Average Error: 0.1 → 0.2
Time: 2.0s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + \sqrt{x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)} \cdot \sqrt{x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)}\right)\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
1 - \left(x \cdot 0.2530000000000000026645352591003756970167 + \sqrt{x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)} \cdot \sqrt{x \cdot \left(x \cdot 0.1199999999999999955591079014993738383055\right)}\right)
double f(double x) {
        double r70161 = 1.0;
        double r70162 = x;
        double r70163 = 0.253;
        double r70164 = 0.12;
        double r70165 = r70162 * r70164;
        double r70166 = r70163 + r70165;
        double r70167 = r70162 * r70166;
        double r70168 = r70161 - r70167;
        return r70168;
}
↓
double f(double x) {
        double r70169 = 1.0;
        double r70170 = x;
        double r70171 = 0.253;
        double r70172 = r70170 * r70171;
        double r70173 = 0.12;
        double r70174 = r70170 * r70173;
        double r70175 = r70170 * r70174;
        double r70176 = sqrt(r70175);
        double r70177 = r70176 * r70176;
        double r70178 = r70172 + r70177;
        double r70179 = r70169 - r70178;
        return r70179;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.2

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

  6. Final simplification0.2

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

Reproduce

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