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

Average Error: 29.7 → 2.1

Time: 34.0s

Precision: binary64

Cost: 52808

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y}{z \cdot z}\\ \mathbf{if}\;z \leq -1.337631693389215 \cdot 10^{+79}:\\ \;\;\;\;3.13060547623 \cdot y + x\\ \mathbf{elif}\;z \leq 51000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(y, 3.13060547623, t \cdot t_1\right) + \left(\left(\frac{y}{z} \cdot 36.52704169880642\right) \cdot \left(-1 - \frac{-15.234687407}{z}\right) + t_1 \cdot -98.5170599679272\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* z z))))
   (if (<= z -1.337631693389215e+79)
     (+ (* 3.13060547623 y) x)
     (if (<= z 51000000000.0)
       (fma
        y
        (/
         (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
         (fma
          z
          (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
          0.607771387771))
        x)
       (+
        x
        (+
         (fma y 3.13060547623 (* t t_1))
         (+
          (* (* (/ y z) 36.52704169880642) (- -1.0 (/ -15.234687407 z)))
          (* t_1 -98.5170599679272))))))))

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 = y / (z * z);
	double tmp;
	if (z <= -1.337631693389215e+79) {
		tmp = (3.13060547623 * y) + x;
	} else if (z <= 51000000000.0) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = x + (fma(y, 3.13060547623, (t * t_1)) + ((((y / z) * 36.52704169880642) * (-1.0 - (-15.234687407 / z))) + (t_1 * -98.5170599679272)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(z * z))
	tmp = 0.0
	if (z <= -1.337631693389215e+79)
		tmp = Float64(Float64(3.13060547623 * y) + x);
	elseif (z <= 51000000000.0)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = Float64(x + Float64(fma(y, 3.13060547623, Float64(t * t_1)) + Float64(Float64(Float64(Float64(y / z) * 36.52704169880642) * Float64(-1.0 - Float64(-15.234687407 / z))) + Float64(t_1 * -98.5170599679272))));
	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[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.337631693389215e+79], N[(N[(3.13060547623 * y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 51000000000.0], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623 + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y / z), $MachinePrecision] * 36.52704169880642), $MachinePrecision] * N[(-1.0 - N[(-15.234687407 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * -98.5170599679272), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	29.7
Target	1.1
Herbie	2.1

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

Derivation

1. Split input into 3 regimes

2. if z < -1.337631693389215e79

   1. Initial program 64.0

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

   2. Simplified 64.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 0 points increase in error, 1 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)): 2 points increase in error, 0 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): 17 points increase in error, 15 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 1.7

      \[\leadsto \color{blue}{3.13060547623 \cdot y + x} \]

   if -1.337631693389215e79 < z < 5.1e10

   1. Initial program 3.4

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

   2. Simplified 1.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 0 points increase in error, 1 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)): 2 points increase in error, 0 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): 17 points increase in error, 15 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

   if 5.1e10 < z

   1. Initial program 56.7

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

   2. Taylor expanded in z around inf 9.4

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

   3. Simplified 3.2

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{z \cdot z} \cdot t\right) + \left(\left(\frac{y}{z} \cdot 36.52704169880642\right) \cdot \left(-1 - \frac{-15.234687407}{z}\right) + \frac{y}{z \cdot z} \cdot -98.5170599679272\right)\right)} \]
      Proof
      (+.f64 (fma.f64 y 313060547623/100000000000 (*.f64 (/.f64 y (*.f64 z z)) t)) (+.f64 (*.f64 (*.f64 (/.f64 y z) 3652704169880641883561/100000000000000000000) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 y 313060547623/100000000000 (*.f64 (/.f64 y (Rewrite<= unpow2_binary64 (pow.f64 z 2))) t)) (+.f64 (*.f64 (*.f64 (/.f64 y z) 3652704169880641883561/100000000000000000000) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 y 313060547623/100000000000 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y t) (pow.f64 z 2)))) (+.f64 (*.f64 (*.f64 (/.f64 y z) 3652704169880641883561/100000000000000000000) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 27 points increase in error, 4 points decrease in error
      (+.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y 313060547623/100000000000) (/.f64 (*.f64 y t) (pow.f64 z 2)))) (+.f64 (*.f64 (*.f64 (/.f64 y z) 3652704169880641883561/100000000000000000000) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 313060547623/100000000000 y)) (/.f64 (*.f64 y t) (pow.f64 z 2))) (+.f64 (*.f64 (*.f64 (/.f64 y z) 3652704169880641883561/100000000000000000000) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (+.f64 (*.f64 (*.f64 (/.f64 y z) 3652704169880641883561/100000000000000000000) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (*.f64 (*.f64 (/.f64 y z) (Rewrite<= metadata-eval (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000))) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 4 points increase in error, 8 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (*.f64 (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 z (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000)))) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 3 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000)) z)) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 1 points increase in error, 3 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (*.f64 (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))) z) (-.f64 -1 (/.f64 -15234687407/1000000000 z))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 5 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (*.f64 (/.f64 -15234687407/1000000000 z) (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -15234687407/1000000000 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))) (*.f64 z z)))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 1 points increase in error, 5 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (/.f64 (*.f64 -15234687407/1000000000 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))) (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (Rewrite<= associate-*r/_binary64 (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))) (*.f64 (/.f64 y (*.f64 z z)) -98517059967927196814627/1000000000000000000000))): 2 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (*.f64 (/.f64 y (Rewrite<= unpow2_binary64 (pow.f64 z 2))) -98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (*.f64 (/.f64 y (pow.f64 z 2)) (Rewrite<= metadata-eval (neg.f64 98517059967927196814627/1000000000000000000000))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 y (pow.f64 z 2)) 98517059967927196814627/1000000000000000000000))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (+.f64 (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 (/.f64 y (pow.f64 z 2))) 98517059967927196814627/1000000000000000000000)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (-.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))) (*.f64 (neg.f64 (/.f64 y (pow.f64 z 2))) 98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z))) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))) (*.f64 (neg.f64 (/.f64 y (pow.f64 z 2))) 98517059967927196814627/1000000000000000000000)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)))) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (*.f64 (neg.f64 (/.f64 y (pow.f64 z 2))) 98517059967927196814627/1000000000000000000000)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (*.f64 (/.f64 y (pow.f64 z 2)) 98517059967927196814627/1000000000000000000000))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (*.f64 -15234687407/1000000000 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (Rewrite<= *-commutative_binary64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -15234687407/1000000000 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))) (pow.f64 z 2)))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 2 points increase in error, 2 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) -15234687407/1000000000)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (*.f64 (Rewrite=> distribute-rgt-out--_binary64 (*.f64 y (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000))) -15234687407/1000000000) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 2 points increase in error, 3 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (Rewrite=> associate-*l*_binary64 (*.f64 y (*.f64 (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000) -15234687407/1000000000))) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 2 points increase in error, 3 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (*.f64 y (*.f64 (Rewrite=> metadata-eval 3652704169880641883561/100000000000000000000) -15234687407/1000000000)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 9 points increase in error, 4 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (*.f64 y (Rewrite=> metadata-eval -55647806218377003596563527016327/100000000000000000000000000000)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (*.f64 y (Rewrite<= metadata-eval (*.f64 -3652704169880641883561/100000000000000000000 15234687407/1000000000))) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (*.f64 y (*.f64 (Rewrite<= metadata-eval (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)) 15234687407/1000000000)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 4 points increase in error, 9 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)) 15234687407/1000000000)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 3 points increase in error, 2 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (*.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) 15234687407/1000000000) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 3 points increase in error, 2 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)))) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (Rewrite<= associate-*r/_binary64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))): 2 points increase in error, 2 points decrease in error
      (Rewrite=> associate--l-_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)) (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))))): 1 points increase in error, 1 points decrease in error
      (-.f64 (Rewrite=> +-commutative_binary64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)) z)))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y))) z))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 (-.f64 (*.f64 -55833770631/5000000000 y) (*.f64 -4769379582500641883561/100000000000000000000 y)))) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (neg.f64 (Rewrite=> distribute-rgt-out--_binary64 (*.f64 y (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000)))) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (Rewrite=> distribute-rgt-neg-in_binary64 (*.f64 y (neg.f64 (-.f64 -55833770631/5000000000 -4769379582500641883561/100000000000000000000)))) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (*.f64 y (neg.f64 (Rewrite=> metadata-eval 3652704169880641883561/100000000000000000000))) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (*.f64 y (Rewrite=> metadata-eval -3652704169880641883561/100000000000000000000)) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (*.f64 y (Rewrite<= metadata-eval (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000))) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (/.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 55833770631/5000000000 y) z) (/.f64 (*.f64 4769379582500641883561/100000000000000000000 y) z)))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (-.f64 (Rewrite<= associate-*r/_binary64 (*.f64 55833770631/5000000000 (/.f64 y z))) (/.f64 (*.f64 4769379582500641883561/100000000000000000000 y) z))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (-.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (Rewrite<= associate-*r/_binary64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z))))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 313060547623/100000000000 y)) (*.f64 55833770631/5000000000 (/.f64 y z))) (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (+.f64 (*.f64 313060547623/100000000000 y) (*.f64 55833770631/5000000000 (/.f64 y z))))) (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (*.f64 313060547623/100000000000 y)))) (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z))) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate--l-_binary64 (-.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (*.f64 313060547623/100000000000 y))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))))): 0 points increase in error, 1 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (*.f64 313060547623/100000000000 y))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.337631693389215 \cdot 10^{+79}:\\ \;\;\;\;3.13060547623 \cdot y + x\\ \mathbf{elif}\;z \leq 51000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(y, 3.13060547623, t \cdot \frac{y}{z \cdot z}\right) + \left(\left(\frac{y}{z} \cdot 36.52704169880642\right) \cdot \left(-1 - \frac{-15.234687407}{z}\right) + \frac{y}{z \cdot z} \cdot -98.5170599679272\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.8
Cost	14984

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\frac{t}{z \cdot z} + \left(\frac{\frac{457.9610022158428}{z}}{z} + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right)\right), x\right)\\ \mathbf{if}\;z \leq -8600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 114000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	1.8
Cost	8648

\[\begin{array}{l} t_1 := \frac{y}{z \cdot z}\\ \mathbf{if}\;z \leq -8600000:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{\frac{457.9610022158428}{z}}{z} + \left(\frac{-36.52704169880642}{z} + \frac{t}{z \cdot z}\right)\right), x\right)\\ \mathbf{elif}\;z \leq 114000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(y, 3.13060547623, t \cdot t_1\right) + \left(\left(\frac{y}{z} \cdot 36.52704169880642\right) \cdot \left(-1 - \frac{-15.234687407}{z}\right) + t_1 \cdot -98.5170599679272\right)\right)\\ \end{array} \]

Alternative 3
Error	1.7
Cost	7880

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, 3.13060547623 + \left(\frac{\frac{457.9610022158428}{z}}{z} + \left(\frac{-36.52704169880642}{z} + \frac{t}{z \cdot z}\right)\right), x\right)\\ \mathbf{if}\;z \leq -8600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 114000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	3.2
Cost	4676

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq 10^{+304}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;3.13060547623 \cdot y + x\\ \end{array} \]

Alternative 5
Error	3.8
Cost	1992

\[\begin{array}{l} t_1 := 3.13060547623 \cdot y + x\\ \mathbf{if}\;z \leq -0.0065:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 114000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	5.4
Cost	1864

\[\begin{array}{l} t_1 := 3.13060547623 \cdot y + x\\ \mathbf{if}\;z \leq -0.0065:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 114000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	6.1
Cost	1480

\[\begin{array}{l} t_1 := 3.13060547623 \cdot y + x\\ \mathbf{if}\;z \leq -0.0065:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 + b \cdot -32.324150453290734\right)\right) + \left(x + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	29.3
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -52341305471380775000:\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{elif}\;y \leq 17002594.337174367:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.691958078162371 \cdot 10^{+52}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;3.13060547623 \cdot y\\ \end{array} \]

Alternative 9
Error	9.4
Cost	712

\[\begin{array}{l} t_1 := 3.13060547623 \cdot y + x\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 114000:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	20.8
Cost	584

\[\begin{array}{l} t_1 := 3.13060547623 \cdot y + x\\ \mathbf{if}\;z \leq 1.8 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	28.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -52341305471380775000:\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{elif}\;y \leq 1.6916352273401425 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;3.13060547623 \cdot y\\ \end{array} \]

Alternative 12
Error	32.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(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))))