Average Error: 0.1 → 0.2
Time: 2.2s
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 r125264 = 1.0;
        double r125265 = x;
        double r125266 = 0.253;
        double r125267 = 0.12;
        double r125268 = r125265 * r125267;
        double r125269 = r125266 + r125268;
        double r125270 = r125265 * r125269;
        double r125271 = r125264 - r125270;
        return r125271;
}
↓
double f(double x) {
        double r125272 = 1.0;
        double r125273 = 0.12;
        double r125274 = x;
        double r125275 = 2.0;
        double r125276 = pow(r125274, r125275);
        double r125277 = r125273 * r125276;
        double r125278 = 0.253;
        double r125279 = r125278 * r125274;
        double r125280 = r125277 + r125279;
        double r125281 = r125272 - r125280;
        return r125281;
}

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. Applied associate--r+0.1

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

  5. Simplified0.1

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

  6. Taylor expanded around 0 0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))