Average Error: 26.8 → 0.6
Time: 12.8s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.37322170457412272 \cdot 10^{60} \lor \neg \left(x \le 4.54262428893722098 \cdot 10^{64}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001} \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\\ \end{array}\]
\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 -4.37322170457412272 \cdot 10^{60} \lor \neg \left(x \le 4.54262428893722098 \cdot 10^{64}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\frac{x - 2}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001} \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)\\

\end{array}
double f(double x, double y, double z) {
        double r283534 = x;
        double r283535 = 2.0;
        double r283536 = r283534 - r283535;
        double r283537 = 4.16438922228;
        double r283538 = r283534 * r283537;
        double r283539 = 78.6994924154;
        double r283540 = r283538 + r283539;
        double r283541 = r283540 * r283534;
        double r283542 = 137.519416416;
        double r283543 = r283541 + r283542;
        double r283544 = r283543 * r283534;
        double r283545 = y;
        double r283546 = r283544 + r283545;
        double r283547 = r283546 * r283534;
        double r283548 = z;
        double r283549 = r283547 + r283548;
        double r283550 = r283536 * r283549;
        double r283551 = 43.3400022514;
        double r283552 = r283534 + r283551;
        double r283553 = r283552 * r283534;
        double r283554 = 263.505074721;
        double r283555 = r283553 + r283554;
        double r283556 = r283555 * r283534;
        double r283557 = 313.399215894;
        double r283558 = r283556 + r283557;
        double r283559 = r283558 * r283534;
        double r283560 = 47.066876606;
        double r283561 = r283559 + r283560;
        double r283562 = r283550 / r283561;
        return r283562;
}
↓
double f(double x, double y, double z) {
        double r283563 = x;
        double r283564 = -4.373221704574123e+60;
        bool r283565 = r283563 <= r283564;
        double r283566 = 4.542624288937221e+64;
        bool r283567 = r283563 <= r283566;
        double r283568 = !r283567;
        bool r283569 = r283565 || r283568;
        double r283570 = y;
        double r283571 = 2.0;
        double r283572 = pow(r283563, r283571);
        double r283573 = r283570 / r283572;
        double r283574 = 4.16438922228;
        double r283575 = r283574 * r283563;
        double r283576 = r283573 + r283575;
        double r283577 = 110.1139242984811;
        double r283578 = r283576 - r283577;
        double r283579 = 2.0;
        double r283580 = r283563 - r283579;
        double r283581 = 43.3400022514;
        double r283582 = r283563 + r283581;
        double r283583 = r283582 * r283563;
        double r283584 = 263.505074721;
        double r283585 = r283583 + r283584;
        double r283586 = r283585 * r283563;
        double r283587 = 313.399215894;
        double r283588 = r283586 + r283587;
        double r283589 = r283588 * r283563;
        double r283590 = 47.066876606;
        double r283591 = r283589 + r283590;
        double r283592 = r283580 / r283591;
        double r283593 = r283563 * r283574;
        double r283594 = 78.6994924154;
        double r283595 = r283593 + r283594;
        double r283596 = r283595 * r283563;
        double r283597 = 137.519416416;
        double r283598 = r283596 + r283597;
        double r283599 = r283598 * r283563;
        double r283600 = r283599 + r283570;
        double r283601 = r283600 * r283563;
        double r283602 = z;
        double r283603 = r283601 + r283602;
        double r283604 = r283592 * r283603;
        double r283605 = r283569 ? r283578 : r283604;
        return r283605;
}

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

Original26.8
Target0.4
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 < -4.373221704574123e+60 or 4.542624288937221e+64 < x

    1. Initial program 63.9

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

    2. Taylor expanded around inf 0.2

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

    if -4.373221704574123e+60 < x < 4.542624288937221e+64

    1. Initial program 1.9

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    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 associate-/r/0.9

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.37322170457412272 \cdot 10^{60} \lor \neg \left(x \le 4.54262428893722098 \cdot 10^{64}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001} \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))