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

Average Error: 29.6 → 1.1

Time: 20.7s

Precision: binary64

Cost: 46536

Math

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

↓

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
           (+
            3.13060547623
            (+
             (+ (/ 457.9610022158428 (* z z)) (/ t (* z z)))
             (/ -36.52704169880642 z)))))))
   (if (<= z -4.8e+44)
     t_1
     (if (<= z 6.5e+35)
       (+
        x
        (/
         y
         (/
          (fma
           (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
           z
           0.607771387771)
          (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b))))
       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 * (3.13060547623 + (((457.9610022158428 / (z * z)) + (t / (z * z))) + (-36.52704169880642 / z))));
	double tmp;
	if (z <= -4.8e+44) {
		tmp = t_1;
	} else if (z <= 6.5e+35) {
		tmp = x + (y / (fma(fma(fma((z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b)));
	} 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(3.13060547623 + Float64(Float64(Float64(457.9610022158428 / Float64(z * z)) + Float64(t / Float64(z * z))) + Float64(-36.52704169880642 / z)))))
	tmp = 0.0
	if (z <= -4.8e+44)
		tmp = t_1;
	elseif (z <= 6.5e+35)
		tmp = Float64(x + Float64(y / Float64(fma(fma(fma(Float64(z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b))));
	else
		tmp = 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[(x + N[(y * N[(3.13060547623 + N[(N[(N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+44], t$95$1, If[LessEqual[z, 6.5e+35], N[(x + N[(y / N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	29.6
Target	1.1
Herbie	1.1

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

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000026e44 or 6.5000000000000003e35 < z

   1. Initial program 59.6

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

   2. Simplified 57.7

      \[\leadsto \color{blue}{x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{y}}} \]
      Proof
      (+.f64 x (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t) a) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t)) a) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 1 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z)) t) a) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t)) a)) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z)) a) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a)) b)) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z)) b) (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (/.f64 (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 z 15234687407/1000000000)) 314690115749/10000000000)) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (/.f64 (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 z 15234687407/1000000000) z)) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (/.f64 (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000)) 119400905721/10000000000)) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (/.f64 (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z)) 119400905721/10000000000) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000)) 607771387771/1000000000000)) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)) 607771387771/1000000000000) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) y) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))): 12 points increase in error, 14 points decrease in error
      (+.f64 x (/.f64 (Rewrite<= *-commutative_binary64 (*.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))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around inf 8.9

      \[\leadsto x + \color{blue}{\left(\left(11.1667541262 \cdot \frac{y}{z} + \left(3.13060547623 \cdot y + \left(y \cdot t - \left(15.234687407 \cdot \left(11.1667541262 \cdot y - 47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) \cdot {\left(\frac{1}{z}\right)}^{2}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}\right)} \]

   4. Simplified 8.9

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(\frac{\frac{1}{z}}{z}, y \cdot t - y \cdot -457.9610022158428, y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\right)} \]
      Proof
      (+.f64 (fma.f64 (/.f64 (/.f64 1 z) z) (-.f64 (*.f64 y t) (*.f64 y -45796100221584283915100827016327/100000000000000000000000000000)) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (/.f64 1 z) 1)) z) (-.f64 (*.f64 y t) (*.f64 y -45796100221584283915100827016327/100000000000000000000000000000)) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 1 z) (/.f64 1 z))) (-.f64 (*.f64 y t) (*.f64 y -45796100221584283915100827016327/100000000000000000000000000000)) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 7 points increase in error, 9 points decrease in error
      (+.f64 (fma.f64 (Rewrite<= unpow2_binary64 (pow.f64 (/.f64 1 z) 2)) (-.f64 (*.f64 y t) (*.f64 y -45796100221584283915100827016327/100000000000000000000000000000)) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (*.f64 y (Rewrite<= metadata-eval (+.f64 98517059967927196814627/1000000000000000000000 -55647806218377003596563527016327/100000000000000000000000000000)))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (*.f64 y (+.f64 98517059967927196814627/1000000000000000000000 (Rewrite<= metadata-eval (*.f64 3652704169880641883561/100000000000000000000 -15234687407/1000000000))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (*.f64 y (+.f64 98517059967927196814627/1000000000000000000000 (*.f64 (Rewrite<= metadata-eval (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000)) -15234687407/1000000000)))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 10 points increase in error, 14 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 y 98517059967927196814627/1000000000000000000000) (*.f64 y (*.f64 (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000) -15234687407/1000000000))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 3 points increase in error, 3 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (+.f64 (*.f64 y 98517059967927196814627/1000000000000000000000) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000)) -15234687407/1000000000)))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 3 points increase in error, 1 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (+.f64 (*.f64 y 98517059967927196814627/1000000000000000000000) (*.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))) -15234687407/1000000000))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 6 points increase in error, 5 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (+.f64 (*.f64 y 98517059967927196814627/1000000000000000000000) (Rewrite<= *-commutative_binary64 (*.f64 -15234687407/1000000000 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 -15234687407/1000000000 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (Rewrite=> associate--r+_binary64 (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 -15234687407/1000000000 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 1 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) -15234687407/1000000000))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 (Rewrite=> distribute-rgt-out--_binary64 (*.f64 y (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000))) -15234687407/1000000000)) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 5 points increase in error, 6 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (Rewrite=> associate-*l*_binary64 (*.f64 y (*.f64 (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000) -15234687407/1000000000)))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 1 points increase in error, 3 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 y (*.f64 (Rewrite=> metadata-eval 3652704169880641883561/100000000000000000000) -15234687407/1000000000))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 13 points increase in error, 10 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 y (Rewrite=> metadata-eval -55647806218377003596563527016327/100000000000000000000000000000))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 y (Rewrite<= metadata-eval (*.f64 -3652704169880641883561/100000000000000000000 15234687407/1000000000)))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 y (*.f64 (Rewrite<= metadata-eval (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)) 15234687407/1000000000))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 10 points increase in error, 13 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)) 15234687407/1000000000))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 3 points increase in error, 1 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (*.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) 15234687407/1000000000)) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 6 points increase in error, 5 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (-.f64 (*.f64 y t) (*.f64 98517059967927196814627/1000000000000000000000 y)) (Rewrite<= *-commutative_binary64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (Rewrite=> associate--l-_binary64 (-.f64 (*.f64 y t) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 y) (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)))))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 1 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y)))) (*.f64 y 313060547623/100000000000)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (Rewrite<= *-commutative_binary64 (*.f64 313060547623/100000000000 y))) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (pow.f64 (/.f64 1 z) 2) (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y)))) (*.f64 313060547623/100000000000 y))) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (pow.f64 (/.f64 1 z) 2))) (*.f64 313060547623/100000000000 y)) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 313060547623/100000000000 y) (*.f64 (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (pow.f64 (/.f64 1 z) 2)))) (*.f64 (/.f64 y z) -3652704169880641883561/100000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 313060547623/100000000000 y) (*.f64 (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (pow.f64 (/.f64 1 z) 2))) (*.f64 (/.f64 y z) (Rewrite<= metadata-eval (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 313060547623/100000000000 y) (*.f64 (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (pow.f64 (/.f64 1 z) 2))) (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 313060547623/100000000000 y) (*.f64 (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (pow.f64 (/.f64 1 z) 2))) (*.f64 55833770631/5000000000 (/.f64 y z))) (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)))): 1 points increase in error, 3 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) (*.f64 (-.f64 (*.f64 y t) (+.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (*.f64 98517059967927196814627/1000000000000000000000 y))) (pow.f64 (/.f64 1 z) 2))))) (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z))): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in y around 0 1.4

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

   6. Simplified 1.4

      \[\leadsto x + \color{blue}{y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) - \frac{36.52704169880642}{z}\right)\right)} \]
      Proof
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 3652704169880641883561/100000000000000000000 z)))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1)) (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 3652704169880641883561/100000000000000000000 z)))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (/.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1) (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (/.f64 t (*.f64 z z))) (/.f64 3652704169880641883561/100000000000000000000 z)))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2)))) (/.f64 t (*.f64 z z))) (/.f64 3652704169880641883561/100000000000000000000 z)))): 6 points increase in error, 5 points decrease in error
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (/.f64 3652704169880641883561/100000000000000000000 z)))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= metadata-eval (*.f64 3652704169880641883561/100000000000000000000 1)) z)))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (+.f64 313060547623/100000000000 (-.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (Rewrite<= associate-*r/_binary64 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2)))) (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))))): 0 points increase in error, 1 points decrease in error

   if -4.80000000000000026e44 < z < 6.5000000000000003e35

   1. Initial program 1.7

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

   2. Simplified 0.7

      \[\leadsto \color{blue}{x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]
      Proof
      (+.f64 x (/.f64 y (/.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 z 15234687407/1000000000) z 314690115749/10000000000) z 119400905721/10000000000) z 607771387771/1000000000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 z 313060547623/100000000000 55833770631/5000000000) z t) z a) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000)) z 119400905721/10000000000) z 607771387771/1000000000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 z 313060547623/100000000000 55833770631/5000000000) z t) z a) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000)) z 607771387771/1000000000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 z 313060547623/100000000000 55833770631/5000000000) z t) z a) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 z 313060547623/100000000000 55833770631/5000000000) z t) z a) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (fma.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) z t) z a) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t)) z a) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a)) z b)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (/.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= associate-/l*_binary64 (/.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)))): 18 points increase in error, 16 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 1.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.3
Cost	14088

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_3 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \frac{9.800690647801265 \cdot {z}^{4} + \left(z \cdot z\right) \cdot -124.69639771500472}{z \cdot \left(z \cdot 3.13060547623 + -11.1667541262\right)}\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	1.3
Cost	7112

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_3 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(3.13060547623 \cdot \left(z \cdot z\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	1.3
Cost	6984

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ t_2 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+285}:\\ \;\;\;\;x + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	2.1
Cost	2248

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \mathbf{if}\;z \leq -3100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 115000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	3.5
Cost	1864

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \mathbf{if}\;z \leq -860000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	7.9
Cost	1608

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \mathbf{if}\;z \leq -1.35:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	5.6
Cost	1608

\[\begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\right)\\ \mathbf{if}\;z \leq -3100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.21:\\ \;\;\;\;x + \left(z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) + \left(y \cdot b\right) \cdot -32.324150453290734\right) + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	9.5
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}{b}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \end{array} \]

Alternative 9
Error	9.4
Cost	968

\[\begin{array}{l} t_1 := x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot 11.9400905721}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	9.6
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{3.7269864963038164}{z}}\\ \end{array} \]

Alternative 11
Error	18.3
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-111}:\\ \;\;\;\;x + 0.2683132876901312 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	9.6
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	9.6
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-45}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	18.2
Cost	584

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	27.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+81}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 16
Error	31.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022325 
(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))))