Average Error: 0.1 → 0.2
Time: 19.3s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(0.1199999999999999955591079014993738383055 \cdot {x}^{2} + 0.2530000000000000026645352591003756970167 \cdot x\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(0.1199999999999999955591079014993738383055 \cdot {x}^{2} + 0.2530000000000000026645352591003756970167 \cdot x\right)
double f(double x) {
        double r70122 = 1.0;
        double r70123 = x;
        double r70124 = 0.253;
        double r70125 = 0.12;
        double r70126 = r70123 * r70125;
        double r70127 = r70124 + r70126;
        double r70128 = r70123 * r70127;
        double r70129 = r70122 - r70128;
        return r70129;
}
↓
double f(double x) {
        double r70130 = 1.0;
        double r70131 = 0.12;
        double r70132 = x;
        double r70133 = 2.0;
        double r70134 = pow(r70132, r70133);
        double r70135 = r70131 * r70134;
        double r70136 = 0.253;
        double r70137 = r70136 * r70132;
        double r70138 = r70135 + r70137;
        double r70139 = r70130 - r70138;
        return r70139;
}

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. Simplified0.1

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

  4. Applied add-cube-cbrt0.4

    \[\leadsto 1 - x \cdot \color{blue}{\left(\left(\sqrt[3]{x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167} \cdot \sqrt[3]{x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167}\right) \cdot \sqrt[3]{x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167}\right)}\]

  5. Applied associate-*r*0.4

    \[\leadsto 1 - \color{blue}{\left(x \cdot \left(\sqrt[3]{x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167} \cdot \sqrt[3]{x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167}\right)\right) \cdot \sqrt[3]{x \cdot 0.1199999999999999955591079014993738383055 + 0.2530000000000000026645352591003756970167}}\]

  6. Taylor expanded around 0 0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))