Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} \cdot \left(2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812\right)}{2.307529999999999859028321225196123123169 - x \cdot 0.2706100000000000171951342053944244980812} - x
double f(double x) {
        double r69260 = 2.30753;
        double r69261 = x;
        double r69262 = 0.27061;
        double r69263 = r69261 * r69262;
        double r69264 = r69260 + r69263;
        double r69265 = 1.0;
        double r69266 = 0.99229;
        double r69267 = 0.04481;
        double r69268 = r69261 * r69267;
        double r69269 = r69266 + r69268;
        double r69270 = r69261 * r69269;
        double r69271 = r69265 + r69270;
        double r69272 = r69264 / r69271;
        double r69273 = r69272 - r69261;
        return r69273;
}
↓
double f(double x) {
        double r69274 = x;
        double r69275 = 0.27061;
        double r69276 = r69274 * r69275;
        double r69277 = 2.30753;
        double r69278 = r69276 + r69277;
        double r69279 = 1.0;
        double r69280 = 0.99229;
        double r69281 = 0.04481;
        double r69282 = r69274 * r69281;
        double r69283 = r69280 + r69282;
        double r69284 = r69274 * r69283;
        double r69285 = r69279 + r69284;
        double r69286 = r69278 / r69285;
        double r69287 = r69277 - r69276;
        double r69288 = r69286 * r69287;
        double r69289 = r69288 / r69287;
        double r69290 = r69289 - r69274;
        return r69290;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}}} - x\]
  4. Using strategy rm

  5. Applied flip-+16.1

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

  6. Applied associate-/r/16.1

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

  7. Applied associate-/r*16.1

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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))