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

Average Error: 29.8 → 0.7

Time: 29.5s

Precision: binary64

Cost: 46536

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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
         (fma
          y
          (+
           (+
            (+ (/ 457.9610022158428 (* z z)) (/ t (* z z)))
            (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
           (+ 3.13060547623 (/ -36.52704169880642 z)))
          x)))
   (if (<= z -7.2e+49)
     t_1
     (if (<= z 2.1e+14)
       (+
        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 = fma(y, ((((457.9610022158428 / (z * z)) + (t / (z * z))) + ((a + (-5864.8025282699045 + (t * -15.234687407))) / pow(z, 3.0))) + (3.13060547623 + (-36.52704169880642 / z))), x);
	double tmp;
	if (z <= -7.2e+49) {
		tmp = t_1;
	} else if (z <= 2.1e+14) {
		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 = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 / Float64(z * z)) + Float64(t / Float64(z * z))) + Float64(Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407))) / (z ^ 3.0))) + Float64(3.13060547623 + Float64(-36.52704169880642 / z))), x)
	tmp = 0.0
	if (z <= -7.2e+49)
		tmp = t_1;
	elseif (z <= 2.1e+14)
		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[(y * N[(N[(N[(N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -7.2e+49], t$95$1, If[LessEqual[z, 2.1e+14], 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	29.8
Target	1.2
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999993e49 or 2.1e14 < z

   1. Initial program 58.8

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

   2. Simplified 56.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      Proof
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t)) a)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a)) b)) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 1 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 z 15234687407/1000000000)) 314690115749/10000000000)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 z 15234687407/1000000000) z)) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000)) 119400905721/10000000000)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000)) 607771387771/1000000000000))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (/.f64 (+.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))) x)): 1 points increase in error, 1 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_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))) x): 16 points increase in error, 8 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.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)))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in z around -inf 0.7

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

   4. Simplified 0.7

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)}, x\right) \]
      Proof
      (+.f64 (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 -586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1)) (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 -586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (/.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1) (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 -586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2)))) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 -586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (/.f64 (+.f64 a (+.f64 -586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 (Rewrite<= metadata-eval (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 -697689271335479999750499226480922330294089/100000000000000000000000000000000000000)) (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000))) (*.f64 t -15234687407/1000000000))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 1 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (Rewrite<= associate-+r+_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000) (*.f64 t -15234687407/1000000000))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (Rewrite<= distribute-rgt-in_binary64 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a)) (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 (Rewrite<= metadata-eval (neg.f64 15234687407/1000000000)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 (neg.f64 15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000)) (*.f64 (neg.f64 15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 (Rewrite=> metadata-eval -15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (Rewrite=> associate-+l+_binary64 (+.f64 a (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (Rewrite<= distribute-neg-out_binary64 (+.f64 (neg.f64 a) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 a)) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)))))) (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (+.f64 313060547623/100000000000 (/.f64 (Rewrite<= metadata-eval (neg.f64 3652704169880641883561/100000000000000000000)) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (+.f64 313060547623/100000000000 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (+.f64 313060547623/100000000000 (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 3652704169880641883561/100000000000000000000 1)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (+.f64 313060547623/100000000000 (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (Rewrite<= sub-neg_binary64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) 313060547623/100000000000) (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))))) (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))): 0 points increase in error, 0 points decrease in error

   if -7.19999999999999993e49 < z < 2.1e14

   1. Initial program 1.4

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

   2. Simplified 0.8

      \[\leadsto \color{blue}{x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]
      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))))): 1 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)))): 15 points increase in error, 10 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.4
Cost	16708

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, y \cdot 3.13060547623 + \frac{y}{z \cdot z} \cdot \left(\left(457.9610022158428 + t\right) + \frac{a - \mathsf{fma}\left(t, 15.234687407, 5864.8025282699045\right)}{z}\right)\right)\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-36.52704169880642}{z} + \left(\frac{t}{z \cdot z} + \left(\frac{457.9610022158428}{z \cdot z} + 3.13060547623\right)\right), x\right)\\ \end{array} \]

Alternative 2
Error	1.3
Cost	14984

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	1.9
Cost	14152

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-36.52704169880642}{z} + \left(\frac{t}{z \cdot z} + \left(\frac{457.9610022158428}{z \cdot z} + 3.13060547623\right)\right), x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, x + \frac{y}{\frac{z \cdot z}{457.9610022158428 + t}}\right)\right)\\ \end{array} \]

Alternative 4
Error	1.9
Cost	7880

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{-36.52704169880642}{z} + \left(\frac{t}{z \cdot z} + \left(\frac{457.9610022158428}{z \cdot z} + 3.13060547623\right)\right), x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	2.8
Cost	6856

\[\begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+56}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]

Alternative 6
Error	2.8
Cost	2632

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	3.9
Cost	1992

\[\begin{array}{l} \mathbf{if}\;z \leq -920:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \frac{\frac{t}{z} \cdot -0.10203362558171805}{z}\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 8
Error	5.4
Cost	1480

\[\begin{array}{l} \mathbf{if}\;z \leq -2400:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \frac{\frac{t}{z} \cdot -0.10203362558171805}{z}\right)}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 + b \cdot -32.324150453290734\right)\right) + \left(x + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9
Error	9.4
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \frac{\frac{t}{z} \cdot -0.10203362558171805}{z}\right)}\\ \mathbf{elif}\;z \leq -3.35 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 23000000000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 10
Error	9.4
Cost	1096

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-100}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 90000000000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	9.4
Cost	844

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-100}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 23000000000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	9.5
Cost	844

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-100}:\\ \;\;\;\;x + z \cdot \left(a \cdot \left(y \cdot 1.6453555072203998\right)\right)\\ \mathbf{elif}\;z \leq 23000000000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	9.4
Cost	844

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-100}:\\ \;\;\;\;x + \left(a \cdot 1.6453555072203998\right) \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 45000000000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	19.5
Cost	716

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -3 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-7}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	9.8
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 80000000000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	9.8
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 80000000000000:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	9.8
Cost	712

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 23000000000000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	28.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+159}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+149}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]

Alternative 19
Error	32.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022330 
(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))))