Average Error: 26.3 → 0.7
Time: 14.6s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.37134358210142024 \cdot 10^{57} \lor \neg \left(x \le 6.95058600294961662 \cdot 10^{46}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right) \cdot \frac{1}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]
\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 -2.37134358210142024 \cdot 10^{57} \lor \neg \left(x \le 6.95058600294961662 \cdot 10^{46}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\frac{x - 2}{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right) \cdot \frac{1}{\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 r436526 = x;
        double r436527 = 2.0;
        double r436528 = r436526 - r436527;
        double r436529 = 4.16438922228;
        double r436530 = r436526 * r436529;
        double r436531 = 78.6994924154;
        double r436532 = r436530 + r436531;
        double r436533 = r436532 * r436526;
        double r436534 = 137.519416416;
        double r436535 = r436533 + r436534;
        double r436536 = r436535 * r436526;
        double r436537 = y;
        double r436538 = r436536 + r436537;
        double r436539 = r436538 * r436526;
        double r436540 = z;
        double r436541 = r436539 + r436540;
        double r436542 = r436528 * r436541;
        double r436543 = 43.3400022514;
        double r436544 = r436526 + r436543;
        double r436545 = r436544 * r436526;
        double r436546 = 263.505074721;
        double r436547 = r436545 + r436546;
        double r436548 = r436547 * r436526;
        double r436549 = 313.399215894;
        double r436550 = r436548 + r436549;
        double r436551 = r436550 * r436526;
        double r436552 = 47.066876606;
        double r436553 = r436551 + r436552;
        double r436554 = r436542 / r436553;
        return r436554;
}
↓
double f(double x, double y, double z) {
        double r436555 = x;
        double r436556 = -2.3713435821014202e+57;
        bool r436557 = r436555 <= r436556;
        double r436558 = 6.950586002949617e+46;
        bool r436559 = r436555 <= r436558;
        double r436560 = !r436559;
        bool r436561 = r436557 || r436560;
        double r436562 = y;
        double r436563 = 2.0;
        double r436564 = pow(r436555, r436563);
        double r436565 = r436562 / r436564;
        double r436566 = 4.16438922228;
        double r436567 = r436566 * r436555;
        double r436568 = r436565 + r436567;
        double r436569 = 110.1139242984811;
        double r436570 = r436568 - r436569;
        double r436571 = 2.0;
        double r436572 = r436555 - r436571;
        double r436573 = 43.3400022514;
        double r436574 = r436555 + r436573;
        double r436575 = r436574 * r436555;
        double r436576 = 263.505074721;
        double r436577 = r436575 + r436576;
        double r436578 = r436577 * r436555;
        double r436579 = 313.399215894;
        double r436580 = r436578 + r436579;
        double r436581 = r436580 * r436555;
        double r436582 = 47.066876606;
        double r436583 = r436581 + r436582;
        double r436584 = 1.0;
        double r436585 = r436555 * r436566;
        double r436586 = 78.6994924154;
        double r436587 = r436585 + r436586;
        double r436588 = r436587 * r436555;
        double r436589 = 137.519416416;
        double r436590 = r436588 + r436589;
        double r436591 = r436590 * r436555;
        double r436592 = r436591 + r436562;
        double r436593 = r436592 * r436555;
        double r436594 = z;
        double r436595 = r436593 + r436594;
        double r436596 = r436584 / r436595;
        double r436597 = r436583 * r436596;
        double r436598 = r436572 / r436597;
        double r436599 = r436561 ? r436570 : r436598;
        return r436599;
}

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

Original26.3
Target0.4
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.3713435821014202e+57 or 6.950586002949617e+46 < x

    1. Initial program 62.0

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

    2. Taylor expanded around inf 0.5

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

    if -2.3713435821014202e+57 < x < 6.950586002949617e+46

    1. Initial program 1.1

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

    3. Applied associate-/l*0.7

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

    5. Applied div-inv0.7

      \[\leadsto \frac{x - 2}{\color{blue}{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right) \cdot \frac{1}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.37134358210142024 \cdot 10^{57} \lor \neg \left(x \le 6.95058600294961662 \cdot 10^{46}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right) \cdot \frac{1}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* 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) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))