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

Percentage Accurate: 58.3% → 97.9%

Time: 12.9s

Alternatives: 14

Speedup: 11.3×

Specification

Math

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

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))))

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));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

public static 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));
}

Python

def code(x, y, z, t, a, 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))

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 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));
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]

Initial Program: 58.3% accurate, 1.0× speedup

Math

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

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))))

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));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

public static 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));
}

Python

def code(x, y, z, t, a, 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))

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 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));
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]

Alternative 1: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y}{z}}{z}\\ \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right)\right) - \mathsf{fma}\left(-556.47806218377, t\_1, \mathsf{fma}\left(t\_1, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ y z) z)))
   (if (<=
        (/
         (*
          (+
           b
           (* (+ a (* (+ t (* (+ 11.1667541262 (* 3.13060547623 z)) z)) z)) z))
          y)
         (+
          0.607771387771
          (*
           (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
           z)))
        INFINITY)
     (+
      (/
       y
       (/
        (fma
         (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
         z
         0.607771387771)
        (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)))
      x)
     (+
      (-
       (fma (/ t z) (/ y z) (fma (/ y z) 11.1667541262 (* 3.13060547623 y)))
       (fma
        -556.47806218377
        t_1
        (fma t_1 98.5170599679272 (* 47.69379582500642 (/ y z)))))
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y / z) / z;
	double tmp;
	if ((((b + ((a + ((t + ((11.1667541262 + (3.13060547623 * z)) * z)) * z)) * z)) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) <= ((double) INFINITY)) {
		tmp = (y / (fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b))) + x;
	} else {
		tmp = (fma((t / z), (y / z), fma((y / z), 11.1667541262, (3.13060547623 * y))) - fma(-556.47806218377, t_1, fma(t_1, 98.5170599679272, (47.69379582500642 * (y / z))))) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y / z) / z)
	tmp = 0.0
	if (Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(11.1667541262 + Float64(3.13060547623 * z)) * z)) * z)) * z)) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) <= Inf)
		tmp = Float64(Float64(y / Float64(fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b))) + x);
	else
		tmp = Float64(Float64(fma(Float64(t / z), Float64(y / z), fma(Float64(y / z), 11.1667541262, Float64(3.13060547623 * y))) - fma(-556.47806218377, t_1, fma(t_1, 98.5170599679272, Float64(47.69379582500642 * Float64(y / z))))) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(11.1667541262 + N[(3.13060547623 * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y / N[(N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(N[(t / z), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * 11.1667541262 + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-556.47806218377 * t$95$1 + N[(t$95$1 * 98.5170599679272 + N[(47.69379582500642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 92.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      4. clear-num N/A

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      5. un-div-inv N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      7. lower-/.f64 96.8

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

   4. Applied rewrites 96.8%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto x + \frac{\color{blue}{t \cdot \left(y \cdot {z}^{2}\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \frac{\color{blue}{\left(y \cdot {z}^{2}\right) \cdot t}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left(y \cdot {z}^{2}\right) \cdot t}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. *-commutative N/A

         \[\leadsto x + \frac{\color{blue}{\left({z}^{2} \cdot y\right)} \cdot t}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. lower-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\left({z}^{2} \cdot y\right)} \cdot t}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. unpow2 N/A

         \[\leadsto x + \frac{\left(\color{blue}{\left(z \cdot z\right)} \cdot y\right) \cdot t}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. lower-*.f64 12.8

         \[\leadsto x + \frac{\left(\color{blue}{\left(z \cdot z\right)} \cdot y\right) \cdot t}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Applied rewrites 12.8%

      \[\leadsto x + \frac{\color{blue}{\left(\left(z \cdot z\right) \cdot y\right) \cdot t}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{\left(\left(z \cdot z\right) \cdot y\right) \cdot t}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(\left(z \cdot z\right) \cdot y\right) \cdot t}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

      3. lower-+.f64 12.8

         \[\leadsto \color{blue}{\frac{\left(\left(z \cdot z\right) \cdot y\right) \cdot t}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} + x} \]

   7. Applied rewrites 12.8%

      \[\leadsto \color{blue}{\frac{\left(\left(z \cdot z\right) \cdot y\right) \cdot t}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} + x} \]

   8. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{t \cdot y}{{z}^{2}}\right)\right) - \left(\frac{15234687407}{1000000000} \cdot \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{{z}^{2}} + \left(\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z} + \frac{98517059967927196814627}{1000000000000000000000} \cdot \frac{y}{{z}^{2}}\right)\right)\right)} + x \]

   10. Applied rewrites 98.8%

       \[\leadsto \color{blue}{\left(\mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right)\right) - \mathsf{fma}\left(-556.47806218377, \frac{\frac{y}{z}}{z}, \mathsf{fma}\left(\frac{\frac{y}{z}}{z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right)\right) - \mathsf{fma}\left(-556.47806218377, \frac{\frac{y}{z}}{z}, \mathsf{fma}\left(\frac{\frac{y}{z}}{z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\left(1.6453555072203998 \cdot y\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           (+
            b
            (*
             (+ a (* (+ t (* (+ 11.1667541262 (* 3.13060547623 z)) z)) z))
             z))
           y)
          (+
           0.607771387771
           (*
            (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
            z)))))
   (if (<= t_1 -1e+69)
     (* (* b y) 1.6453555072203998)
     (if (<= t_1 5e+75)
       (fma 3.13060547623 y x)
       (if (<= t_1 INFINITY)
         (* (* 1.6453555072203998 y) b)
         (fma 3.13060547623 y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((b + ((a + ((t + ((11.1667541262 + (3.13060547623 * z)) * z)) * z)) * z)) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z));
	double tmp;
	if (t_1 <= -1e+69) {
		tmp = (b * y) * 1.6453555072203998;
	} else if (t_1 <= 5e+75) {
		tmp = fma(3.13060547623, y, x);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (1.6453555072203998 * y) * b;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(11.1667541262 + Float64(3.13060547623 * z)) * z)) * z)) * z)) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z)))
	tmp = 0.0
	if (t_1 <= -1e+69)
		tmp = Float64(Float64(b * y) * 1.6453555072203998);
	elseif (t_1 <= 5e+75)
		tmp = fma(3.13060547623, y, x);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(1.6453555072203998 * y) * b);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(11.1667541262 + N[(3.13060547623 * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+69], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision], If[LessEqual[t$95$1, 5e+75], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(1.6453555072203998 * y), $MachinePrecision] * b), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < -1.0000000000000001e69

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \cdot y} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \cdot y \]

      4. +-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) + \frac{607771387771}{1000000000000}}} \cdot y \]

      5. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot z} + \frac{607771387771}{1000000000000}} \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right), z, \frac{607771387771}{1000000000000}\right)}} \cdot y \]

      7. +-commutative N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      8. *-commutative N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z} + \frac{119400905721}{10000000000}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right), z, \frac{119400905721}{10000000000}\right)}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      10. +-commutative N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{15234687407}{1000000000} + z\right) + \frac{314690115749}{10000000000}}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      11. *-commutative N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{15234687407}{1000000000} + z\right) \cdot z} + \frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{15234687407}{1000000000} + z, z, \frac{314690115749}{10000000000}\right)}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      13. lower-+.f64 53.9

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{15.234687407 + z}, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y \]

   5. Applied rewrites 53.9%

      \[\leadsto \color{blue}{\frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 51.0%

      \[\leadsto 1.6453555072203998 \cdot \color{blue}{\left(b \cdot y\right)} \]

   if -1.0000000000000001e69 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 5.0000000000000002e75 or +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 49.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 83.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 83.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if 5.0000000000000002e75 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 87.6%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \cdot y} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \cdot y \]

      4. +-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) + \frac{607771387771}{1000000000000}}} \cdot y \]

      5. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot z} + \frac{607771387771}{1000000000000}} \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right), z, \frac{607771387771}{1000000000000}\right)}} \cdot y \]

      7. +-commutative N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      8. *-commutative N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z} + \frac{119400905721}{10000000000}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right), z, \frac{119400905721}{10000000000}\right)}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      10. +-commutative N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{15234687407}{1000000000} + z\right) + \frac{314690115749}{10000000000}}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      11. *-commutative N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{15234687407}{1000000000} + z\right) \cdot z} + \frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{15234687407}{1000000000} + z, z, \frac{314690115749}{10000000000}\right)}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      13. lower-+.f64 54.4

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{15.234687407 + z}, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y \]

   5. Applied rewrites 54.4%

      \[\leadsto \color{blue}{\frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y} \]
   6. Step-by-step derivation

   7. Applied rewrites 54.6%

      \[\leadsto \frac{b \cdot y}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]
   9. Step-by-step derivation

   10. Applied rewrites 48.6%

       \[\leadsto 1.6453555072203998 \cdot \color{blue}{\left(b \cdot y\right)} \]
   11. Step-by-step derivation

   12. Applied rewrites 48.7%

       \[\leadsto \color{blue}{\left(1.6453555072203998 \cdot y\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\left(1.6453555072203998 \cdot y\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot y\right) \cdot 1.6453555072203998\\ t_2 := \frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* b y) 1.6453555072203998))
        (t_2
         (/
          (*
           (+
            b
            (*
             (+ a (* (+ t (* (+ 11.1667541262 (* 3.13060547623 z)) z)) z))
             z))
           y)
          (+
           0.607771387771
           (*
            (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
            z)))))
   (if (<= t_2 -1e+69)
     t_1
     (if (<= t_2 5e+75)
       (fma 3.13060547623 y x)
       (if (<= t_2 INFINITY) t_1 (fma 3.13060547623 y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * y) * 1.6453555072203998;
	double t_2 = ((b + ((a + ((t + ((11.1667541262 + (3.13060547623 * z)) * z)) * z)) * z)) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z));
	double tmp;
	if (t_2 <= -1e+69) {
		tmp = t_1;
	} else if (t_2 <= 5e+75) {
		tmp = fma(3.13060547623, y, x);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * y) * 1.6453555072203998)
	t_2 = Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(11.1667541262 + Float64(3.13060547623 * z)) * z)) * z)) * z)) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z)))
	tmp = 0.0
	if (t_2 <= -1e+69)
		tmp = t_1;
	elseif (t_2 <= 5e+75)
		tmp = fma(3.13060547623, y, x);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(11.1667541262 + N[(3.13060547623 * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+69], t$95$1, If[LessEqual[t$95$2, 5e+75], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(3.13060547623 * y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < -1.0000000000000001e69 or 5.0000000000000002e75 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 85.2%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \cdot y} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \cdot y} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \cdot y \]

      4. +-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) + \frac{607771387771}{1000000000000}}} \cdot y \]

      5. *-commutative N/A

         \[\leadsto \frac{b}{\color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot z} + \frac{607771387771}{1000000000000}} \cdot y \]

      6. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\color{blue}{\mathsf{fma}\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right), z, \frac{607771387771}{1000000000000}\right)}} \cdot y \]

      7. +-commutative N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      8. *-commutative N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z} + \frac{119400905721}{10000000000}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{b}{\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right), z, \frac{119400905721}{10000000000}\right)}, z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      10. +-commutative N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{z \cdot \left(\frac{15234687407}{1000000000} + z\right) + \frac{314690115749}{10000000000}}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      11. *-commutative N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\left(\frac{15234687407}{1000000000} + z\right) \cdot z} + \frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      12. lower-fma.f64 N/A

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{15234687407}{1000000000} + z, z, \frac{314690115749}{10000000000}\right)}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} \cdot y \]

      13. lower-+.f64 54.1

          \[\leadsto \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{15.234687407 + z}, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y \]

   5. Applied rewrites 54.1%

      \[\leadsto \color{blue}{\frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.9%

      \[\leadsto 1.6453555072203998 \cdot \color{blue}{\left(b \cdot y\right)} \]

   if -1.0000000000000001e69 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 5.0000000000000002e75 or +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 49.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 83.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 83.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq -1 \cdot 10^{+69}:\\ \;\;\;\;\left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right)\right) - \mathsf{fma}\left(-36.52704169880642 \cdot \frac{y}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        (+
         b
         (* (+ a (* (+ t (* (+ 11.1667541262 (* 3.13060547623 z)) z)) z)) z))
        y)
       (+
        0.607771387771
        (*
         (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
         z)))
      INFINITY)
   (+
    (/
     y
     (/
      (fma
       (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
       z
       0.607771387771)
      (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)))
    x)
   (+
    (-
     (fma (/ t z) (/ y z) (fma (/ y z) 11.1667541262 (* 3.13060547623 y)))
     (fma
      (* -36.52704169880642 (/ y z))
      (/ 15.234687407 z)
      (fma (/ y (* z z)) 98.5170599679272 (* 47.69379582500642 (/ y z)))))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((b + ((a + ((t + ((11.1667541262 + (3.13060547623 * z)) * z)) * z)) * z)) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) <= ((double) INFINITY)) {
		tmp = (y / (fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b))) + x;
	} else {
		tmp = (fma((t / z), (y / z), fma((y / z), 11.1667541262, (3.13060547623 * y))) - fma((-36.52704169880642 * (y / z)), (15.234687407 / z), fma((y / (z * z)), 98.5170599679272, (47.69379582500642 * (y / z))))) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(11.1667541262 + Float64(3.13060547623 * z)) * z)) * z)) * z)) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) <= Inf)
		tmp = Float64(Float64(y / Float64(fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b))) + x);
	else
		tmp = Float64(Float64(fma(Float64(t / z), Float64(y / z), fma(Float64(y / z), 11.1667541262, Float64(3.13060547623 * y))) - fma(Float64(-36.52704169880642 * Float64(y / z)), Float64(15.234687407 / z), fma(Float64(y / Float64(z * z)), 98.5170599679272, Float64(47.69379582500642 * Float64(y / z))))) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(11.1667541262 + N[(3.13060547623 * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y / N[(N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(N[(t / z), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * 11.1667541262 + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] * N[(15.234687407 / z), $MachinePrecision] + N[(N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] * 98.5170599679272 + N[(47.69379582500642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 92.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      4. clear-num N/A

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      5. un-div-inv N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      7. lower-/.f64 96.8

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

   4. Applied rewrites 96.8%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 0.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      4. clear-num N/A

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      5. un-div-inv N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      7. lower-/.f64 0.0

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

   4. Applied rewrites 0.0%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]

   5. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{t \cdot y}{{z}^{2}}\right)\right) - \left(\frac{15234687407}{1000000000} \cdot \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{{z}^{2}} + \left(\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z} + \frac{98517059967927196814627}{1000000000000000000000} \cdot \frac{y}{{z}^{2}}\right)\right)\right)} \]

   7. Applied rewrites 98.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right)\right) - \mathsf{fma}\left(-36.52704169880642 \cdot \frac{y}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right)\right) - \mathsf{fma}\left(-36.52704169880642 \cdot \frac{y}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((b + ((a + ((t + ((11.1667541262 + (3.13060547623 * z)) * z)) * z)) * z)) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) <= ((double) INFINITY)) {
		tmp = (y / (fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b))) + x;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(11.1667541262 + Float64(3.13060547623 * z)) * z)) * z)) * z)) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) <= Inf)
		tmp = Float64(Float64(y / Float64(fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b))) + x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(11.1667541262 + N[(3.13060547623 * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y / N[(N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 92.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. associate-/l* N/A

         \[\leadsto x + \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      4. clear-num N/A

         \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      5. un-div-inv N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      6. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}} \]

      7. lower-/.f64 96.8

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

   4. Applied rewrites 96.8%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 97.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((((b + ((a + ((t + ((11.1667541262 + (3.13060547623 * z)) * z)) * z)) * z)) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) <= ((double) INFINITY)) {
		tmp = fma((fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(Float64(b + Float64(Float64(a + Float64(Float64(t + Float64(Float64(11.1667541262 + Float64(3.13060547623 * z)) * z)) * z)) * z)) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) <= Inf)
		tmp = fma(Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(N[(b + N[(N[(a + N[(N[(t + N[(N[(11.1667541262 + N[(3.13060547623 * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 92.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x \]

      5. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot y} + x \]

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}, y, x\right)} \]

   4. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)} \]

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 97.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(b + \left(a + \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right) \cdot z\right) \cdot z\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x - \frac{\mathsf{fma}\left(\frac{t \cdot y - \mathsf{fma}\left(98.5170599679272, y, -556.47806218377 \cdot y\right)}{z}, -1, 36.52704169880642 \cdot y\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+74)
   (fma 3.13060547623 y x)
   (if (<= z 1.1e+20)
     (+
      (/
       (* (fma (fma t z a) z b) y)
       (+
        0.607771387771
        (*
         (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
         z)))
      x)
     (fma
      3.13060547623
      y
      (-
       x
       (/
        (fma
         (/ (- (* t y) (fma 98.5170599679272 y (* -556.47806218377 y))) z)
         -1.0
         (* 36.52704169880642 y))
        z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+74) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 1.1e+20) {
		tmp = ((fma(fma(t, z, a), z, b) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) + x;
	} else {
		tmp = fma(3.13060547623, y, (x - (fma((((t * y) - fma(98.5170599679272, y, (-556.47806218377 * y))) / z), -1.0, (36.52704169880642 * y)) / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+74)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 1.1e+20)
		tmp = Float64(Float64(Float64(fma(fma(t, z, a), z, b) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) + x);
	else
		tmp = fma(3.13060547623, y, Float64(x - Float64(fma(Float64(Float64(Float64(t * y) - fma(98.5170599679272, y, Float64(-556.47806218377 * y))) / z), -1.0, Float64(36.52704169880642 * y)) / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+74], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 1.1e+20], N[(N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + N[(x - N[(N[(N[(N[(N[(t * y), $MachinePrecision] - N[(98.5170599679272 * y + N[(-556.47806218377 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + N[(36.52704169880642 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e74

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.8999999999999999e74 < z < 1.1e20

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(z \cdot \left(a + t \cdot z\right) + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(a + t \cdot z\right) \cdot z} + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a + t \cdot z, z, b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(\color{blue}{t \cdot z + a}, z, b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-fma.f64 97.3

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(t, z, a\right)}, z, b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Applied rewrites 97.3%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   if 1.1e20 < z

   1. Initial program 14.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{\color{blue}{b \cdot y}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. lower-*.f64 39.5

         \[\leadsto x + \frac{\color{blue}{b \cdot y}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Applied rewrites 39.5%

      \[\leadsto x + \frac{\color{blue}{b \cdot y}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   8. Applied rewrites 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x - \frac{\mathsf{fma}\left(\frac{t \cdot y - \mathsf{fma}\left(98.5170599679272, y, y \cdot -556.47806218377\right)}{z}, -1, y \cdot 36.52704169880642\right)}{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x - \frac{\mathsf{fma}\left(\frac{t \cdot y - \mathsf{fma}\left(98.5170599679272, y, -556.47806218377 \cdot y\right)}{z}, -1, 36.52704169880642 \cdot y\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right) - \frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(t, y, \mathsf{fma}\left(-98.5170599679272, y, 556.47806218377 \cdot y\right)\right)}{z}, -1, 36.52704169880642 \cdot y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+74)
   (fma 3.13060547623 y x)
   (if (<= z 1.1e+20)
     (+
      (/
       (* (fma (fma t z a) z b) y)
       (+
        0.607771387771
        (*
         (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
         z)))
      x)
     (-
      (fma 3.13060547623 y x)
      (/
       (fma
        (/ (fma t y (fma -98.5170599679272 y (* 556.47806218377 y))) z)
        -1.0
        (* 36.52704169880642 y))
       z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+74) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 1.1e+20) {
		tmp = ((fma(fma(t, z, a), z, b) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) + x;
	} else {
		tmp = fma(3.13060547623, y, x) - (fma((fma(t, y, fma(-98.5170599679272, y, (556.47806218377 * y))) / z), -1.0, (36.52704169880642 * y)) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+74)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 1.1e+20)
		tmp = Float64(Float64(Float64(fma(fma(t, z, a), z, b) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) + x);
	else
		tmp = Float64(fma(3.13060547623, y, x) - Float64(fma(Float64(fma(t, y, fma(-98.5170599679272, y, Float64(556.47806218377 * y))) / z), -1.0, Float64(36.52704169880642 * y)) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+74], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 1.1e+20], N[(N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(3.13060547623 * y + x), $MachinePrecision] - N[(N[(N[(N[(t * y + N[(-98.5170599679272 * y + N[(556.47806218377 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + N[(36.52704169880642 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e74

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 100.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.8999999999999999e74 < z < 1.1e20

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(z \cdot \left(a + t \cdot z\right) + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(a + t \cdot z\right) \cdot z} + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a + t \cdot z, z, b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(\color{blue}{t \cdot z + a}, z, b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-fma.f64 97.3

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(t, z, a\right)}, z, b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Applied rewrites 97.3%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   if 1.1e20 < z

   1. Initial program 14.2%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Applied rewrites 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right) - \frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(t, y, \mathsf{fma}\left(-98.5170599679272, y, y \cdot 556.47806218377\right)\right)}{z}, -1, 36.52704169880642 \cdot y\right)}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right) - \frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(t, y, \mathsf{fma}\left(-98.5170599679272, y, 556.47806218377 \cdot y\right)\right)}{z}, -1, 36.52704169880642 \cdot y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+74)
   (fma 3.13060547623 y x)
   (if (<= z 4e+30)
     (+
      (/
       (* (fma (fma t z a) z b) y)
       (+
        0.607771387771
        (*
         (+ 11.9400905721 (* (+ 31.4690115749 (* (+ 15.234687407 z) z)) z))
         z)))
      x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+74) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 4e+30) {
		tmp = ((fma(fma(t, z, a), z, b) * y) / (0.607771387771 + ((11.9400905721 + ((31.4690115749 + ((15.234687407 + z) * z)) * z)) * z))) + x;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+74)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 4e+30)
		tmp = Float64(Float64(Float64(fma(fma(t, z, a), z, b) * y) / Float64(0.607771387771 + Float64(Float64(11.9400905721 + Float64(Float64(31.4690115749 + Float64(Float64(15.234687407 + z) * z)) * z)) * z))) + x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+74], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 4e+30], N[(N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * y), $MachinePrecision] / N[(0.607771387771 + N[(N[(11.9400905721 + N[(N[(31.4690115749 + N[(N[(15.234687407 + z), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e74 or 4.0000000000000001e30 < z

   1. Initial program 4.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 94.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 94.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.8999999999999999e74 < z < 4.0000000000000001e30

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\left(z \cdot \left(a + t \cdot z\right) + b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\color{blue}{\left(a + t \cdot z\right) \cdot z} + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a + t \cdot z, z, b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(\color{blue}{t \cdot z + a}, z, b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-fma.f64 96.1

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(t, z, a\right)}, z, b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Applied rewrites 96.1%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+30}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right) \cdot y}{0.607771387771 + \left(11.9400905721 + \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right) \cdot z\right) \cdot z} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\left(-y\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right), -1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+74)
   (fma 3.13060547623 y x)
   (if (<= z 2.25e+18)
     (fma
      (*
       (- y)
       (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b))
      -1.6453555072203998
      x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+74) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 2.25e+18) {
		tmp = fma((-y * fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b)), -1.6453555072203998, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+74)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 2.25e+18)
		tmp = fma(Float64(Float64(-y) * fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b)), -1.6453555072203998, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+74], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 2.25e+18], N[(N[((-y) * N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision] * -1.6453555072203998 + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8999999999999999e74 or 2.25e18 < z

   1. Initial program 8.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 91.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 91.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.8999999999999999e74 < z < 2.25e18

   1. Initial program 97.4%

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

   4. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(-y\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right), \frac{-1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\left(-y\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), z, t\right), z, a\right), z, b\right), \color{blue}{\frac{-1000000000000}{607771387771}}, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 92.4%

      \[\leadsto \mathsf{fma}\left(\left(-y\right) \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right), \color{blue}{-1.6453555072203998}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 90.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-32.324150453290734, b, 1.6453555072203998 \cdot a\right), z, 1.6453555072203998 \cdot b\right) \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.7e+18)
   (fma 3.13060547623 y x)
   (if (<= z 1.36e+16)
     (+
      (*
       (fma
        (fma -32.324150453290734 b (* 1.6453555072203998 a))
        z
        (* 1.6453555072203998 b))
       y)
      x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.7e+18) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 1.36e+16) {
		tmp = (fma(fma(-32.324150453290734, b, (1.6453555072203998 * a)), z, (1.6453555072203998 * b)) * y) + x;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.7e+18)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 1.36e+16)
		tmp = Float64(Float64(fma(fma(-32.324150453290734, b, Float64(1.6453555072203998 * a)), z, Float64(1.6453555072203998 * b)) * y) + x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.7e+18], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 1.36e+16], N[(N[(N[(N[(-32.324150453290734 * b + N[(1.6453555072203998 * a), $MachinePrecision]), $MachinePrecision] * z + N[(1.6453555072203998 * b), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e18 or 1.36e16 < z

   1. Initial program 11.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 88.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -2.7e18 < z < 1.36e16

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \left(\frac{1000000000000}{607771387771} \cdot \color{blue}{\left(y \cdot b\right)} + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto x + \left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot y\right) \cdot b} + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]

      4. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\color{blue}{\frac{1000000000000}{607771387771} \cdot y}, b, z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \cdot z}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \cdot z}\right) \]

      7. associate-*r* N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y} - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \cdot z\right) \]

      8. associate-*r* N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \color{blue}{\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) \cdot y}\right) \cdot z\right) \]

      9. distribute-rgt-out-- N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \color{blue}{\left(y \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)} \cdot z\right) \]

      10. lower-*.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \color{blue}{\left(y \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)} \cdot z\right) \]

      11. sub-neg N/A

          \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a + \left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)\right)}\right) \cdot z\right) \]

      12. lower-fma.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \left(y \cdot \color{blue}{\mathsf{fma}\left(\frac{1000000000000}{607771387771}, a, \mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)}\right) \cdot z\right) \]

      13. distribute-lft-neg-in N/A

          \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \left(y \cdot \mathsf{fma}\left(\frac{1000000000000}{607771387771}, a, \color{blue}{\left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441}\right)\right) \cdot b}\right)\right) \cdot z\right) \]

      14. lower-*.f64 N/A

          \[\leadsto x + \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot y, b, \left(y \cdot \mathsf{fma}\left(\frac{1000000000000}{607771387771}, a, \color{blue}{\left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441}\right)\right) \cdot b}\right)\right) \cdot z\right) \]

      15. metadata-eval 75.5

          \[\leadsto x + \mathsf{fma}\left(1.6453555072203998 \cdot y, b, \left(y \cdot \mathsf{fma}\left(1.6453555072203998, a, \color{blue}{-32.324150453290734} \cdot b\right)\right) \cdot z\right) \]

   5. Applied rewrites 75.5%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(1.6453555072203998 \cdot y, b, \left(y \cdot \mathsf{fma}\left(1.6453555072203998, a, -32.324150453290734 \cdot b\right)\right) \cdot z\right)} \]

   6. Taylor expanded in y around 0

      \[\leadsto x + y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b + z \cdot \left(\frac{-11940090572100000000000000}{369386059793087248348441} \cdot b + \frac{1000000000000}{607771387771} \cdot a\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 90.4%

      \[\leadsto x + \mathsf{fma}\left(\mathsf{fma}\left(-32.324150453290734, b, 1.6453555072203998 \cdot a\right), z, 1.6453555072203998 \cdot b\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-32.324150453290734, b, 1.6453555072203998 \cdot a\right), z, 1.6453555072203998 \cdot b\right) \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e+18)
   (fma 3.13060547623 y x)
   (if (<= z 9e+14)
     (fma (* b y) 1.6453555072203998 x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.05e+18) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 9e+14) {
		tmp = fma((b * y), 1.6453555072203998, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.05e+18)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 9e+14)
		tmp = fma(Float64(b * y), 1.6453555072203998, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.05e+18], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 9e+14], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e18 or 9e14 < z

   1. Initial program 12.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

      2. lower-fma.f64 87.3

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 87.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -2.05e18 < z < 9e14

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + x} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(b \cdot y\right) \cdot \frac{1000000000000}{607771387771}} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, \frac{1000000000000}{607771387771}, x\right)} \]

      4. lower-*.f64 80.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{b \cdot y}, 1.6453555072203998, x\right) \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 62.6% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(3.13060547623, y, x\right) \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (fma 3.13060547623 y x))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(3.13060547623, y, x);
}

Julia

function code(x, y, z, t, a, b)
	return fma(3.13060547623, y, x)
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(3.13060547623 * y + x), $MachinePrecision]

Derivation

1. Initial program 61.1%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

   2. lower-fma.f64 61.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

5. Applied rewrites 61.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
6. Add Preprocessing

Alternative 14: 21.8% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ 3.13060547623 \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* 3.13060547623 y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 3.13060547623 * y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 3.13060547623d0 * y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 3.13060547623 * y;
}

Python

def code(x, y, z, t, a, b):
	return 3.13060547623 * y

Julia

function code(x, y, z, t, a, b)
	return Float64(3.13060547623 * y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 3.13060547623 * y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(3.13060547623 * y), $MachinePrecision]

Derivation

1. Initial program 61.1%

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

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\frac{313060547623}{100000000000} \cdot y + x} \]

   2. lower-fma.f64 61.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

5. Applied rewrites 61.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]
7. Step-by-step derivation

8. Applied rewrites 22.3%

   \[\leadsto 3.13060547623 \cdot \color{blue}{y} \]
9. Add Preprocessing

Developer Target 1: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z)))
           (/ y 1.0)))))
   (if (< z -6.499344996252632e+53)
     t_1
     (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))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = 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)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((3.13060547623d0 - (36.527041698806414d0 / z)) + (t / (z * z))) * (y / 1.0d0))
    if (z < (-6.499344996252632d+53)) then
        tmp = t_1
    else if (z < 7.066965436914287d+59) then
        tmp = x + (y / ((((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0) / ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = 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)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0))
	tmp = 0
	if z < -6.499344996252632e+53:
		tmp = t_1
	elif z < 7.066965436914287e+59:
		tmp = 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)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(3.13060547623 - Float64(36.527041698806414 / z)) + Float64(t / Float64(z * z))) * Float64(y / 1.0)))
	tmp = 0.0
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	tmp = 0.0;
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = 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)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(3.13060547623 - N[(36.527041698806414 / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -6.499344996252632e+53], t$95$1, If[Less[z, 7.066965436914287e+59], N[(x + N[(y / N[(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] / 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]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024331 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -649934499625263200000000000000000000000000000000000000) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))) (if (< z 706696543691428700000000000000000000000000000000000000000000) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)))) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))))))

  (+ 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))))