Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \frac{1}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
\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}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
double f(double x) {
        double r90581 = 2.30753;
        double r90582 = x;
        double r90583 = 0.27061;
        double r90584 = r90582 * r90583;
        double r90585 = r90581 + r90584;
        double r90586 = 1.0;
        double r90587 = 0.99229;
        double r90588 = 0.04481;
        double r90589 = r90582 * r90588;
        double r90590 = r90587 + r90589;
        double r90591 = r90582 * r90590;
        double r90592 = r90586 + r90591;
        double r90593 = r90585 / r90592;
        double r90594 = r90593 - r90582;
        return r90594;
}
↓
double f(double x) {
        double r90595 = 2.30753;
        double r90596 = x;
        double r90597 = 0.27061;
        double r90598 = r90596 * r90597;
        double r90599 = r90595 + r90598;
        double r90600 = 1.0;
        double r90601 = 1.0;
        double r90602 = 0.99229;
        double r90603 = 0.04481;
        double r90604 = r90596 * r90603;
        double r90605 = r90602 + r90604;
        double r90606 = r90596 * r90605;
        double r90607 = r90601 + r90606;
        double r90608 = r90600 / r90607;
        double r90609 = r90599 * r90608;
        double r90610 = r90609 - r90596;
        return r90610;
}

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

    \[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(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))