + r60780;
        double r60782 = r60777 * r60781;
        double r60783 = r60776 - r60782;
        return r60783;
}
↓
double f(double x) {
        double r60784 = 1.0;
        double r60785 = 0.253;
        double r60786 = x;
        double r60787 = r60785 * r60786;
        double r60788 = r60786 * r60786;
        double r60789 = 0.12;
        double r60790 = r60788 * r60789;
        double r60791 = r60787 + r60790;
        double r60792 = r60784 - r60791;
        return r60792;
}

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. Simplified0.1

    \[\leadsto 1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + \color{blue}{\left(x \cdot 0.1199999999999999955591079014993738383055\right) \cdot x}\right)\]
  5. Using strategy rm

  6. Applied pow10.1

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

  7. Applied pow10.1

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

  8. Applied pow10.1

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

  9. Applied pow-prod-down0.1

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

  10. Applied pow-prod-down0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  (- 1.0 (* x (+ 0.253 (* x 0.12)))))