Average Error: 27.1 → 1.0
Time: 26.7s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -15065553983705802800 \lor \neg \left(x \le 7.1286734755880646 \cdot 10^{35}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}
↓
\begin{array}{l}
\mathbf{if}\;x \le -15065553983705802800 \lor \neg \left(x \le 7.1286734755880646 \cdot 10^{35}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\

\end{array}
double f(double x, double y, double z) {
        double r227524 = x;
        double r227525 = 2.0;
        double r227526 = r227524 - r227525;
        double r227527 = 4.16438922228;
        double r227528 = r227524 * r227527;
        double r227529 = 78.6994924154;
        double r227530 = r227528 + r227529;
        double r227531 = r227530 * r227524;
        double r227532 = 137.519416416;
        double r227533 = r227531 + r227532;
        double r227534 = r227533 * r227524;
        double r227535 = y;
        double r227536 = r227534 + r227535;
        double r227537 = r227536 * r227524;
        double r227538 = z;
        double r227539 = r227537 + r227538;
        double r227540 = r227526 * r227539;
        double r227541 = 43.3400022514;
        double r227542 = r227524 + r227541;
        double r227543 = r227542 * r227524;
        double r227544 = 263.505074721;
        double r227545 = r227543 + r227544;
        double r227546 = r227545 * r227524;
        double r227547 = 313.399215894;
        double r227548 = r227546 + r227547;
        double r227549 = r227548 * r227524;
        double r227550 = 47.066876606;
        double r227551 = r227549 + r227550;
        double r227552 = r227540 / r227551;
        return r227552;
}
↓
double f(double x, double y, double z) {
        double r227553 = x;
        double r227554 = -1.5065553983705803e+19;
        bool r227555 = r227553 <= r227554;
        double r227556 = 7.128673475588065e+35;
        bool r227557 = r227553 <= r227556;
        double r227558 = !r227557;
        bool r227559 = r227555 || r227558;
        double r227560 = y;
        double r227561 = 2.0;
        double r227562 = pow(r227553, r227561);
        double r227563 = r227560 / r227562;
        double r227564 = 4.16438922228;
        double r227565 = r227564 * r227553;
        double r227566 = r227563 + r227565;
        double r227567 = 110.1139242984811;
        double r227568 = r227566 - r227567;
        double r227569 = 2.0;
        double r227570 = r227553 - r227569;
        double r227571 = 43.3400022514;
        double r227572 = r227553 + r227571;
        double r227573 = r227572 * r227553;
        double r227574 = 263.505074721;
        double r227575 = r227573 + r227574;
        double r227576 = r227575 * r227553;
        double r227577 = 313.399215894;
        double r227578 = r227576 + r227577;
        double r227579 = r227578 * r227553;
        double r227580 = 47.066876606;
        double r227581 = r227579 + r227580;
        double r227582 = r227553 * r227564;
        double r227583 = 78.6994924154;
        double r227584 = r227582 + r227583;
        double r227585 = r227584 * r227553;
        double r227586 = 137.519416416;
        double r227587 = r227585 + r227586;
        double r227588 = r227587 * r227553;
        double r227589 = r227588 + r227560;
        double r227590 = r227589 * r227553;
        double r227591 = z;
        double r227592 = r227590 + r227591;
        double r227593 = r227581 / r227592;
        double r227594 = r227570 / r227593;
        double r227595 = r227559 ? r227568 : r227594;
        return r227595;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original27.1
Target0.6
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.5065553983705803e+19 or 7.128673475588065e+35 < x

    1. Initial program 58.3

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    2. Taylor expanded around inf 1.7

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]

    if -1.5065553983705803e+19 < x < 7.128673475588065e+35

    1. Initial program 0.5

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied associate-/l*0.4

      \[\leadsto \color{blue}{\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -15065553983705802800 \lor \neg \left(x \le 7.1286734755880646 \cdot 10^{35}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))