Average Error: 0.0 → 0.1
Time: 10.6s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x
double f(double x) {
        double r82461 = 2.30753;
        double r82462 = x;
        double r82463 = 0.27061;
        double r82464 = r82462 * r82463;
        double r82465 = r82461 + r82464;
        double r82466 = 1.0;
        double r82467 = 0.99229;
        double r82468 = 0.04481;
        double r82469 = r82462 * r82468;
        double r82470 = r82467 + r82469;
        double r82471 = r82462 * r82470;
        double r82472 = r82466 + r82471;
        double r82473 = r82465 / r82472;
        double r82474 = r82473 - r82462;
        return r82474;
}
↓
double f(double x) {
        double r82475 = 1.0;
        double r82476 = 1.0;
        double r82477 = x;
        double r82478 = 0.99229;
        double r82479 = 0.04481;
        double r82480 = r82477 * r82479;
        double r82481 = r82478 + r82480;
        double r82482 = r82477 * r82481;
        double r82483 = r82476 + r82482;
        double r82484 = sqrt(r82483);
        double r82485 = 2.30753;
        double r82486 = 0.27061;
        double r82487 = r82477 * r82486;
        double r82488 = r82485 + r82487;
        double r82489 = r82484 / r82488;
        double r82490 = r82475 / r82489;
        double r82491 = r82490 / r82484;
        double r82492 = r82491 - r82477;
        return r82492;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \frac{2.30753 + x \cdot 0.27061000000000002}{\color{blue}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]

  4. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}} - x\]
  5. Using strategy rm

  6. Applied clear-num0.1

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

  7. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}}{2.30753 + x \cdot 0.27061000000000002}}}{\sqrt{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))