Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D

Average Error: 29.5 → 0.7

Time: 45.5s

Precision: binary64

Cost: 21896

Math

\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

↓

\[\begin{array}{l} t_1 := x + y \cdot \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(3.13060547623 + \left(\frac{t}{{z}^{2}} - 36.52704169880642 \cdot \frac{1}{z}\right)\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(t + 457.9610022158428\right) \cdot -15.234687407\right)}{{z}^{3}}\right)\right)\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1080000000000:\\ \;\;\;\;x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  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))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           y
           (+
            (* 457.9610022158428 (/ 1.0 (pow z 2.0)))
            (+
             (+
              3.13060547623
              (- (/ t (pow z 2.0)) (* 36.52704169880642 (/ 1.0 z))))
             (-
              (/
               (-
                (- a)
                (+
                 1112.0901850848957
                 (* (+ t 457.9610022158428) -15.234687407)))
               (pow z 3.0)))))))))
   (if (<= z -2.15e+36)
     t_1
     (if (<= z 1080000000000.0)
       (+
        x
        (*
         (+
          (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
          b)
         (/
          y
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * ((457.9610022158428 * (1.0 / pow(z, 2.0))) + ((3.13060547623 + ((t / pow(z, 2.0)) - (36.52704169880642 * (1.0 / z)))) + -((-a - (1112.0901850848957 + ((t + 457.9610022158428) * -15.234687407))) / pow(z, 3.0)))));
	double tmp;
	if (z <= -2.15e+36) {
		tmp = t_1;
	} else if (z <= 1080000000000.0) {
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((457.9610022158428d0 * (1.0d0 / (z ** 2.0d0))) + ((3.13060547623d0 + ((t / (z ** 2.0d0)) - (36.52704169880642d0 * (1.0d0 / z)))) + -((-a - (1112.0901850848957d0 + ((t + 457.9610022158428d0) * (-15.234687407d0)))) / (z ** 3.0d0)))))
    if (z <= (-2.15d+36)) then
        tmp = t_1
    else if (z <= 1080000000000.0d0) then
        tmp = x + (((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 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));
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * ((457.9610022158428 * (1.0 / Math.pow(z, 2.0))) + ((3.13060547623 + ((t / Math.pow(z, 2.0)) - (36.52704169880642 * (1.0 / z)))) + -((-a - (1112.0901850848957 + ((t + 457.9610022158428) * -15.234687407))) / Math.pow(z, 3.0)))));
	double tmp;
	if (z <= -2.15e+36) {
		tmp = t_1;
	} else if (z <= 1080000000000.0) {
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return 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))

↓

def code(x, y, z, t, a, b):
	t_1 = x + (y * ((457.9610022158428 * (1.0 / math.pow(z, 2.0))) + ((3.13060547623 + ((t / math.pow(z, 2.0)) - (36.52704169880642 * (1.0 / z)))) + -((-a - (1112.0901850848957 + ((t + 457.9610022158428) * -15.234687407))) / math.pow(z, 3.0)))))
	tmp = 0
	if z <= -2.15e+36:
		tmp = t_1
	elif z <= 1080000000000.0:
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(Float64(457.9610022158428 * Float64(1.0 / (z ^ 2.0))) + Float64(Float64(3.13060547623 + Float64(Float64(t / (z ^ 2.0)) - Float64(36.52704169880642 * Float64(1.0 / z)))) + Float64(-Float64(Float64(Float64(-a) - Float64(1112.0901850848957 + Float64(Float64(t + 457.9610022158428) * -15.234687407))) / (z ^ 3.0)))))))
	tmp = 0.0
	if (z <= -2.15e+36)
		tmp = t_1;
	elseif (z <= 1080000000000.0)
		tmp = Float64(x + Float64(Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * Float64(y / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 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));
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * ((457.9610022158428 * (1.0 / (z ^ 2.0))) + ((3.13060547623 + ((t / (z ^ 2.0)) - (36.52704169880642 * (1.0 / z)))) + -((-a - (1112.0901850848957 + ((t + 457.9610022158428) * -15.234687407))) / (z ^ 3.0)))));
	tmp = 0.0;
	if (z <= -2.15e+36)
		tmp = t_1;
	elseif (z <= 1080000000000.0)
		tmp = x + (((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b) * (y / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(457.9610022158428 * N[(1.0 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(3.13060547623 + N[(N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] - N[(36.52704169880642 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-N[(N[((-a) - N[(1112.0901850848957 + N[(N[(t + 457.9610022158428), $MachinePrecision] * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.15e+36], t$95$1, If[LessEqual[z, 1080000000000.0], N[(x + N[(N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	29.5
Target	1.0
Herbie	0.7

\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000002e36 or 1.08e12 < z

   1. Initial program 58.4

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Simplified 55.6

      \[\leadsto \color{blue}{x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}} \]
      Proof

      [Start] 58.4	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-2 [=>] 58.4	\[ x + \frac{\color{blue}{\left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-49 [=>] 55.6	\[ x + \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} \]
      rational.json-simplify-2 [=>] 55.6	\[ x + y \cdot \frac{\color{blue}{z \cdot \left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right)} + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-2 [=>] 55.6	\[ x + y \cdot \frac{z \cdot \left(\color{blue}{z \cdot \left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right)} + a\right) + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-2 [=>] 55.6	\[ x + y \cdot \frac{z \cdot \left(z \cdot \left(\color{blue}{z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)} + t\right) + a\right) + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   3. Taylor expanded in z around -inf 1.0

      \[\leadsto x + y \cdot \color{blue}{\left(\left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right) - 36.52704169880642 \cdot \frac{1}{z}\right)} \]

   4. Simplified 1.0

      \[\leadsto x + y \cdot \color{blue}{\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(3.13060547623 + \left(\frac{t}{{z}^{2}} - 36.52704169880642 \cdot \frac{1}{z}\right)\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(t + 457.9610022158428\right) \cdot -15.234687407\right)}{{z}^{3}}\right)\right)\right)} \]
      Proof

      [Start] 1.0	\[ x + y \cdot \left(\left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right) - 36.52704169880642 \cdot \frac{1}{z}\right) \]
      rational.json-simplify-48 [=>] 1.0	\[ x + y \cdot \color{blue}{\left(\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right) + \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\right)} \]
      rational.json-simplify-1 [=>] 1.0	\[ x + y \cdot \color{blue}{\left(\left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right) + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right)} \]
      rational.json-simplify-41 [<=] 1.0	\[ x + y \cdot \left(\left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right) + \color{blue}{\left(-1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}} + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right)}\right) \]
      rational.json-simplify-41 [=>] 1.0	\[ x + y \cdot \color{blue}{\left(-1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}} + \left(\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\right)\right)} \]
      rational.json-simplify-1 [=>] 1.0	\[ x + y \cdot \left(-1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}} + \color{blue}{\left(\left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right) + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right)}\right) \]
      rational.json-simplify-41 [=>] 1.0	\[ x + y \cdot \left(-1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}} + \color{blue}{\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\right)\right)}\right) \]
      rational.json-simplify-41 [=>] 1.0	\[ x + y \cdot \color{blue}{\left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(\frac{t}{{z}^{2}} + \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\right) + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)} \]

   if -2.15000000000000002e36 < z < 1.08e12

   1. Initial program 1.0

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Simplified 0.5

      \[\leadsto \color{blue}{x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}} \]
      Proof

      [Start] 1.0	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-49 [=>] 0.5	\[ x + \color{blue}{\left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \frac{y}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}} \]
      rational.json-simplify-2 [=>] 0.5	\[ x + \left(\color{blue}{z \cdot \left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right)} + b\right) \cdot \frac{y}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-2 [=>] 0.5	\[ x + \left(z \cdot \left(\color{blue}{z \cdot \left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right)} + a\right) + b\right) \cdot \frac{y}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      rational.json-simplify-2 [=>] 0.5	\[ x + \left(z \cdot \left(z \cdot \left(\color{blue}{z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)} + t\right) + a\right) + b\right) \cdot \frac{y}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(3.13060547623 + \left(\frac{t}{{z}^{2}} - 36.52704169880642 \cdot \frac{1}{z}\right)\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(t + 457.9610022158428\right) \cdot -15.234687407\right)}{{z}^{3}}\right)\right)\right)\\ \mathbf{elif}\;z \leq 1080000000000:\\ \;\;\;\;x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\left(3.13060547623 + \left(\frac{t}{{z}^{2}} - 36.52704169880642 \cdot \frac{1}{z}\right)\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(t + 457.9610022158428\right) \cdot -15.234687407\right)}{{z}^{3}}\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.2
Cost	14536

\[\begin{array}{l} t_1 := x + y \cdot \left(\left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+52}:\\ \;\;\;\;x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	2.0
Cost	2632

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+54}:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	2.2
Cost	2632

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+55}:\\ \;\;\;\;x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	3.1
Cost	2504

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.82 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1080000000000:\\ \;\;\;\;x + \frac{1}{\frac{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(z \cdot \left(z \cdot 11.1667541262 + t\right) + a\right) + b}}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	3.1
Cost	2376

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1080000000000:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot 11.1667541262 + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	4.1
Cost	2248

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{z \cdot \left(z \cdot 31.4690115749 + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \end{array} \]

Alternative 7
Error	4.1
Cost	1992

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{z \cdot 11.9400905721 + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	4.1
Cost	1736

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot 11.1667541262 + t\right) + a\right) + b}{z \cdot 11.9400905721 + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	4.2
Cost	1480

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{if}\;z \leq -100000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x + \left(z \cdot \left(z \cdot \left(z \cdot 11.1667541262 + t\right) + a\right) + b\right) \cdot \left(1.6453555072203998 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	5.8
Cost	1352

\[\begin{array}{l} \mathbf{if}\;z \leq -11600:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;x + y \cdot \left(\left(1.6453555072203998 \cdot a - 32.324150453290734 \cdot b\right) \cdot z + 1.6453555072203998 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 11
Error	4.3
Cost	1352

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{if}\;z \leq -48000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{\left(z \cdot \left(z \cdot t + a\right) + b\right) \cdot 3.2907110144407996}{\frac{2}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	5.8
Cost	1096

\[\begin{array}{l} \mathbf{if}\;z \leq -12800:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(a \cdot z\right) + y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 13
Error	9.1
Cost	968

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -12800:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;x + y \cdot \left(b \cdot \left(1.6453555072203998 + -32.324150453290734 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	9.1
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -15500:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-18}:\\ \;\;\;\;x + y \cdot \left(b \cdot \left(1.6453555072203998 + -32.324150453290734 \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 15
Error	5.8
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -15000:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - 36.52704169880642 \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-18}:\\ \;\;\;\;x + \left(a \cdot z + b\right) \cdot \left(1.6453555072203998 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 16
Error	9.1
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -10500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 70000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	31.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-249}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	19.0
Cost	584

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	32.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(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 1.0))) (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))))