Average Error: 26.5 → 1.0
Time: 7.6s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\left(\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)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r489514 = x;
        double r489515 = 2.0;
        double r489516 = r489514 - r489515;
        double r489517 = 4.16438922228;
        double r489518 = r489514 * r489517;
        double r489519 = 78.6994924154;
        double r489520 = r489518 + r489519;
        double r489521 = r489520 * r489514;
        double r489522 = 137.519416416;
        double r489523 = r489521 + r489522;
        double r489524 = r489523 * r489514;
        double r489525 = y;
        double r489526 = r489524 + r489525;
        double r489527 = r489526 * r489514;
        double r489528 = z;
        double r489529 = r489527 + r489528;
        double r489530 = r489516 * r489529;
        double r489531 = 43.3400022514;
        double r489532 = r489514 + r489531;
        double r489533 = r489532 * r489514;
        double r489534 = 263.505074721;
        double r489535 = r489533 + r489534;
        double r489536 = r489535 * r489514;
        double r489537 = 313.399215894;
        double r489538 = r489536 + r489537;
        double r489539 = r489538 * r489514;
        double r489540 = 47.066876606;
        double r489541 = r489539 + r489540;
        double r489542 = r489530 / r489541;
        return r489542;
}
↓
double f(double x, double y, double z) {
        double r489543 = x;
        double r489544 = -6.759357258045804e+26;
        bool r489545 = r489543 <= r489544;
        double r489546 = 2.3371063637595438e+32;
        bool r489547 = r489543 <= r489546;
        double r489548 = !r489547;
        bool r489549 = r489545 || r489548;
        double r489550 = y;
        double r489551 = 2.0;
        double r489552 = pow(r489543, r489551);
        double r489553 = r489550 / r489552;
        double r489554 = 4.16438922228;
        double r489555 = r489554 * r489543;
        double r489556 = r489553 + r489555;
        double r489557 = 110.1139242984811;
        double r489558 = r489556 - r489557;
        double r489559 = 2.0;
        double r489560 = r489543 - r489559;
        double r489561 = r489543 * r489554;
        double r489562 = 78.6994924154;
        double r489563 = r489561 + r489562;
        double r489564 = r489563 * r489543;
        double r489565 = 137.519416416;
        double r489566 = r489564 + r489565;
        double r489567 = r489566 * r489543;
        double r489568 = r489567 + r489550;
        double r489569 = r489568 * r489543;
        double r489570 = z;
        double r489571 = r489569 + r489570;
        double r489572 = r489560 * r489571;
        double r489573 = 1.0;
        double r489574 = 43.3400022514;
        double r489575 = r489543 + r489574;
        double r489576 = r489575 * r489543;
        double r489577 = 263.505074721;
        double r489578 = r489576 + r489577;
        double r489579 = r489578 * r489543;
        double r489580 = 313.399215894;
        double r489581 = r489579 + r489580;
        double r489582 = r489581 * r489543;
        double r489583 = 47.066876606;
        double r489584 = r489582 + r489583;
        double r489585 = r489573 / r489584;
        double r489586 = r489572 * r489585;
        double r489587 = r489549 ? r489558 : r489586;
        return r489587;
}

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

Original26.5
Target0.4
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 < -6.759357258045804e+26 or 2.3371063637595438e+32 < 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 1.0

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

    if -6.759357258045804e+26 < x < 2.3371063637595438e+32

    1. Initial program 0.6

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

    3. Applied div-inv0.9

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.75935725804580378 \cdot 10^{26} \lor \neg \left(x \le 2.33710636375954375 \cdot 10^{32}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\right) \cdot \frac{1}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))