Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{\mathsf{fma}\left(x, 0.2706100000000000171951342053944244980812, 2.307529999999999859028321225196123123169\right)}{\mathsf{fma}\left(\mathsf{fma}\left(x, 0.04481000000000000260680366181986755691469, 0.992290000000000005364597654988756403327\right), x, 1\right)} - x\]
\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(\mathsf{fma}\left(x, 0.04481000000000000260680366181986755691469, 0.992290000000000005364597654988756403327\right), x, 1\right)} - x
double f(double x) {
        double r2899659 = 2.30753;
        double r2899660 = x;
        double r2899661 = 0.27061;
        double r2899662 = r2899660 * r2899661;
        double r2899663 = r2899659 + r2899662;
        double r2899664 = 1.0;
        double r2899665 = 0.99229;
        double r2899666 = 0.04481;
        double r2899667 = r2899660 * r2899666;
        double r2899668 = r2899665 + r2899667;
        double r2899669 = r2899660 * r2899668;
        double r2899670 = r2899664 + r2899669;
        double r2899671 = r2899663 / r2899670;
        double r2899672 = r2899671 - r2899660;
        return r2899672;
}
↓
double f(double x) {
        double r2899673 = x;
        double r2899674 = 0.27061;
        double r2899675 = 2.30753;
        double r2899676 = fma(r2899673, r2899674, r2899675);
        double r2899677 = 0.04481;
        double r2899678 = 0.99229;
        double r2899679 = fma(r2899673, r2899677, r2899678);
        double r2899680 = 1.0;
        double r2899681 = fma(r2899679, r2899673, r2899680);
        double r2899682 = r2899676 / r2899681;
        double r2899683 = r2899682 - r2899673;
        return r2899683;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(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))