Average Error: 29.3 → 1.2
Time: 49.6s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -84818411132363805548408619842590998528:\\ \;\;\;\;\left(\left(\frac{t}{\frac{z}{\frac{y}{z}}} + y \cdot 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right) + x\\ \mathbf{elif}\;z \le 6602793195626197349740452721828298752:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.16675412620000074070958362426608800888 + 3.130605476229999961645944495103321969509 \cdot z\right)\right)\right)}{0.6077713877710000378584709324059076607227 + \left(11.94009057210000079862766142468899488449 + z \cdot \left(31.46901157490000144889563671313226222992 + z \cdot \left(15.2346874069999991263557603815570473671 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{t}{\frac{z}{\frac{y}{z}}} + y \cdot 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right) + x\\ \end{array}\]
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 -84818411132363805548408619842590998528:\\
\;\;\;\;\left(\left(\frac{t}{\frac{z}{\frac{y}{z}}} + y \cdot 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right) + x\\

\mathbf{elif}\;z \le 6602793195626197349740452721828298752:\\
\;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.16675412620000074070958362426608800888 + 3.130605476229999961645944495103321969509 \cdot z\right)\right)\right)}{0.6077713877710000378584709324059076607227 + \left(11.94009057210000079862766142468899488449 + z \cdot \left(31.46901157490000144889563671313226222992 + z \cdot \left(15.2346874069999991263557603815570473671 + z\right)\right)\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\frac{t}{\frac{z}{\frac{y}{z}}} + y \cdot 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r19849598 = x;
        double r19849599 = y;
        double r19849600 = z;
        double r19849601 = 3.13060547623;
        double r19849602 = r19849600 * r19849601;
        double r19849603 = 11.1667541262;
        double r19849604 = r19849602 + r19849603;
        double r19849605 = r19849604 * r19849600;
        double r19849606 = t;
        double r19849607 = r19849605 + r19849606;
        double r19849608 = r19849607 * r19849600;
        double r19849609 = a;
        double r19849610 = r19849608 + r19849609;
        double r19849611 = r19849610 * r19849600;
        double r19849612 = b;
        double r19849613 = r19849611 + r19849612;
        double r19849614 = r19849599 * r19849613;
        double r19849615 = 15.234687407;
        double r19849616 = r19849600 + r19849615;
        double r19849617 = r19849616 * r19849600;
        double r19849618 = 31.4690115749;
        double r19849619 = r19849617 + r19849618;
        double r19849620 = r19849619 * r19849600;
        double r19849621 = 11.9400905721;
        double r19849622 = r19849620 + r19849621;
        double r19849623 = r19849622 * r19849600;
        double r19849624 = 0.607771387771;
        double r19849625 = r19849623 + r19849624;
        double r19849626 = r19849614 / r19849625;
        double r19849627 = r19849598 + r19849626;
        return r19849627;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r19849628 = z;
        double r19849629 = -8.481841113236381e+37;
        bool r19849630 = r19849628 <= r19849629;
        double r19849631 = t;
        double r19849632 = y;
        double r19849633 = r19849632 / r19849628;
        double r19849634 = r19849628 / r19849633;
        double r19849635 = r19849631 / r19849634;
        double r19849636 = 3.13060547623;
        double r19849637 = r19849632 * r19849636;
        double r19849638 = r19849635 + r19849637;
        double r19849639 = 36.527041698806414;
        double r19849640 = r19849639 * r19849633;
        double r19849641 = r19849638 - r19849640;
        double r19849642 = x;
        double r19849643 = r19849641 + r19849642;
        double r19849644 = 6.602793195626197e+36;
        bool r19849645 = r19849628 <= r19849644;
        double r19849646 = b;
        double r19849647 = a;
        double r19849648 = 11.1667541262;
        double r19849649 = r19849636 * r19849628;
        double r19849650 = r19849648 + r19849649;
        double r19849651 = r19849628 * r19849650;
        double r19849652 = r19849631 + r19849651;
        double r19849653 = r19849628 * r19849652;
        double r19849654 = r19849647 + r19849653;
        double r19849655 = r19849628 * r19849654;
        double r19849656 = r19849646 + r19849655;
        double r19849657 = 0.607771387771;
        double r19849658 = 11.9400905721;
        double r19849659 = 31.4690115749;
        double r19849660 = 15.234687407;
        double r19849661 = r19849660 + r19849628;
        double r19849662 = r19849628 * r19849661;
        double r19849663 = r19849659 + r19849662;
        double r19849664 = r19849628 * r19849663;
        double r19849665 = r19849658 + r19849664;
        double r19849666 = r19849665 * r19849628;
        double r19849667 = r19849657 + r19849666;
        double r19849668 = r19849656 / r19849667;
        double r19849669 = r19849632 * r19849668;
        double r19849670 = r19849642 + r19849669;
        double r19849671 = r19849645 ? r19849670 : r19849643;
        double r19849672 = r19849630 ? r19849643 : r19849671;
        return r19849672;
}

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

Original29.3
Target1.0
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.481841113236381e+37 or 6.602793195626197e+36 < z

    1. Initial program 59.9

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

    2. Taylor expanded around inf 9.1

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

    3. Simplified1.8

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

    5. Applied associate-/l*1.8

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

    if -8.481841113236381e+37 < z < 6.602793195626197e+36

    1. Initial program 1.4

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

    3. Applied *-un-lft-identity1.4

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right)}}\]

    4. Applied times-frac0.6

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}}\]

    5. Simplified0.6

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -84818411132363805548408619842590998528:\\ \;\;\;\;\left(\left(\frac{t}{\frac{z}{\frac{y}{z}}} + y \cdot 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right) + x\\ \mathbf{elif}\;z \le 6602793195626197349740452721828298752:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.16675412620000074070958362426608800888 + 3.130605476229999961645944495103321969509 \cdot z\right)\right)\right)}{0.6077713877710000378584709324059076607227 + \left(11.94009057210000079862766142468899488449 + z \cdot \left(31.46901157490000144889563671313226222992 + z \cdot \left(15.2346874069999991263557603815570473671 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{t}{\frac{z}{\frac{y}{z}}} + y \cdot 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (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 1.0)))))

  (+ 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))))