Average Error: 0.0 → 0.0
Time: 13.3s
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 r59198 = 2.30753;
        double r59199 = x;
        double r59200 = 0.27061;
        double r59201 = r59199 * r59200;
        double r59202 = r59198 + r59201;
        double r59203 = 1.0;
        double r59204 = 0.99229;
        double r59205 = 0.04481;
        double r59206 = r59199 * r59205;
        double r59207 = r59204 + r59206;
        double r59208 = r59199 * r59207;
        double r59209 = r59203 + r59208;
        double r59210 = r59202 / r59209;
        double r59211 = r59210 - r59199;
        return r59211;
}
↓
double f(double x) {
        double r59212 = 2.30753;
        double r59213 = x;
        double r59214 = 0.27061;
        double r59215 = r59213 * r59214;
        double r59216 = r59212 + r59215;
        double r59217 = 1.0;
        double r59218 = 0.99229;
        double r59219 = cbrt(r59218);
        double r59220 = r59219 * r59219;
        double r59221 = 0.04481;
        double r59222 = r59213 * r59221;
        double r59223 = fma(r59220, r59219, r59222);
        double r59224 = r59213 * r59223;
        double r59225 = r59217 + r59224;
        double r59226 = r59216 / r59225;
        double r59227 = r59226 - r59213;
        return r59227;
}

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))