Average Error: 0.0 → 0.0
Time: 23.4s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
↓
\[\frac{\frac{\frac{0.27061 \cdot x + 2.30753}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}} - x\]
\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x
↓
\frac{\frac{\frac{0.27061 \cdot x + 2.30753}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}} - x
double f(double x) {
        double r4057308 = 2.30753;
        double r4057309 = x;
        double r4057310 = 0.27061;
        double r4057311 = r4057309 * r4057310;
        double r4057312 = r4057308 + r4057311;
        double r4057313 = 1.0;
        double r4057314 = 0.99229;
        double r4057315 = 0.04481;
        double r4057316 = r4057309 * r4057315;
        double r4057317 = r4057314 + r4057316;
        double r4057318 = r4057309 * r4057317;
        double r4057319 = r4057313 + r4057318;
        double r4057320 = r4057312 / r4057319;
        double r4057321 = r4057320 - r4057309;
        return r4057321;
}
↓
double f(double x) {
        double r4057322 = 0.27061;
        double r4057323 = x;
        double r4057324 = r4057322 * r4057323;
        double r4057325 = 2.30753;
        double r4057326 = r4057324 + r4057325;
        double r4057327 = 0.04481;
        double r4057328 = r4057323 * r4057327;
        double r4057329 = 0.99229;
        double r4057330 = r4057328 + r4057329;
        double r4057331 = r4057323 * r4057330;
        double r4057332 = 1.0;
        double r4057333 = r4057331 + r4057332;
        double r4057334 = cbrt(r4057333);
        double r4057335 = r4057326 / r4057334;
        double r4057336 = r4057335 / r4057334;
        double r4057337 = r4057336 / r4057334;
        double r4057338 = r4057337 - r4057323;
        return r4057338;
}

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

    \[\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto \frac{2.30753 + x \cdot 0.27061}{\color{blue}{\left(\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \cdot \sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}\right) \cdot \sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}} - x\]

  4. Applied associate-/r*0.0

    \[\leadsto \color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} \cdot \sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}} - x\]
  5. Using strategy rm

  6. Applied associate-/r*0.0

    \[\leadsto \frac{\color{blue}{\frac{\frac{2.30753 + x \cdot 0.27061}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}}}}{\sqrt[3]{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}} - x\]

  7. Final simplification0.0

    \[\leadsto \frac{\frac{\frac{0.27061 \cdot x + 2.30753}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}}}{\sqrt[3]{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}} - x\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))