Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\mathsf{fma}\left(2.30753 + x \cdot 0.27061000000000002, \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}, -x\right)
double f(double x) {
        double r72448 = 2.30753;
        double r72449 = x;
        double r72450 = 0.27061;
        double r72451 = r72449 * r72450;
        double r72452 = r72448 + r72451;
        double r72453 = 1.0;
        double r72454 = 0.99229;
        double r72455 = 0.04481;
        double r72456 = r72449 * r72455;
        double r72457 = r72454 + r72456;
        double r72458 = r72449 * r72457;
        double r72459 = r72453 + r72458;
        double r72460 = r72452 / r72459;
        double r72461 = r72460 - r72449;
        return r72461;
}
↓
double f(double x) {
        double r72462 = 2.30753;
        double r72463 = x;
        double r72464 = 0.27061;
        double r72465 = r72463 * r72464;
        double r72466 = r72462 + r72465;
        double r72467 = 1.0;
        double r72468 = 1.0;
        double r72469 = 0.99229;
        double r72470 = 0.04481;
        double r72471 = r72463 * r72470;
        double r72472 = r72469 + r72471;
        double r72473 = r72463 * r72472;
        double r72474 = r72468 + r72473;
        double r72475 = r72467 / r72474;
        double r72476 = -r72463;
        double r72477 = fma(r72466, r72475, r72476);
        return r72477;
}

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. Applied fma-neg0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +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))