Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
double f(double x) {
        double r347 = 2.30753;
        double r348 = x;
        double r349 = 0.27061;
        double r350 = r348 * r349;
        double r351 = r347 + r350;
        double r352 = 1.0;
        double r353 = 0.99229;
        double r354 = 0.04481;
        double r355 = r348 * r354;
        double r356 = r353 + r355;
        double r357 = r348 * r356;
        double r358 = r352 + r357;
        double r359 = r351 / r358;
        double r360 = r359 - r348;
        return r360;
}
↓
double f(double x) {
        double r361 = 2.30753;
        double r362 = x;
        double r363 = 0.27061;
        double r364 = r362 * r363;
        double r365 = r361 + r364;
        double r366 = 1.0;
        double r367 = 1.0;
        double r368 = 0.99229;
        double r369 = 0.04481;
        double r370 = r362 * r369;
        double r371 = r368 + r370;
        double r372 = r362 * r371;
        double r373 = r367 + r372;
        double r374 = r366 / r373;
        double r375 = r365 * r374;
        double r376 = r375 - r362;
        return r376;
}

Error

Bits error versus x

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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 div-inv0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 
(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))