Average Error: 26.7 → 1.1
Time: 7.3s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.44052802145114724 \cdot 10^{47} \lor \neg \left(x \le 481036343538563580\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\frac{\left(x \cdot x - 43.3400022514000014 \cdot 43.3400022514000014\right) \cdot x}{x - 43.3400022514000014} + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -1.44052802145114724 \cdot 10^{47} \lor \neg \left(x \le 481036343538563580\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\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(\frac{\left(x \cdot x - 43.3400022514000014 \cdot 43.3400022514000014\right) \cdot x}{x - 43.3400022514000014} + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r399480 = x;
        double r399481 = 2.0;
        double r399482 = r399480 - r399481;
        double r399483 = 4.16438922228;
        double r399484 = r399480 * r399483;
        double r399485 = 78.6994924154;
        double r399486 = r399484 + r399485;
        double r399487 = r399486 * r399480;
        double r399488 = 137.519416416;
        double r399489 = r399487 + r399488;
        double r399490 = r399489 * r399480;
        double r399491 = y;
        double r399492 = r399490 + r399491;
        double r399493 = r399492 * r399480;
        double r399494 = z;
        double r399495 = r399493 + r399494;
        double r399496 = r399482 * r399495;
        double r399497 = 43.3400022514;
        double r399498 = r399480 + r399497;
        double r399499 = r399498 * r399480;
        double r399500 = 263.505074721;
        double r399501 = r399499 + r399500;
        double r399502 = r399501 * r399480;
        double r399503 = 313.399215894;
        double r399504 = r399502 + r399503;
        double r399505 = r399504 * r399480;
        double r399506 = 47.066876606;
        double r399507 = r399505 + r399506;
        double r399508 = r399496 / r399507;
        return r399508;
}
↓
double f(double x, double y, double z) {
        double r399509 = x;
        double r399510 = -1.4405280214511472e+47;
        bool r399511 = r399509 <= r399510;
        double r399512 = 4.810363435385636e+17;
        bool r399513 = r399509 <= r399512;
        double r399514 = !r399513;
        bool r399515 = r399511 || r399514;
        double r399516 = y;
        double r399517 = 2.0;
        double r399518 = pow(r399509, r399517);
        double r399519 = r399516 / r399518;
        double r399520 = 4.16438922228;
        double r399521 = r399520 * r399509;
        double r399522 = r399519 + r399521;
        double r399523 = 110.1139242984811;
        double r399524 = r399522 - r399523;
        double r399525 = 2.0;
        double r399526 = r399509 - r399525;
        double r399527 = r399509 * r399520;
        double r399528 = 78.6994924154;
        double r399529 = r399527 + r399528;
        double r399530 = r399529 * r399509;
        double r399531 = 137.519416416;
        double r399532 = r399530 + r399531;
        double r399533 = r399532 * r399509;
        double r399534 = r399533 + r399516;
        double r399535 = r399534 * r399509;
        double r399536 = z;
        double r399537 = r399535 + r399536;
        double r399538 = r399526 * r399537;
        double r399539 = r399509 * r399509;
        double r399540 = 43.3400022514;
        double r399541 = r399540 * r399540;
        double r399542 = r399539 - r399541;
        double r399543 = r399542 * r399509;
        double r399544 = r399509 - r399540;
        double r399545 = r399543 / r399544;
        double r399546 = 263.505074721;
        double r399547 = r399545 + r399546;
        double r399548 = r399547 * r399509;
        double r399549 = 313.399215894;
        double r399550 = r399548 + r399549;
        double r399551 = r399550 * r399509;
        double r399552 = 47.066876606;
        double r399553 = r399551 + r399552;
        double r399554 = r399538 / r399553;
        double r399555 = r399515 ? r399524 : r399554;
        return r399555;
}

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
Target0.5
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.4405280214511472e+47 or 4.810363435385636e+17 < x

    1. Initial program 58.5

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

    2. Taylor expanded around inf 1.5

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

    if -1.4405280214511472e+47 < x < 4.810363435385636e+17

    1. Initial program 0.7

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

    3. Applied flip-+0.7

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

    4. Applied associate-*l/0.7

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.44052802145114724 \cdot 10^{47} \lor \neg \left(x \le 481036343538563580\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\frac{\left(x \cdot x - 43.3400022514000014 \cdot 43.3400022514000014\right) \cdot x}{x - 43.3400022514000014} + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(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)))