Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x\]
\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}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x
double f(double x) {
        double r78427 = 2.30753;
        double r78428 = x;
        double r78429 = 0.27061;
        double r78430 = r78428 * r78429;
        double r78431 = r78427 + r78430;
        double r78432 = 1.0;
        double r78433 = 0.99229;
        double r78434 = 0.04481;
        double r78435 = r78428 * r78434;
        double r78436 = r78433 + r78435;
        double r78437 = r78428 * r78436;
        double r78438 = r78432 + r78437;
        double r78439 = r78431 / r78438;
        double r78440 = r78439 - r78428;
        return r78440;
}
↓
double f(double x) {
        double r78441 = 2.30753;
        double r78442 = x;
        double r78443 = 0.27061;
        double r78444 = r78442 * r78443;
        double r78445 = r78441 + r78444;
        double r78446 = 1.0;
        double r78447 = 0.04481;
        double r78448 = 0.99229;
        double r78449 = fma(r78447, r78442, r78448);
        double r78450 = 1.0;
        double r78451 = fma(r78442, r78449, r78450);
        double r78452 = r78451 * r78446;
        double r78453 = r78446 / r78452;
        double r78454 = r78445 * r78453;
        double r78455 = r78454 - r78442;
        return r78455;
}

Error

Bits error versus x

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(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))