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

Average Error: 25.8 → 0.5

Time: 21.4s

Precision: binary64

Cost: 23752

Math

\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

↓

\[\begin{array}{l} t_0 := \frac{x + -2}{0.24013125253755718}\\ t_1 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+72}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x}{\frac{-47.066876606 - x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right)}{-y}} + \left(\frac{\left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right) \cdot {x}^{2}}{t_1} + \frac{z}{t_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (/
  (*
   (- x 2.0)
   (+
    (*
     (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y)
     x)
    z))
  (+
   (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
   47.066876606)))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (+ x -2.0) 0.24013125253755718))
        (t_1
         (+
          47.066876606
          (*
           x
           (+
            313.399215894
            (* x (+ 263.505074721 (* x (+ x 43.3400022514)))))))))
   (if (<= x -8.2e+76)
     t_0
     (if (<= x 1.75e+72)
       (*
        (+ x -2.0)
        (+
         (/
          x
          (/
           (-
            -47.066876606
            (*
             x
             (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)))
           (- y)))
         (+
          (/
           (*
            (+ 137.519416416 (* x (+ 78.6994924154 (* x 4.16438922228))))
            (pow x 2.0))
           t_1)
          (/ z t_1))))
       t_0))))

C

double code(double x, double y, double z) {
	return ((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606);
}

↓

double code(double x, double y, double z) {
	double t_0 = (x + -2.0) / 0.24013125253755718;
	double t_1 = 47.066876606 + (x * (313.399215894 + (x * (263.505074721 + (x * (x + 43.3400022514))))));
	double tmp;
	if (x <= -8.2e+76) {
		tmp = t_0;
	} else if (x <= 1.75e+72) {
		tmp = (x + -2.0) * ((x / ((-47.066876606 - (x * fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894))) / -y)) + ((((137.519416416 + (x * (78.6994924154 + (x * 4.16438922228)))) * pow(x, 2.0)) / t_1) + (z / t_1)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x - 2.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606))
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(x + -2.0) / 0.24013125253755718)
	t_1 = Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * Float64(263.505074721 + Float64(x * Float64(x + 43.3400022514)))))))
	tmp = 0.0
	if (x <= -8.2e+76)
		tmp = t_0;
	elseif (x <= 1.75e+72)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(x / Float64(Float64(-47.066876606 - Float64(x * fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894))) / Float64(-y))) + Float64(Float64(Float64(Float64(137.519416416 + Float64(x * Float64(78.6994924154 + Float64(x * 4.16438922228)))) * (x ^ 2.0)) / t_1) + Float64(z / t_1))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(x + 43.3400022514), $MachinePrecision] * x), $MachinePrecision] + 263.505074721), $MachinePrecision] * x), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + -2.0), $MachinePrecision] / 0.24013125253755718), $MachinePrecision]}, Block[{t$95$1 = N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * N[(263.505074721 + N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+76], t$95$0, If[LessEqual[x, 1.75e+72], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(x / N[(N[(-47.066876606 - N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(137.519416416 + N[(x * N[(78.6994924154 + N[(x * 4.16438922228), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Target

Original	25.8
Target	0.9
Herbie	0.5

\[\begin{array}{l} \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999997e76 or 1.75000000000000005e72 < x

   1. Initial program 64.0

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   2. Simplified 63.6

      \[\leadsto \color{blue}{\frac{x + -2}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x + 43.3400022514, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), x, 137.519416416\right), x, y\right), x, z\right)}}} \]
      Proof
      (/.f64 (+.f64 x -2) (/.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 x 216700011257/5000000000) x 263505074721/1000000000) x 156699607947/500000000) x 23533438303/500000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) x 4297481763/31250000) x y) x z))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 2))) (/.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 x 216700011257/5000000000) x 263505074721/1000000000) x 156699607947/500000000) x 23533438303/500000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) x 4297481763/31250000) x y) x z))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (+.f64 x 216700011257/5000000000) x 263505074721/1000000000) x 156699607947/500000000) x 23533438303/500000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) x 4297481763/31250000) x y) x z))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) x 156699607947/500000000) x 23533438303/500000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) x 4297481763/31250000) x y) x z))): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000)) x 23533438303/500000000) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) x 4297481763/31250000) x y) x z))): 1 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 x 104109730557/25000000000 393497462077/5000000000) x 4297481763/31250000) x y) x z))): 0 points increase in error, 1 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000) (fma.f64 (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000)) x 4297481763/31250000) x y) x z))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000) (fma.f64 (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000)) x y) x z))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000) (fma.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y)) x z))): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)))): 1 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))): 21 points increase in error, 25 points decrease in error

   3. Taylor expanded in x around inf 0.9

      \[\leadsto \frac{x + -2}{\color{blue}{0.24013125253755718}} \]

   if -8.1999999999999997e76 < x < 1.75000000000000005e72

   1. Initial program 3.7

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606} \]

   2. Simplified 1.1

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]
      Proof
      (*.f64 (+.f64 x -2) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 2))) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 2)) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000)) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000)) 4297481763/31250000)) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x)) 4297481763/31250000) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000)) y)) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x)) y) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y)) z)) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x)) z) (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (fma.f64 x (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 x 216700011257/5000000000)) 263505074721/1000000000)) 156699607947/500000000) 23533438303/500000000))): 1 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (fma.f64 x (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 x 216700011257/5000000000) x)) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) 156699607947/500000000)) 23533438303/500000000))): 1 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x)) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000)) 23533438303/500000000)))): 0 points increase in error, 1 points decrease in error
      (*.f64 (-.f64 x 2) (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x)) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))): 11 points increase in error, 4 points decrease in error

   3. Taylor expanded in y around 0 1.1

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(\frac{y \cdot x}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \left(\frac{\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot {x}^{2}}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right)\right)} \]

   4. Applied egg-rr 1.1

      \[\leadsto \left(x + -2\right) \cdot \left(\color{blue}{\left(x \cdot \left(-y\right)\right) \cdot \frac{1}{-\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} + \left(\frac{\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot {x}^{2}}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right)\right) \]

   5. Simplified 0.3

      \[\leadsto \left(x + -2\right) \cdot \left(\color{blue}{\frac{x}{\frac{-47.066876606 - x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right)}{-y}}} + \left(\frac{\left(137.519416416 + \left(78.6994924154 + 4.16438922228 \cdot x\right) \cdot x\right) \cdot {x}^{2}}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606} + \frac{z}{\left(313.399215894 + \left(263.505074721 + x \cdot \left(43.3400022514 + x\right)\right) \cdot x\right) \cdot x + 47.066876606}\right)\right) \]
      Proof
      (/.f64 x (/.f64 (-.f64 -23533438303/500000000 (*.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (Rewrite<= metadata-eval (-.f64 0 23533438303/500000000)) (*.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (*.f64 x (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000)) 156699607947/500000000)))) (neg.f64 y))): 0 points increase in error, 1 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (*.f64 x (+.f64 (*.f64 x (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 x (+.f64 x 216700011257/5000000000)) 263505074721/1000000000))) 156699607947/500000000))) (neg.f64 y))): 1 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (Rewrite<= +-commutative_binary64 (+.f64 216700011257/5000000000 x))) 263505074721/1000000000)) 156699607947/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (*.f64 x (+.f64 (*.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 216700011257/5000000000 x) x)) 263505074721/1000000000)) 156699607947/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (*.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x)) 156699607947/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (*.f64 x (Rewrite<= +-commutative_binary64 (+.f64 156699607947/500000000 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x))))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 (-.f64 0 23533438303/500000000) (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 156699607947/500000000 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x)) x))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 0 (+.f64 23533438303/500000000 (*.f64 (+.f64 156699607947/500000000 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x)) x)))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (+.f64 156699607947/500000000 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x)) x) 23533438303/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 x (+.f64 156699607947/500000000 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x)))) 23533438303/500000000)) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (*.f64 x (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000) x) 156699607947/500000000))) 23533438303/500000000)) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (*.f64 x (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 x (+.f64 (*.f64 (+.f64 216700011257/5000000000 x) x) 263505074721/1000000000))) 156699607947/500000000)) 23533438303/500000000)) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 x (+.f64 216700011257/5000000000 x))) 263505074721/1000000000)) 156699607947/500000000)) 23533438303/500000000)) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (*.f64 x (+.f64 (*.f64 x (+.f64 (*.f64 x (Rewrite=> +-commutative_binary64 (+.f64 x 216700011257/5000000000))) 263505074721/1000000000)) 156699607947/500000000)) 23533438303/500000000)) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (*.f64 x (+.f64 (*.f64 x (Rewrite<= fma-udef_binary64 (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000))) 156699607947/500000000)) 23533438303/500000000)) (neg.f64 y))): 0 points increase in error, 1 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (+.f64 (*.f64 x (Rewrite<= fma-udef_binary64 (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000))) 23533438303/500000000)) (neg.f64 y))): 1 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (-.f64 0 (Rewrite<= fma-udef_binary64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (neg.f64 y))): 1 points increase in error, 0 points decrease in error
      (/.f64 x (/.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))) (neg.f64 y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x (neg.f64 y)) (neg.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000)))): 51 points increase in error, 19 points decrease in error
      (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 x (neg.f64 y)) 1)) (neg.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 (*.f64 x (neg.f64 y)) (/.f64 1 (neg.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000))))): 46 points increase in error, 17 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+72}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x}{\frac{-47.066876606 - x \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right)}{-y}} + \left(\frac{\left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right) \cdot {x}^{2}}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.8
Cost	15560

\[\begin{array}{l} t_0 := \frac{1}{x \cdot x} \cdot \left(y + \frac{z + y \cdot -45.3400022514}{x}\right) + \mathsf{fma}\left(4.16438922228, x, -8.32877844456\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 50000000000000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + \left(43.3400022514 \cdot {x}^{2} + \left(x \cdot 263.505074721 + {x}^{3}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.5
Cost	8904

\[\begin{array}{l} t_0 := \frac{1}{x \cdot x} \cdot \left(y + \frac{z + y \cdot -45.3400022514}{x}\right) + \mathsf{fma}\left(4.16438922228, x, -8.32877844456\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4000000000000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.5
Cost	7880

\[\begin{array}{l} t_0 := \frac{1}{x \cdot x} \cdot \left(y + \frac{z + y \cdot -45.3400022514}{x}\right) + \mathsf{fma}\left(4.16438922228, x, -8.32877844456\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 62000000000000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	1.4
Cost	7752

\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ t_1 := \frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{t_0}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{t_0}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+291}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot 4.16438922228 + z \cdot \left(\frac{x}{t_0} + 2 \cdot \frac{-1}{t_0}\right)\\ \end{array} \]

Alternative 5
Error	1.6
Cost	7240

\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ t_1 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{t_0}\right)\\ t_2 := \frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)\right)}{t_0}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	1.1
Cost	3656

\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ t_1 := \frac{x + -2}{0.24013125253755718}\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+72}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t_0} + \frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + x \cdot 4.16438922228\right)\right)\right)}{t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	2.9
Cost	2120

\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ t_1 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{t_0}\right)\\ \mathbf{if}\;x \leq -2600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	5.3
Cost	1736

\[\begin{array}{l} t_0 := \left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-5}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	15.6
Cost	1488

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot y}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \left(z \cdot 0.0212463641547976 + -0.14147091005106402 \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 10
Error	15.6
Cost	1360

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot y}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 0.85:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 11
Error	14.1
Cost	1356

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-128}:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{elif}\;x \leq 4400:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \left(y \cdot 0.0212463641547976\right) + \left(4.16438922228 + z \cdot 0.0212463641547976\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 12
Error	6.8
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 13
Error	15.6
Cost	1104

\[\begin{array}{l} t_0 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 14
Error	15.6
Cost	1104

\[\begin{array}{l} t_0 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 15
Error	15.6
Cost	1104

\[\begin{array}{l} t_0 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{x + -2}{\frac{\frac{47.066876606}{y}}{x}}\\ \mathbf{elif}\;x \leq 2200:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 16
Error	15.6
Cost	1104

\[\begin{array}{l} t_0 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-27}:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot y}{313.399215894 + \frac{47.066876606}{x}}\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternative 17
Error	15.6
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.85:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 18
Error	15.6
Cost	976

\[\begin{array}{l} t_0 := \frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 19
Error	15.7
Cost	848

\[\begin{array}{l} t_0 := x \cdot 4.16438922228 + -110.1139242984811\\ \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-88}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 1.46 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.82:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 20
Error	15.7
Cost	848

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-27}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 0.46:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 21
Error	15.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-26}:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 22
Error	15.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-88}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 23
Error	15.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1250000000000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 1350:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 24
Error	35.9
Cost	192

\[x \cdot 4.16438922228 \]

Reproduce

herbie shell --seed 2022325 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))