Average Error: 26.8 → 1.0
Time: 19.3s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -5.7633448860088183 \cdot 10^{26} \lor \neg \left(x \le 6.1474264141626379 \cdot 10^{26}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(43.3400022514000014 \cdot {x}^{2} + \left(263.50507472100003 \cdot x + {x}^{3}\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]
\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 -5.7633448860088183 \cdot 10^{26} \lor \neg \left(x \le 6.1474264141626379 \cdot 10^{26}\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(43.3400022514000014 \cdot {x}^{2} + \left(263.50507472100003 \cdot x + {x}^{3}\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}
double f(double x, double y, double z) {
        double r535704 = x;
        double r535705 = 2.0;
        double r535706 = r535704 - r535705;
        double r535707 = 4.16438922228;
        double r535708 = r535704 * r535707;
        double r535709 = 78.6994924154;
        double r535710 = r535708 + r535709;
        double r535711 = r535710 * r535704;
        double r535712 = 137.519416416;
        double r535713 = r535711 + r535712;
        double r535714 = r535713 * r535704;
        double r535715 = y;
        double r535716 = r535714 + r535715;
        double r535717 = r535716 * r535704;
        double r535718 = z;
        double r535719 = r535717 + r535718;
        double r535720 = r535706 * r535719;
        double r535721 = 43.3400022514;
        double r535722 = r535704 + r535721;
        double r535723 = r535722 * r535704;
        double r535724 = 263.505074721;
        double r535725 = r535723 + r535724;
        double r535726 = r535725 * r535704;
        double r535727 = 313.399215894;
        double r535728 = r535726 + r535727;
        double r535729 = r535728 * r535704;
        double r535730 = 47.066876606;
        double r535731 = r535729 + r535730;
        double r535732 = r535720 / r535731;
        return r535732;
}
↓
double f(double x, double y, double z) {
        double r535733 = x;
        double r535734 = -5.763344886008818e+26;
        bool r535735 = r535733 <= r535734;
        double r535736 = 6.147426414162638e+26;
        bool r535737 = r535733 <= r535736;
        double r535738 = !r535737;
        bool r535739 = r535735 || r535738;
        double r535740 = y;
        double r535741 = 2.0;
        double r535742 = pow(r535733, r535741);
        double r535743 = r535740 / r535742;
        double r535744 = 4.16438922228;
        double r535745 = r535744 * r535733;
        double r535746 = r535743 + r535745;
        double r535747 = 110.1139242984811;
        double r535748 = r535746 - r535747;
        double r535749 = 2.0;
        double r535750 = r535733 - r535749;
        double r535751 = r535733 * r535744;
        double r535752 = 78.6994924154;
        double r535753 = r535751 + r535752;
        double r535754 = r535753 * r535733;
        double r535755 = 137.519416416;
        double r535756 = r535754 + r535755;
        double r535757 = r535756 * r535733;
        double r535758 = r535757 + r535740;
        double r535759 = r535758 * r535733;
        double r535760 = z;
        double r535761 = r535759 + r535760;
        double r535762 = r535750 * r535761;
        double r535763 = 43.3400022514;
        double r535764 = r535763 * r535742;
        double r535765 = 263.505074721;
        double r535766 = r535765 * r535733;
        double r535767 = 3.0;
        double r535768 = pow(r535733, r535767);
        double r535769 = r535766 + r535768;
        double r535770 = r535764 + r535769;
        double r535771 = 313.399215894;
        double r535772 = r535770 + r535771;
        double r535773 = r535772 * r535733;
        double r535774 = 47.066876606;
        double r535775 = r535773 + r535774;
        double r535776 = r535762 / r535775;
        double r535777 = r535739 ? r535748 : r535776;
        return r535777;
}

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
Target0.5
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 < -5.763344886008818e+26 or 6.147426414162638e+26 < x

    1. Initial program 57.5

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

    2. Taylor expanded around inf 1.5

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

    if -5.763344886008818e+26 < x < 6.147426414162638e+26

    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. Taylor expanded around 0 0.6

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

    3. Simplified0.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -5.7633448860088183 \cdot 10^{26} \lor \neg \left(x \le 6.1474264141626379 \cdot 10^{26}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(43.3400022514000014 \cdot {x}^{2} + \left(263.50507472100003 \cdot x + {x}^{3}\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 
(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)))