Average Error: 29.2 → 1.6
Time: 25.5s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2552320556936620790683030666608640 \lor \neg \left(z \le 871.6899146722846580814803019165992736816\right):\\ \;\;\;\;\left(y \cdot 3.130605476229999961645944495103321969509 + \left(\frac{t}{z} \cdot \frac{y}{z} - \frac{36.52704169880641416057187598198652267456 \cdot y}{z}\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{b + \left(z \cdot a + \left(z \cdot z\right) \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right)}{\left(\left(\left(15.2346874069999991263557603815570473671 + z\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\ \end{array}\]
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 -2552320556936620790683030666608640 \lor \neg \left(z \le 871.6899146722846580814803019165992736816\right):\\
\;\;\;\;\left(y \cdot 3.130605476229999961645944495103321969509 + \left(\frac{t}{z} \cdot \frac{y}{z} - \frac{36.52704169880641416057187598198652267456 \cdot y}{z}\right)\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r294559 = x;
        double r294560 = y;
        double r294561 = z;
        double r294562 = 3.13060547623;
        double r294563 = r294561 * r294562;
        double r294564 = 11.1667541262;
        double r294565 = r294563 + r294564;
        double r294566 = r294565 * r294561;
        double r294567 = t;
        double r294568 = r294566 + r294567;
        double r294569 = r294568 * r294561;
        double r294570 = a;
        double r294571 = r294569 + r294570;
        double r294572 = r294571 * r294561;
        double r294573 = b;
        double r294574 = r294572 + r294573;
        double r294575 = r294560 * r294574;
        double r294576 = 15.234687407;
        double r294577 = r294561 + r294576;
        double r294578 = r294577 * r294561;
        double r294579 = 31.4690115749;
        double r294580 = r294578 + r294579;
        double r294581 = r294580 * r294561;
        double r294582 = 11.9400905721;
        double r294583 = r294581 + r294582;
        double r294584 = r294583 * r294561;
        double r294585 = 0.607771387771;
        double r294586 = r294584 + r294585;
        double r294587 = r294575 / r294586;
        double r294588 = r294559 + r294587;
        return r294588;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r294589 = z;
        double r294590 = -2.5523205569366208e+33;
        bool r294591 = r294589 <= r294590;
        double r294592 = 871.6899146722847;
        bool r294593 = r294589 <= r294592;
        double r294594 = !r294593;
        bool r294595 = r294591 || r294594;
        double r294596 = y;
        double r294597 = 3.13060547623;
        double r294598 = r294596 * r294597;
        double r294599 = t;
        double r294600 = r294599 / r294589;
        double r294601 = r294596 / r294589;
        double r294602 = r294600 * r294601;
        double r294603 = 36.527041698806414;
        double r294604 = r294603 * r294596;
        double r294605 = r294604 / r294589;
        double r294606 = r294602 - r294605;
        double r294607 = r294598 + r294606;
        double r294608 = x;
        double r294609 = r294607 + r294608;
        double r294610 = b;
        double r294611 = a;
        double r294612 = r294589 * r294611;
        double r294613 = r294589 * r294589;
        double r294614 = r294597 * r294589;
        double r294615 = 11.1667541262;
        double r294616 = r294614 + r294615;
        double r294617 = r294589 * r294616;
        double r294618 = r294599 + r294617;
        double r294619 = r294613 * r294618;
        double r294620 = r294612 + r294619;
        double r294621 = r294610 + r294620;
        double r294622 = 15.234687407;
        double r294623 = r294622 + r294589;
        double r294624 = r294623 * r294589;
        double r294625 = 31.4690115749;
        double r294626 = r294624 + r294625;
        double r294627 = r294626 * r294589;
        double r294628 = 11.9400905721;
        double r294629 = r294627 + r294628;
        double r294630 = r294629 * r294589;
        double r294631 = 0.607771387771;
        double r294632 = r294630 + r294631;
        double r294633 = r294621 / r294632;
        double r294634 = r294633 * r294596;
        double r294635 = r294608 + r294634;
        double r294636 = r294595 ? r294609 : r294635;
        return r294636;
}

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

Original29.2
Target0.9
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.5523205569366208e+33 or 871.6899146722847 < z

    1. Initial program 57.1

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

    2. Simplified54.0

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

    3. Taylor expanded around inf 8.7

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

    4. Simplified2.5

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

    if -2.5523205569366208e+33 < z < 871.6899146722847

    1. Initial program 0.7

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

    2. Simplified0.3

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

    4. Applied distribute-lft-in0.3

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

    5. Simplified0.7

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2552320556936620790683030666608640 \lor \neg \left(z \le 871.6899146722846580814803019165992736816\right):\\ \;\;\;\;\left(y \cdot 3.130605476229999961645944495103321969509 + \left(\frac{t}{z} \cdot \frac{y}{z} - \frac{36.52704169880641416057187598198652267456 \cdot y}{z}\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{b + \left(z \cdot a + \left(z \cdot z\right) \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right)}{\left(\left(\left(15.2346874069999991263557603815570473671 + z\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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))))