Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \mathsf{fma}\left(\sqrt[3]{0.992290000000000005364597654988756403327} \cdot \sqrt[3]{0.992290000000000005364597654988756403327}, \sqrt[3]{0.992290000000000005364597654988756403327}, x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \mathsf{fma}\left(\sqrt[3]{0.992290000000000005364597654988756403327} \cdot \sqrt[3]{0.992290000000000005364597654988756403327}, \sqrt[3]{0.992290000000000005364597654988756403327}, x \cdot 0.04481000000000000260680366181986755691469\right)} - x
double f(double x) {
        double r66236 = 2.30753;
        double r66237 = x;
        double r66238 = 0.27061;
        double r66239 = r66237 * r66238;
        double r66240 = r66236 + r66239;
        double r66241 = 1.0;
        double r66242 = 0.99229;
        double r66243 = 0.04481;
        double r66244 = r66237 * r66243;
        double r66245 = r66242 + r66244;
        double r66246 = r66237 * r66245;
        double r66247 = r66241 + r66246;
        double r66248 = r66240 / r66247;
        double r66249 = r66248 - r66237;
        return r66249;
}
↓
double f(double x) {
        double r66250 = 2.30753;
        double r66251 = x;
        double r66252 = 0.27061;
        double r66253 = r66251 * r66252;
        double r66254 = r66250 + r66253;
        double r66255 = 1.0;
        double r66256 = 0.99229;
        double r66257 = cbrt(r66256);
        double r66258 = r66257 * r66257;
        double r66259 = 0.04481;
        double r66260 = r66251 * r66259;
        double r66261 = fma(r66258, r66257, r66260);
        double r66262 = r66251 * r66261;
        double r66263 = r66255 + r66262;
        double r66264 = r66254 / r66263;
        double r66265 = r66264 - r66251;
        return r66265;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(\color{blue}{\left(\sqrt[3]{0.992290000000000005364597654988756403327} \cdot \sqrt[3]{0.992290000000000005364597654988756403327}\right) \cdot \sqrt[3]{0.992290000000000005364597654988756403327}} + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]

  4. Applied fma-def0.0

    \[\leadsto \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \color{blue}{\mathsf{fma}\left(\sqrt[3]{0.992290000000000005364597654988756403327} \cdot \sqrt[3]{0.992290000000000005364597654988756403327}, \sqrt[3]{0.992290000000000005364597654988756403327}, x \cdot 0.04481000000000000260680366181986755691469\right)}} - x\]

  5. Final simplification0.0

    \[\leadsto \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \mathsf{fma}\left(\sqrt[3]{0.992290000000000005364597654988756403327} \cdot \sqrt[3]{0.992290000000000005364597654988756403327}, \sqrt[3]{0.992290000000000005364597654988756403327}, x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]

Reproduce

herbie shell --seed 2019347 +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))