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

Average Accuracy: 53.4% → 97.3%

Time: 46.4s

Precision: binary64

Cost: 77252

Math

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

↓

\[\begin{array}{l} t_1 := 0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_3 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ t_4 := \frac{y \cdot \left(t_3 + b\right)}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \left(y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right)\right) - \mathsf{fma}\left(47.69379582500642, \frac{y}{z}, \mathsf{fma}\left(15.234687407, \frac{y \cdot t - \mathsf{fma}\left(15.234687407, y \cdot -36.52704169880642, y \cdot 98.5170599679272\right)}{{z}^{3}}, \mathsf{fma}\left(31.4690115749, \frac{y \cdot -36.52704169880642}{{z}^{3}}, \mathsf{fma}\left(37.37971293169846, \frac{y}{{z}^{3}}, \mathsf{fma}\left(15.234687407, \frac{y \cdot -36.52704169880642}{z \cdot z}, \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot t_3}{t_2}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, \frac{y}{\frac{{t_1}^{2}}{\frac{t}{z \cdot z}}}, \frac{y}{t_1}\right)\\ \end{array} \]

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
         (+
          0.31942702700572795
          (+ (/ 3.7269864963038164 z) (/ -3.241970391368047 (* z z)))))
        (t_2
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_3
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a)))
        (t_4 (/ (* y (+ t_3 b)) t_2)))
   (if (<= t_4 (- INFINITY))
     (+
      x
      (-
       (fma
        11.1667541262
        (/ y z)
        (+
         (/ a (/ (pow z 3.0) y))
         (+ (* y 3.13060547623) (/ y (/ (* z z) t)))))
       (fma
        47.69379582500642
        (/ y z)
        (fma
         15.234687407
         (/
          (-
           (* y t)
           (fma 15.234687407 (* y -36.52704169880642) (* y 98.5170599679272)))
          (pow z 3.0))
         (fma
          31.4690115749
          (/ (* y -36.52704169880642) (pow z 3.0))
          (fma
           37.37971293169846
           (/ y (pow z 3.0))
           (fma
            15.234687407
            (/ (* y -36.52704169880642) (* z z))
            (/ (* y 98.5170599679272) (* z z)))))))))
     (if (<= t_4 2e+269)
       (+ x (/ (+ (* y b) (* y t_3)) t_2))
       (+
        x
        (fma
         0.10203362558171805
         (/ y (/ (pow t_1 2.0) (/ t (* z z))))
         (/ y 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 = 0.31942702700572795 + ((3.7269864963038164 / z) + (-3.241970391368047 / (z * z)));
	double t_2 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_3 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	double t_4 = (y * (t_3 + b)) / t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = x + (fma(11.1667541262, (y / z), ((a / (pow(z, 3.0) / y)) + ((y * 3.13060547623) + (y / ((z * z) / t))))) - fma(47.69379582500642, (y / z), fma(15.234687407, (((y * t) - fma(15.234687407, (y * -36.52704169880642), (y * 98.5170599679272))) / pow(z, 3.0)), fma(31.4690115749, ((y * -36.52704169880642) / pow(z, 3.0)), fma(37.37971293169846, (y / pow(z, 3.0)), fma(15.234687407, ((y * -36.52704169880642) / (z * z)), ((y * 98.5170599679272) / (z * z))))))));
	} else if (t_4 <= 2e+269) {
		tmp = x + (((y * b) + (y * t_3)) / t_2);
	} else {
		tmp = x + fma(0.10203362558171805, (y / (pow(t_1, 2.0) / (t / (z * z)))), (y / 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(0.31942702700572795 + Float64(Float64(3.7269864963038164 / z) + Float64(-3.241970391368047 / Float64(z * z))))
	t_2 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_3 = Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a))
	t_4 = Float64(Float64(y * Float64(t_3 + b)) / t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(x + Float64(fma(11.1667541262, Float64(y / z), Float64(Float64(a / Float64((z ^ 3.0) / y)) + Float64(Float64(y * 3.13060547623) + Float64(y / Float64(Float64(z * z) / t))))) - fma(47.69379582500642, Float64(y / z), fma(15.234687407, Float64(Float64(Float64(y * t) - fma(15.234687407, Float64(y * -36.52704169880642), Float64(y * 98.5170599679272))) / (z ^ 3.0)), fma(31.4690115749, Float64(Float64(y * -36.52704169880642) / (z ^ 3.0)), fma(37.37971293169846, Float64(y / (z ^ 3.0)), fma(15.234687407, Float64(Float64(y * -36.52704169880642) / Float64(z * z)), Float64(Float64(y * 98.5170599679272) / Float64(z * z)))))))));
	elseif (t_4 <= 2e+269)
		tmp = Float64(x + Float64(Float64(Float64(y * b) + Float64(y * t_3)) / t_2));
	else
		tmp = Float64(x + fma(0.10203362558171805, Float64(y / Float64((t_1 ^ 2.0) / Float64(t / Float64(z * z)))), Float64(y / t_1)));
	end
	return 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[(0.31942702700572795 + N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(-3.241970391368047 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * N[(t$95$3 + b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(x + N[(N[(11.1667541262 * N[(y / z), $MachinePrecision] + N[(N[(a / N[(N[Power[z, 3.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y / N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(47.69379582500642 * N[(y / z), $MachinePrecision] + N[(15.234687407 * N[(N[(N[(y * t), $MachinePrecision] - N[(15.234687407 * N[(y * -36.52704169880642), $MachinePrecision] + N[(y * 98.5170599679272), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(31.4690115749 * N[(N[(y * -36.52704169880642), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(37.37971293169846 * N[(y / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(15.234687407 * N[(N[(y * -36.52704169880642), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 98.5170599679272), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+269], N[(x + N[(N[(N[(y * b), $MachinePrecision] + N[(y * t$95$3), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.10203362558171805 * N[(y / N[(N[Power[t$95$1, 2.0], $MachinePrecision] / N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	53.4%
Target	98.3%
Herbie	97.3%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < -inf.0

   1. Initial program 0.0%

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

   2. Simplified 57.4%

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

      [Start] 0.0	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      associate-*l/ [<=] 57.4	\[ x + \color{blue}{\frac{y}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)} \]
      *-commutative [=>] 57.4	\[ x + \frac{y}{\color{blue}{z \cdot \left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right)} + 0.607771387771} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      fma-def [=>] 57.4	\[ x + \frac{y}{\color{blue}{\mathsf{fma}\left(z, \left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721, 0.607771387771\right)}} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      *-commutative [=>] 57.4	\[ x + \frac{y}{\mathsf{fma}\left(z, \color{blue}{z \cdot \left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right)} + 11.9400905721, 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      fma-def [=>] 57.4	\[ x + \frac{y}{\mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, \left(z + 15.234687407\right) \cdot z + 31.4690115749, 11.9400905721\right)}, 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      *-commutative [=>] 57.4	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{z \cdot \left(z + 15.234687407\right)} + 31.4690115749, 11.9400905721\right), 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      fma-def [=>] 57.4	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \color{blue}{\mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right)}, 11.9400905721\right), 0.607771387771\right)} \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \]
      *-commutative [=>] 57.4	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \left(\color{blue}{z \cdot \left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right)} + b\right) \]
      fma-def [=>] 57.4	\[ x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \color{blue}{\mathsf{fma}\left(z, \left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a, b\right)} \]

   3. Taylor expanded in z around inf 69.3%

      \[\leadsto x + \color{blue}{\left(\left(11.1667541262 \cdot \frac{y}{z} + \left(\frac{a \cdot y}{{z}^{3}} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right)} \]

   4. Simplified 76.6%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \left(y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right)\right) - \mathsf{fma}\left(47.69379582500642, \frac{y}{z}, \mathsf{fma}\left(15.234687407, \frac{y \cdot t - \mathsf{fma}\left(15.234687407, y \cdot -36.52704169880642, y \cdot 98.5170599679272\right)}{{z}^{3}}, \mathsf{fma}\left(31.4690115749, \frac{y \cdot -36.52704169880642}{{z}^{3}}, \mathsf{fma}\left(37.37971293169846, \frac{y}{{z}^{3}}, \mathsf{fma}\left(15.234687407, \frac{y \cdot -36.52704169880642}{z \cdot z}, \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\right)\right)\right)\right)\right)} \]
      Proof

      [Start] 69.3	\[ x + \left(\left(11.1667541262 \cdot \frac{y}{z} + \left(\frac{a \cdot y}{{z}^{3}} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]
      fma-def [=>] 69.3	\[ x + \left(\color{blue}{\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a \cdot y}{{z}^{3}} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right)} - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]
      associate-/l* [=>] 76.7	\[ x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \color{blue}{\frac{a}{\frac{{z}^{3}}{y}}} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]
      +-commutative [=>] 76.7	\[ x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \color{blue}{\left(3.13060547623 \cdot y + \frac{y \cdot t}{{z}^{2}}\right)}\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]
      *-commutative [=>] 76.7	\[ x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \left(\color{blue}{y \cdot 3.13060547623} + \frac{y \cdot t}{{z}^{2}}\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]
      associate-/l* [=>] 76.6	\[ x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \left(y \cdot 3.13060547623 + \color{blue}{\frac{y}{\frac{{z}^{2}}{t}}}\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]
      unpow2 [=>] 76.6	\[ x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \left(y \cdot 3.13060547623 + \frac{y}{\frac{\color{blue}{z \cdot z}}{t}}\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(15.234687407 \cdot \frac{y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{{z}^{3}} + \left(31.4690115749 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{3}} + \left(37.37971293169846 \cdot \frac{y}{{z}^{3}} + \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)\right)\right)\right)\right) \]

   if -inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < 2.0000000000000001e269

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0 99.7%

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

   if 2.0000000000000001e269 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))

   1. Initial program 2.9%

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

   2. Simplified 5.9%

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

      [Start] 2.9	\[ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
      associate-/l* [=>] 5.9	\[ x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\color{blue}{\mathsf{fma}\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721, z, 0.607771387771\right)}}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749, z, 11.9400905721\right)}, z, 0.607771387771\right)}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right)}, z, 11.9400905721\right), z, 0.607771387771\right)}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\color{blue}{\mathsf{fma}\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a, z, b\right)}}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t, z, a\right)}, z, b\right)}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z \cdot 3.13060547623 + 11.1667541262, z, t\right)}, z, a\right), z, b\right)}} \]
      fma-def [=>] 5.9	\[ x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)}, z, t\right), z, a\right), z, b\right)}} \]

   3. Taylor expanded in z around inf 91.9%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]

   4. Simplified 91.9%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]
      Proof

      [Start] 91.9	\[ x + \frac{y}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]
      associate-*r/ [=>] 91.9	\[ x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]
      metadata-eval [=>] 91.9	\[ x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]
      mul-1-neg [=>] 91.9	\[ x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]
      *-commutative [=>] 91.9	\[ x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]
      unpow2 [=>] 91.9	\[ x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   5. Taylor expanded in t around 0 83.3%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)} \]

   6. Simplified 95.3%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(0.10203362558171805, \frac{y}{\frac{{\left(0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)\right)}^{2}}{\frac{t}{z \cdot z}}}, \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)}\right)} \]
      Proof

      [Start] 83.3	\[ x + \left(\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]
      +-commutative [=>] 83.3	\[ x + \color{blue}{\left(0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}} + \frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}}\right)} \]
      fma-def [=>] 83.3	\[ x + \color{blue}{\mathsf{fma}\left(0.10203362558171805, \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}, \frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}}\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq -\infty:\\ \;\;\;\;x + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \frac{a}{\frac{{z}^{3}}{y}} + \left(y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right)\right) - \mathsf{fma}\left(47.69379582500642, \frac{y}{z}, \mathsf{fma}\left(15.234687407, \frac{y \cdot t - \mathsf{fma}\left(15.234687407, y \cdot -36.52704169880642, y \cdot 98.5170599679272\right)}{{z}^{3}}, \mathsf{fma}\left(31.4690115749, \frac{y \cdot -36.52704169880642}{{z}^{3}}, \mathsf{fma}\left(37.37971293169846, \frac{y}{{z}^{3}}, \mathsf{fma}\left(15.234687407, \frac{y \cdot -36.52704169880642}{z \cdot z}, \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, \frac{y}{\frac{{\left(0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)\right)}^{2}}{\frac{t}{z \cdot z}}}, \frac{y}{0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.0%
Cost	27720

\[\begin{array}{l} t_1 := 0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+15}:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, \frac{y}{\frac{{t_1}^{2}}{\frac{t}{z \cdot z}}}, \frac{y}{t_1}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	97.3%
Cost	19720

\[\begin{array}{l} t_1 := 0.31942702700572795 + \left(\frac{3.7269864963038164}{z} + \frac{-3.241970391368047}{z \cdot z}\right)\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_3 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ t_4 := \frac{y \cdot \left(t_3 + b\right)}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot t_3}{t_2}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, \frac{y}{\frac{{t_1}^{2}}{\frac{t}{z \cdot z}}}, \frac{y}{t_1}\right)\\ \end{array} \]

Alternative 3
Accuracy	97.2%
Cost	17348

\[\begin{array}{l} t_1 := 0.31942702700572795 + \frac{3.7269864963038164}{z}\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_3 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ t_4 := \frac{y \cdot \left(t_3 + b\right)}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot t_3}{t_2}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, \frac{\frac{y}{z}}{t_1} \cdot \frac{\frac{t}{z}}{t_1}, \frac{y}{t_1}\right)\\ \end{array} \]

Alternative 4
Accuracy	97.1%
Cost	12872

\[\begin{array}{l} t_1 := 0.31942702700572795 + \frac{3.7269864963038164}{z}\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_3 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ t_4 := \frac{y \cdot \left(t_3 + b\right)}{t_2}\\ t_5 := \frac{y}{t_1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, 9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right), t_5\right)\\ \mathbf{elif}\;t_4 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot t_3}{t_2}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, \frac{\frac{y}{z}}{t_1} \cdot \frac{\frac{t}{z}}{t_1}, t_5\right)\\ \end{array} \]

Alternative 5
Accuracy	97.0%
Cost	12233

\[\begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ t_3 := \frac{y \cdot \left(t_2 + b\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 2 \cdot 10^{+269}\right):\\ \;\;\;\;x + \mathsf{fma}\left(0.10203362558171805, 9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right), \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot t_2}{t_1}\\ \end{array} \]

Alternative 6
Accuracy	95.2%
Cost	7112

\[\begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ t_3 := \frac{y \cdot \left(t_2 + b\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot z}{t}}\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot t_2}{t_1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t}{z} \cdot \frac{0.10203362558171805}{z}\right)}\\ \end{array} \]

Alternative 7
Accuracy	95.2%
Cost	6984

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot z}{t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t}{z} \cdot \frac{0.10203362558171805}{z}\right)}\\ \end{array} \]

Alternative 8
Accuracy	92.1%
Cost	1865

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+41} \lor \neg \left(z \leq 1.22 \cdot 10^{+32}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t}{z} \cdot \frac{0.10203362558171805}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 9
Accuracy	93.6%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;z \leq -23000000 \lor \neg \left(z \leq 2.75 \cdot 10^{+34}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t}{z} \cdot \frac{0.10203362558171805}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 10
Accuracy	91.0%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -52000000 \lor \neg \left(z \leq 2.75 \cdot 10^{+34}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{t}{z} \cdot \frac{0.10203362558171805}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \end{array} \]

Alternative 11
Accuracy	91.0%
Cost	968

\[\begin{array}{l} \mathbf{if}\;z \leq -23000000:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 12
Accuracy	86.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -255000000 \lor \neg \left(z \leq 4.8\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \]

Alternative 13
Accuracy	86.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-25}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{elif}\;z \leq 900:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 14
Accuracy	71.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -15500000000000 \lor \neg \left(z \leq 5.5 \cdot 10^{-10}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15
Accuracy	50.1%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023147 
(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))))