Average Error: 29.8 → 1.3
Time: 21.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.351770489844849963440765979757572867159 \cdot 10^{56} \lor \neg \left(z \le 128535262688296208\right):\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.351770489844849963440765979757572867159 \cdot 10^{56} \lor \neg \left(z \le 128535262688296208\right):\\
\;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r283089 = x;
        double r283090 = y;
        double r283091 = z;
        double r283092 = 3.13060547623;
        double r283093 = r283091 * r283092;
        double r283094 = 11.1667541262;
        double r283095 = r283093 + r283094;
        double r283096 = r283095 * r283091;
        double r283097 = t;
        double r283098 = r283096 + r283097;
        double r283099 = r283098 * r283091;
        double r283100 = a;
        double r283101 = r283099 + r283100;
        double r283102 = r283101 * r283091;
        double r283103 = b;
        double r283104 = r283102 + r283103;
        double r283105 = r283090 * r283104;
        double r283106 = 15.234687407;
        double r283107 = r283091 + r283106;
        double r283108 = r283107 * r283091;
        double r283109 = 31.4690115749;
        double r283110 = r283108 + r283109;
        double r283111 = r283110 * r283091;
        double r283112 = 11.9400905721;
        double r283113 = r283111 + r283112;
        double r283114 = r283113 * r283091;
        double r283115 = 0.607771387771;
        double r283116 = r283114 + r283115;
        double r283117 = r283105 / r283116;
        double r283118 = r283089 + r283117;
        return r283118;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r283119 = z;
        double r283120 = -3.35177048984485e+56;
        bool r283121 = r283119 <= r283120;
        double r283122 = 1.2853526268829621e+17;
        bool r283123 = r283119 <= r283122;
        double r283124 = !r283123;
        bool r283125 = r283121 || r283124;
        double r283126 = x;
        double r283127 = y;
        double r283128 = r283127 / r283119;
        double r283129 = t;
        double r283130 = r283129 / r283119;
        double r283131 = 36.527041698806414;
        double r283132 = r283130 - r283131;
        double r283133 = r283128 * r283132;
        double r283134 = 3.13060547623;
        double r283135 = r283134 * r283127;
        double r283136 = r283133 + r283135;
        double r283137 = r283126 + r283136;
        double r283138 = 15.234687407;
        double r283139 = r283119 + r283138;
        double r283140 = r283139 * r283119;
        double r283141 = 31.4690115749;
        double r283142 = r283140 + r283141;
        double r283143 = r283142 * r283119;
        double r283144 = 11.9400905721;
        double r283145 = r283143 + r283144;
        double r283146 = r283145 * r283119;
        double r283147 = 0.607771387771;
        double r283148 = r283146 + r283147;
        double r283149 = r283119 * r283134;
        double r283150 = 11.1667541262;
        double r283151 = r283149 + r283150;
        double r283152 = r283151 * r283119;
        double r283153 = r283152 + r283129;
        double r283154 = r283153 * r283119;
        double r283155 = a;
        double r283156 = r283154 + r283155;
        double r283157 = r283156 * r283119;
        double r283158 = b;
        double r283159 = r283157 + r283158;
        double r283160 = r283148 / r283159;
        double r283161 = r283127 / r283160;
        double r283162 = r283126 + r283161;
        double r283163 = r283125 ? r283137 : r283162;
        return r283163;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.8
Target1.0
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.35177048984485e+56 or 1.2853526268829621e+17 < z

    1. Initial program 59.6

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt59.6

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)} + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]

    4. Applied associate-*r*59.6

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \sqrt[3]{z}} + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]

    5. Taylor expanded around inf 8.6

      \[\leadsto x + \color{blue}{\left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)}\]

    6. Simplified1.9

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)}\]

    if -3.35177048984485e+56 < z < 1.2853526268829621e+17

    1. Initial program 1.8

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
    2. Using strategy rm

    3. Applied associate-/l*0.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.351770489844849963440765979757572867159 \cdot 10^{56} \lor \neg \left(z \le 128535262688296208\right):\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(\frac{t}{z} - 36.52704169880641416057187598198652267456\right) + 3.130605476229999961645944495103321969509 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))