Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x
double f(double x) {
        double r71277 = 2.30753;
        double r71278 = x;
        double r71279 = 0.27061;
        double r71280 = r71278 * r71279;
        double r71281 = r71277 + r71280;
        double r71282 = 1.0;
        double r71283 = 0.99229;
        double r71284 = 0.04481;
        double r71285 = r71278 * r71284;
        double r71286 = r71283 + r71285;
        double r71287 = r71278 * r71286;
        double r71288 = r71282 + r71287;
        double r71289 = r71281 / r71288;
        double r71290 = r71289 - r71278;
        return r71290;
}
↓
double f(double x) {
        double r71291 = 2.30753;
        double r71292 = x;
        double r71293 = 0.27061;
        double r71294 = r71292 * r71293;
        double r71295 = r71291 + r71294;
        double r71296 = 1.0;
        double r71297 = 0.04481;
        double r71298 = 0.99229;
        double r71299 = fma(r71297, r71292, r71298);
        double r71300 = 1.0;
        double r71301 = fma(r71292, r71299, r71300);
        double r71302 = r71301 * r71296;
        double r71303 = r71296 / r71302;
        double r71304 = r71295 * r71303;
        double r71305 = r71304 - r71292;
        return r71305;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  2. Using strategy rm

  3. Applied div-inv0.0

    \[\leadsto \color{blue}{\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]

  4. Simplified0.0

    \[\leadsto \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1}} - x\]

  5. Final simplification0.0

    \[\leadsto \left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{\mathsf{fma}\left(x, \mathsf{fma}\left(0.044810000000000003, x, 0.992290000000000005\right), 1\right) \cdot 1} - x\]

Reproduce

herbie shell --seed 2020062 +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))