Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x
double f(double x) {
        double r50600 = 2.30753;
        double r50601 = x;
        double r50602 = 0.27061;
        double r50603 = r50601 * r50602;
        double r50604 = r50600 + r50603;
        double r50605 = 1.0;
        double r50606 = 0.99229;
        double r50607 = 0.04481;
        double r50608 = r50601 * r50607;
        double r50609 = r50606 + r50608;
        double r50610 = r50601 * r50609;
        double r50611 = r50605 + r50610;
        double r50612 = r50604 / r50611;
        double r50613 = r50612 - r50601;
        return r50613;
}
↓
double f(double x) {
        double r50614 = x;
        double r50615 = 0.27061;
        double r50616 = 2.30753;
        double r50617 = fma(r50614, r50615, r50616);
        double r50618 = 0.04481;
        double r50619 = 0.99229;
        double r50620 = fma(r50618, r50614, r50619);
        double r50621 = 1.0;
        double r50622 = fma(r50614, r50620, r50621);
        double r50623 = r50617 / r50622;
        double r50624 = r50623 - r50614;
        return r50624;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x}\]

  3. Final simplification0.0

    \[\leadsto \frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.04481000000000000260680366181986755691469, x, 0.992290000000000005364597654988756403327\right), 1\right)} - x\]

Reproduce

herbie shell --seed 2019325 +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))