Average Error: 27.0 → 0.6
Time: 9.0s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.3816591170685381 \cdot 10^{49} \lor \neg \left(x \le 7.8727637619665125 \cdot 10^{73}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{1}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]
\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 -1.3816591170685381 \cdot 10^{49} \lor \neg \left(x \le 7.8727637619665125 \cdot 10^{73}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \cdot \frac{1}{\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 r382333 = x;
        double r382334 = 2.0;
        double r382335 = r382333 - r382334;
        double r382336 = 4.16438922228;
        double r382337 = r382333 * r382336;
        double r382338 = 78.6994924154;
        double r382339 = r382337 + r382338;
        double r382340 = r382339 * r382333;
        double r382341 = 137.519416416;
        double r382342 = r382340 + r382341;
        double r382343 = r382342 * r382333;
        double r382344 = y;
        double r382345 = r382343 + r382344;
        double r382346 = r382345 * r382333;
        double r382347 = z;
        double r382348 = r382346 + r382347;
        double r382349 = r382335 * r382348;
        double r382350 = 43.3400022514;
        double r382351 = r382333 + r382350;
        double r382352 = r382351 * r382333;
        double r382353 = 263.505074721;
        double r382354 = r382352 + r382353;
        double r382355 = r382354 * r382333;
        double r382356 = 313.399215894;
        double r382357 = r382355 + r382356;
        double r382358 = r382357 * r382333;
        double r382359 = 47.066876606;
        double r382360 = r382358 + r382359;
        double r382361 = r382349 / r382360;
        return r382361;
}
↓
double f(double x, double y, double z) {
        double r382362 = x;
        double r382363 = -1.381659117068538e+49;
        bool r382364 = r382362 <= r382363;
        double r382365 = 7.872763761966512e+73;
        bool r382366 = r382362 <= r382365;
        double r382367 = !r382366;
        bool r382368 = r382364 || r382367;
        double r382369 = y;
        double r382370 = 2.0;
        double r382371 = pow(r382362, r382370);
        double r382372 = r382369 / r382371;
        double r382373 = 4.16438922228;
        double r382374 = r382373 * r382362;
        double r382375 = r382372 + r382374;
        double r382376 = 110.1139242984811;
        double r382377 = r382375 - r382376;
        double r382378 = 2.0;
        double r382379 = r382362 - r382378;
        double r382380 = 1.0;
        double r382381 = 43.3400022514;
        double r382382 = r382362 + r382381;
        double r382383 = r382382 * r382362;
        double r382384 = 263.505074721;
        double r382385 = r382383 + r382384;
        double r382386 = r382385 * r382362;
        double r382387 = 313.399215894;
        double r382388 = r382386 + r382387;
        double r382389 = r382388 * r382362;
        double r382390 = 47.066876606;
        double r382391 = r382389 + r382390;
        double r382392 = r382362 * r382373;
        double r382393 = 78.6994924154;
        double r382394 = r382392 + r382393;
        double r382395 = r382394 * r382362;
        double r382396 = 137.519416416;
        double r382397 = r382395 + r382396;
        double r382398 = r382397 * r382362;
        double r382399 = r382398 + r382369;
        double r382400 = r382399 * r382362;
        double r382401 = z;
        double r382402 = r382400 + r382401;
        double r382403 = r382391 / r382402;
        double r382404 = r382380 / r382403;
        double r382405 = r382379 * r382404;
        double r382406 = r382368 ? r382377 : r382405;
        return r382406;
}

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

Original27.0
Target0.5
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.381659117068538e+49 or 7.872763761966512e+73 < x

    1. Initial program 62.8

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

    2. Taylor expanded around inf 0.2

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

    if -1.381659117068538e+49 < x < 7.872763761966512e+73

    1. Initial program 2.5

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

    3. Applied associate-/l*0.9

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

    5. Applied div-inv0.9

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.3816591170685381 \cdot 10^{49} \lor \neg \left(x \le 7.8727637619665125 \cdot 10^{73}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{1}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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)))