Average Error: 0.1 → 0.1
Time: 13.6s
Precision: 64
\[1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)\]
↓
\[\frac{1 \cdot 1 - \left(x \cdot 0.2530000000000000026645352591003756970167\right) \cdot \left(x \cdot 0.2530000000000000026645352591003756970167\right)}{1 + x \cdot 0.2530000000000000026645352591003756970167} - \left(x \cdot 0.1199999999999999955591079014993738383055\right) \cdot x\]
1 - x \cdot \left(0.2530000000000000026645352591003756970167 + x \cdot 0.1199999999999999955591079014993738383055\right)
↓
\frac{1 \cdot 1 - \left(x \cdot 0.2530000000000000026645352591003756970167\right) \cdot \left(x \cdot 0.2530000000000000026645352591003756970167\right)}{1 + x \cdot 0.2530000000000000026645352591003756970167} - \left(x \cdot 0.1199999999999999955591079014993738383055\right) \cdot x
double f(double x) {
        double r70381 = 1.0;
        double r70382 = x;
        double r70383 = 0.253;
        double r70384 = 0.12;
        double r70385 = r70382 * r70384;
        double r70386 = r70383 + r70385;
        double r70387 = r70382 * r70386;
        double r70388 = r70381 - r70387;
        return r70388;
}
↓
double f(double x) {
        double r70389 = 1.0;
        double r70390 = r70389 * r70389;
        double r70391 = x;
        double r70392 = 0.253;
        double r70393 = r70391 * r70392;
        double r70394 = r70393 * r70393;
        double r70395 = r70390 - r70394;
        double r70396 = r70389 + r70393;
        double r70397 = r70395 / r70396;
        double r70398 = 0.12;
        double r70399 = r70391 * r70398;
        double r70400 = r70399 * r70391;
        double r70401 = r70397 - r70400;
        return r70401;
}

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-rgt-in0.1

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

  4. Applied associate--r+0.1

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

  5. Simplified0.1

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

  7. Applied flip--0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (- 1 (* x (+ 0.253 (* x 0.12)))))