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

Average Error: 26.3 → 1.0

Time: 21.7s

Precision: binary64

Cost: 46536

Math

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

↓

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 4.16438922228) (/ (/ (- 130977.50649958357 y) x) x))
          -110.1139242984811)))
   (if (<= x -2.1e+65)
     t_0
     (if (<= x 1.6e+29)
       (/
        (fma
         x
         (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
         z)
        (/
         (fma
          x
          (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
          47.066876606)
         (+ x -2.0)))
       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 * 4.16438922228) - (((130977.50649958357 - y) / x) / x)) + -110.1139242984811;
	double tmp;
	if (x <= -2.1e+65) {
		tmp = t_0;
	} else if (x <= 1.6e+29) {
		tmp = fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / (fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606) / (x + -2.0));
	} 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(Float64(x * 4.16438922228) - Float64(Float64(Float64(130977.50649958357 - y) / x) / x)) + -110.1139242984811)
	tmp = 0.0
	if (x <= -2.1e+65)
		tmp = t_0;
	elseif (x <= 1.6e+29)
		tmp = Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / Float64(fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606) / Float64(x + -2.0)));
	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[(N[(x * 4.16438922228), $MachinePrecision] - N[(N[(N[(130977.50649958357 - y), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + -110.1139242984811), $MachinePrecision]}, If[LessEqual[x, -2.1e+65], t$95$0, If[LessEqual[x, 1.6e+29], N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision] / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	26.3
Target	0.8
Herbie	1.0

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

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999991e65 or 1.59999999999999993e29 < x

   1. Initial program 60.7

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

   2. Simplified 57.3

      \[\leadsto \color{blue}{\left(x + -2\right) \cdot \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}} \]
      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))): 1 points increase in error, 1 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))): 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) (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, 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) (+.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))): 10 points increase in error, 5 points decrease in error

   3. Taylor expanded in x around -inf 1.5

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{130977.50649958357 + -1 \cdot y}{{x}^{2}} + \left(4.16438922228 \cdot x + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811} \]

   4. Simplified 1.5

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(x, 4.16438922228, \frac{3655.1204654076414}{x}\right) - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811} \]
      Proof
      (+.f64 (-.f64 (fma.f64 x 104109730557/25000000000 (/.f64 2284450290879775841688574159837293/625000000000000000000000000000 x)) (/.f64 (/.f64 (-.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 y) x) x)) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (fma.f64 x 104109730557/25000000000 (/.f64 (Rewrite<= metadata-eval (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 1)) x)) (/.f64 (/.f64 (-.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 y) x) x)) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (fma.f64 x 104109730557/25000000000 (Rewrite<= associate-*r/_binary64 (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)))) (/.f64 (/.f64 (-.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 y) x) x)) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x 104109730557/25000000000) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)))) (/.f64 (/.f64 (-.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 y) x) x)) -13764240537310136880149/125000000000000000000): 1 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 104109730557/25000000000 x)) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (/.f64 (/.f64 (-.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 y) x) x)) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (/.f64 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (neg.f64 y))) x) x)) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (/.f64 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 y))) x) x)) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (*.f64 x x)))) -13764240537310136880149/125000000000000000000): 13 points increase in error, 12 points decrease in error
      (+.f64 (-.f64 (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (Rewrite<= unpow2_binary64 (pow.f64 x 2)))) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (neg.f64 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (pow.f64 x 2))))) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (pow.f64 x 2))))) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (pow.f64 x 2))) (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x))))) -13764240537310136880149/125000000000000000000): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (pow.f64 x 2))) (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)))) (Rewrite<= metadata-eval (neg.f64 13764240537310136880149/125000000000000000000))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 409304707811198655637810418659684985388407301/3125000000000000000000000000000000000000 (*.f64 -1 y)) (pow.f64 x 2))) (+.f64 (*.f64 104109730557/25000000000 x) (*.f64 2284450290879775841688574159837293/625000000000000000000000000000 (/.f64 1 x)))) 13764240537310136880149/125000000000000000000)): 0 points increase in error, 0 points decrease in error

   5. Taylor expanded in x around inf 1.5

      \[\leadsto \left(\color{blue}{4.16438922228 \cdot x} - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811 \]

   6. Simplified 1.5

      \[\leadsto \left(\color{blue}{x \cdot 4.16438922228} - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811 \]
      Proof
      (*.f64 x 104109730557/25000000000): 0 points increase in error, 0 points decrease in error
      (Rewrite=> *-commutative_binary64 (*.f64 104109730557/25000000000 x)): 0 points increase in error, 0 points decrease in error

   if -2.09999999999999991e65 < x < 1.59999999999999993e29

   1. Initial program 1.6

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

   2. Simplified 0.6

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x + -2}}} \]
      Proof
      (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (fma.f64 x 104109730557/25000000000 393497462077/5000000000) 4297481763/31250000) y) z) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.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) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.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) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x)) 4297481763/31250000) y) z) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.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) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x)) y) z) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.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)) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 1 points increase in error, 1 points decrease in error
      (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x)) z) (/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (+.f64 x 216700011257/5000000000) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (/.f64 (fma.f64 x (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 x 216700011257/5000000000)) 263505074721/1000000000)) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (/.f64 (fma.f64 x (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 x 216700011257/5000000000) x)) 263505074721/1000000000) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (/.f64 (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000)) 156699607947/500000000)) 23533438303/500000000) (+.f64 x -2))): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (/.f64 (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x)) 156699607947/500000000) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000)) 23533438303/500000000)) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x)) 23533438303/500000000) (+.f64 x -2))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.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 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000) (+.f64 x (Rewrite<= metadata-eval (neg.f64 2))))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.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 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000) (Rewrite<= sub-neg_binary64 (-.f64 x 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z) (-.f64 x 2)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))): 12 points increase in error, 2 points decrease in error
      (/.f64 (Rewrite<= *-commutative_binary64 (*.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)): 0 points increase in error, 0 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;\left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \end{array} \]

Alternatives

Alternative 1
Error	1.4
Cost	7240

\[\begin{array}{l} t_0 := \frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+262}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x + 43.3400022514\right) \cdot \left(x \cdot x\right)\right)}\right)\\ \end{array} \]

Alternative 2
Error	1.1
Cost	3656

\[\begin{array}{l} t_0 := 47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)\\ t_1 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+18}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right)\right)\right)}{t_0} + \frac{z}{t_0}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	2.1
Cost	2376

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -11000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 80000000000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	2.2
Cost	2120

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -9000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 60000000000:\\ \;\;\;\;\frac{\left(x + -2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	4.5
Cost	1992

\[\begin{array}{l} \mathbf{if}\;x \leq -26000000000:\\ \;\;\;\;\left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{47.066876606 + x \cdot \left(313.399215894 + x \cdot \left(263.505074721 + x \cdot \left(x + 43.3400022514\right)\right)\right)} + 0.0212463641547976 \cdot \left(x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-110.1139242984811 + \left(\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + \frac{\frac{y + -130977.50649958357}{x}}{x}\right)\\ \end{array} \]

Alternative 6
Error	4.9
Cost	1352

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.3:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 + z \cdot -0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	4.8
Cost	1352

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	4.8
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + \frac{z}{47.066876606 + x \cdot 313.399215894}\right)\\ \mathbf{else}:\\ \;\;\;\;-110.1139242984811 + \left(\left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right) + \frac{\frac{y + -130977.50649958357}{x}}{x}\right)\\ \end{array} \]

Alternative 9
Error	5.0
Cost	1224

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;0.0212463641547976 \cdot \left(\left(x + -2\right) \cdot \left(x \cdot y\right) + z \cdot \left(x + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	7.0
Cost	1096

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 0.125:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 11
Error	5.0
Cost	1096

\[\begin{array}{l} t_0 := \left(x \cdot 4.16438922228 - \frac{\frac{130977.50649958357 - y}{x}}{x}\right) + -110.1139242984811\\ \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.42:\\ \;\;\;\;\left(x + -2\right) \cdot \left(0.0212463641547976 \cdot \left(x \cdot y\right) + z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	15.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 2.35:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;-110.1139242984811 + \left(x \cdot 4.16438922228 + \frac{3655.1204654076414}{x}\right)\\ \end{array} \]

Alternative 13
Error	15.1
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 0.0037:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718 + \frac{5.86923874282773}{x}}\\ \end{array} \]

Alternative 14
Error	15.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 0.0037:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 15
Error	15.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 0.0037:\\ \;\;\;\;\frac{x + -2}{\frac{47.066876606}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 16
Error	15.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.0037:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]

Alternative 17
Error	15.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 0.0037:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 18
Error	15.2
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;\frac{x + -2}{0.24013125253755718}\\ \mathbf{elif}\;x \leq 0.0037:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 + -110.1139242984811\\ \end{array} \]

Alternative 19
Error	15.3
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -1.18 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 2:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 20
Error	62.5
Cost	192

\[x \cdot -0.3407596943375357 \]

Alternative 21
Error	35.8
Cost	192

\[x \cdot 4.16438922228 \]

Reproduce

herbie shell --seed 2022329 
(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)))