Average Error: 26.9 → 0.7
Time: 6.8s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.6359644172633453 \cdot 10^{37} \lor \neg \left(x \le 1.89433805650411479 \cdot 10^{51}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -3.6359644172633453 \cdot 10^{37} \lor \neg \left(x \le 1.89433805650411479 \cdot 10^{51}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \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(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r391695 = x;
        double r391696 = 2.0;
        double r391697 = r391695 - r391696;
        double r391698 = 4.16438922228;
        double r391699 = r391695 * r391698;
        double r391700 = 78.6994924154;
        double r391701 = r391699 + r391700;
        double r391702 = r391701 * r391695;
        double r391703 = 137.519416416;
        double r391704 = r391702 + r391703;
        double r391705 = r391704 * r391695;
        double r391706 = y;
        double r391707 = r391705 + r391706;
        double r391708 = r391707 * r391695;
        double r391709 = z;
        double r391710 = r391708 + r391709;
        double r391711 = r391697 * r391710;
        double r391712 = 43.3400022514;
        double r391713 = r391695 + r391712;
        double r391714 = r391713 * r391695;
        double r391715 = 263.505074721;
        double r391716 = r391714 + r391715;
        double r391717 = r391716 * r391695;
        double r391718 = 313.399215894;
        double r391719 = r391717 + r391718;
        double r391720 = r391719 * r391695;
        double r391721 = 47.066876606;
        double r391722 = r391720 + r391721;
        double r391723 = r391711 / r391722;
        return r391723;
}
↓
double f(double x, double y, double z) {
        double r391724 = x;
        double r391725 = -3.6359644172633453e+37;
        bool r391726 = r391724 <= r391725;
        double r391727 = 1.8943380565041148e+51;
        bool r391728 = r391724 <= r391727;
        double r391729 = !r391728;
        bool r391730 = r391726 || r391729;
        double r391731 = y;
        double r391732 = 2.0;
        double r391733 = pow(r391724, r391732);
        double r391734 = r391731 / r391733;
        double r391735 = 4.16438922228;
        double r391736 = r391735 * r391724;
        double r391737 = r391734 + r391736;
        double r391738 = 110.1139242984811;
        double r391739 = r391737 - r391738;
        double r391740 = 2.0;
        double r391741 = r391724 - r391740;
        double r391742 = r391724 * r391735;
        double r391743 = 78.6994924154;
        double r391744 = r391742 + r391743;
        double r391745 = r391744 * r391724;
        double r391746 = 137.519416416;
        double r391747 = r391745 + r391746;
        double r391748 = r391747 * r391724;
        double r391749 = r391748 + r391731;
        double r391750 = r391749 * r391724;
        double r391751 = z;
        double r391752 = r391750 + r391751;
        double r391753 = 43.3400022514;
        double r391754 = r391724 + r391753;
        double r391755 = r391754 * r391724;
        double r391756 = 263.505074721;
        double r391757 = r391755 + r391756;
        double r391758 = cbrt(r391757);
        double r391759 = r391758 * r391758;
        double r391760 = r391758 * r391724;
        double r391761 = r391759 * r391760;
        double r391762 = 313.399215894;
        double r391763 = r391761 + r391762;
        double r391764 = r391763 * r391724;
        double r391765 = 47.066876606;
        double r391766 = r391764 + r391765;
        double r391767 = r391752 / r391766;
        double r391768 = r391741 * r391767;
        double r391769 = r391730 ? r391739 : r391768;
        return r391769;
}

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

Original26.9
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.6359644172633453e+37 or 1.8943380565041148e+51 < x

    1. Initial program 61.1

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

    2. Taylor expanded around inf 0.8

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

    if -3.6359644172633453e+37 < x < 1.8943380565041148e+51

    1. Initial program 0.9

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

    3. Applied *-un-lft-identity0.9

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

    4. Applied times-frac0.5

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

    5. Simplified0.5

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

    7. Applied add-cube-cbrt0.6

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

    8. Applied associate-*l*0.6

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.6359644172633453 \cdot 10^{37} \lor \neg \left(x \le 1.89433805650411479 \cdot 10^{51}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot \sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003}\right) \cdot \left(\sqrt[3]{\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003} \cdot x\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 
(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)))