Average Error: 26.7 → 0.8
Time: 22.2s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.9294508035473342 \cdot 10^{50} \lor \neg \left(x \le 4.467348150850489 \cdot 10^{62}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - 2}{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}}{\frac{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]
\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 -2.9294508035473342 \cdot 10^{50} \lor \neg \left(x \le 4.467348150850489 \cdot 10^{62}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x - 2}{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}}{\frac{\sqrt{\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 r486380 = x;
        double r486381 = 2.0;
        double r486382 = r486380 - r486381;
        double r486383 = 4.16438922228;
        double r486384 = r486380 * r486383;
        double r486385 = 78.6994924154;
        double r486386 = r486384 + r486385;
        double r486387 = r486386 * r486380;
        double r486388 = 137.519416416;
        double r486389 = r486387 + r486388;
        double r486390 = r486389 * r486380;
        double r486391 = y;
        double r486392 = r486390 + r486391;
        double r486393 = r486392 * r486380;
        double r486394 = z;
        double r486395 = r486393 + r486394;
        double r486396 = r486382 * r486395;
        double r486397 = 43.3400022514;
        double r486398 = r486380 + r486397;
        double r486399 = r486398 * r486380;
        double r486400 = 263.505074721;
        double r486401 = r486399 + r486400;
        double r486402 = r486401 * r486380;
        double r486403 = 313.399215894;
        double r486404 = r486402 + r486403;
        double r486405 = r486404 * r486380;
        double r486406 = 47.066876606;
        double r486407 = r486405 + r486406;
        double r486408 = r486396 / r486407;
        return r486408;
}
↓
double f(double x, double y, double z) {
        double r486409 = x;
        double r486410 = -2.9294508035473342e+50;
        bool r486411 = r486409 <= r486410;
        double r486412 = 4.467348150850489e+62;
        bool r486413 = r486409 <= r486412;
        double r486414 = !r486413;
        bool r486415 = r486411 || r486414;
        double r486416 = y;
        double r486417 = 2.0;
        double r486418 = pow(r486409, r486417);
        double r486419 = r486416 / r486418;
        double r486420 = 4.16438922228;
        double r486421 = r486420 * r486409;
        double r486422 = r486419 + r486421;
        double r486423 = 110.1139242984811;
        double r486424 = r486422 - r486423;
        double r486425 = 2.0;
        double r486426 = r486409 - r486425;
        double r486427 = 43.3400022514;
        double r486428 = r486409 + r486427;
        double r486429 = r486428 * r486409;
        double r486430 = 263.505074721;
        double r486431 = r486429 + r486430;
        double r486432 = r486431 * r486409;
        double r486433 = 313.399215894;
        double r486434 = r486432 + r486433;
        double r486435 = r486434 * r486409;
        double r486436 = 47.066876606;
        double r486437 = r486435 + r486436;
        double r486438 = sqrt(r486437);
        double r486439 = r486426 / r486438;
        double r486440 = r486409 * r486420;
        double r486441 = 78.6994924154;
        double r486442 = r486440 + r486441;
        double r486443 = r486442 * r486409;
        double r486444 = 137.519416416;
        double r486445 = r486443 + r486444;
        double r486446 = r486445 * r486409;
        double r486447 = r486446 + r486416;
        double r486448 = r486447 * r486409;
        double r486449 = z;
        double r486450 = r486448 + r486449;
        double r486451 = r486438 / r486450;
        double r486452 = r486439 / r486451;
        double r486453 = r486415 ? r486424 : r486452;
        return r486453;
}

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

Original26.7
Target0.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.9294508035473342e+50 or 4.467348150850489e+62 < x

    1. Initial program 63.1

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

    2. Taylor expanded around inf 0.3

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

    if -2.9294508035473342e+50 < x < 4.467348150850489e+62

    1. Initial program 1.8

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

    3. Applied associate-/l*0.8

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

    5. Applied *-un-lft-identity0.8

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

    6. Applied add-sqr-sqrt1.0

      \[\leadsto \frac{x - 2}{\frac{\color{blue}{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001} \cdot \sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}}{1 \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}}\]

    7. Applied times-frac1.1

      \[\leadsto \frac{x - 2}{\color{blue}{\frac{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}{1} \cdot \frac{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}}\]

    8. Applied associate-/r*1.1

      \[\leadsto \color{blue}{\frac{\frac{x - 2}{\frac{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}{1}}}{\frac{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}}\]

    9. Simplified1.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.9294508035473342 \cdot 10^{50} \lor \neg \left(x \le 4.467348150850489 \cdot 10^{62}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x - 2}{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}}{\frac{\sqrt{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 
(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)))