Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{1}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right)}{\mathsf{fma}\left(0.27061000000000002, x, 2.30753\right)}} - x
double f(double x) {
        double r53518 = 2.30753;
        double r53519 = x;
        double r53520 = 0.27061;
        double r53521 = r53519 * r53520;
        double r53522 = r53518 + r53521;
        double r53523 = 1.0;
        double r53524 = 0.99229;
        double r53525 = 0.04481;
        double r53526 = r53519 * r53525;
        double r53527 = r53524 + r53526;
        double r53528 = r53519 * r53527;
        double r53529 = r53523 + r53528;
        double r53530 = r53522 / r53529;
        double r53531 = r53530 - r53519;
        return r53531;
}
↓
double f(double x) {
        double r53532 = 1.0;
        double r53533 = x;
        double r53534 = 0.04481;
        double r53535 = 0.99229;
        double r53536 = fma(r53534, r53533, r53535);
        double r53537 = 1.0;
        double r53538 = fma(r53533, r53536, r53537);
        double r53539 = 0.27061;
        double r53540 = 2.30753;
        double r53541 = fma(r53539, r53533, r53540);
        double r53542 = r53538 / r53541;
        double r53543 = r53532 / r53542;
        double r53544 = r53543 - r53533;
        return r53544;
}

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 clear-num0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 +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))