Average Error: 0.1 → 0.2
Time: 3.0s
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 r80940 = 1.0;
        double r80941 = x;
        double r80942 = 0.253;
        double r80943 = 0.12;
        double r80944 = r80941 * r80943;
        double r80945 = r80942 + r80944;
        double r80946 = r80941 * r80945;
        double r80947 = r80940 - r80946;
        return r80947;
}
↓
double f(double x) {
        double r80948 = 1.0;
        double r80949 = x;
        double r80950 = 0.253;
        double r80951 = r80949 * r80950;
        double r80952 = 0.12;
        double r80953 = r80949 * r80952;
        double r80954 = r80949 * r80953;
        double r80955 = sqrt(r80954);
        double r80956 = r80955 * r80955;
        double r80957 = r80951 + r80956;
        double r80958 = r80948 - r80957;
        return r80958;
}

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)))))