Average Error: 0.0 → 0.1
Time: 3.2s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}}{\sqrt{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}
double f(double x) {
        double r97456 = x;
        double r97457 = 2.30753;
        double r97458 = 0.27061;
        double r97459 = r97456 * r97458;
        double r97460 = r97457 + r97459;
        double r97461 = 1.0;
        double r97462 = 0.99229;
        double r97463 = 0.04481;
        double r97464 = r97456 * r97463;
        double r97465 = r97462 + r97464;
        double r97466 = r97465 * r97456;
        double r97467 = r97461 + r97466;
        double r97468 = r97460 / r97467;
        double r97469 = r97456 - r97468;
        return r97469;
}
↓
double f(double x) {
        double r97470 = x;
        double r97471 = 2.30753;
        double r97472 = 0.27061;
        double r97473 = r97470 * r97472;
        double r97474 = r97471 + r97473;
        double r97475 = 1.0;
        double r97476 = 0.99229;
        double r97477 = 0.04481;
        double r97478 = r97470 * r97477;
        double r97479 = r97476 + r97478;
        double r97480 = r97479 * r97470;
        double r97481 = r97475 + r97480;
        double r97482 = sqrt(r97481);
        double r97483 = r97474 / r97482;
        double r97484 = r97483 / r97482;
        double r97485 = r97470 - r97484;
        return r97485;
}

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

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))