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

Percentage Accurate: 59.2% → 97.9%

Time: 23.5s

Alternatives: 17

Speedup: 2.5×

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: 59.2% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\\ \mathbf{if}\;\frac{y \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{t\_1}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        (t_2
         (+
          b
          (*
           z
           (+ a (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)))))))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ x (/ y (/ t_1 t_2)))
     (+
      (* -36.52704169880642 (/ y z))
      (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))));
	double tmp;
	if (((y * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y / (t_1 / t_2));
	} else {
		tmp = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))));
	double tmp;
	if (((y * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (y / (t_1 / t_2));
	} else {
		tmp = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))
	t_2 = b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))
	tmp = 0
	if ((y * t_2) / t_1) <= math.inf:
		tmp = x + (y / (t_1 / t_2))
	else:
		tmp = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	t_2 = Float64(b + Float64(z * Float64(a + Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)))))
	tmp = 0.0
	if (Float64(Float64(y * t_2) / t_1) <= Inf)
		tmp = Float64(x + Float64(y / Float64(t_1 / t_2)));
	else
		tmp = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	t_2 = b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))));
	tmp = 0.0;
	if (((y * t_2) / t_1) <= Inf)
		tmp = x + (y / (t_1 / t_2));
	else
		tmp = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y / N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 97.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(\left(\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}\right), \color{blue}{\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}\right)\right)\right) \]

   4. Applied egg-rr 99.0%

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

   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

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

   5. Simplified 98.9%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 63.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 63.7%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 99.9%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 99.9%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}{b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+43}:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (* -36.52704169880642 (/ y z))
          (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z))))))))
   (if (<= z -5.5e+62)
     t_1
     (if (<= z 3.35e+43)
       (+
        x
        (*
         (+
          b
          (* z (+ a (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)))))
         (/
          y
          (+
           0.607771387771
           (*
            z
            (+
             11.9400905721
             (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -5.5e+62) {
		tmp = t_1;
	} else if (z <= 3.35e+43) {
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))));
	} 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 = ((-36.52704169880642d0) * (y / z)) + (x + (y * (3.13060547623d0 + ((t + 457.9610022158428d0) / (z * z)))))
    if (z <= (-5.5d+62)) then
        tmp = t_1
    else if (z <= 3.35d+43) then
        tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t))))) * (y / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0)))))))))
    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 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -5.5e+62) {
		tmp = t_1;
	} else if (z <= 3.35e+43) {
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	tmp = 0
	if z <= -5.5e+62:
		tmp = t_1
	elif z <= 3.35e+43:
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -5.5e+62)
		tmp = t_1;
	elseif (z <= 3.35e+43)
		tmp = Float64(x + Float64(Float64(b + Float64(z * Float64(a + Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t))))) * Float64(y / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407))))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	tmp = 0.0;
	if (z <= -5.5e+62)
		tmp = t_1;
	elseif (z <= 3.35e+43)
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+62], t$95$1, If[LessEqual[z, 3.35e+43], N[(x + N[(N[(b + N[(z * N[(a + N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999997e62 or 3.34999999999999988e43 < z

   1. Initial program 4.6%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 98.2%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 65.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 65.1%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 99.1%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 99.1%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]

   if -5.4999999999999997e62 < z < 3.34999999999999988e43

   1. Initial program 98.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y}{\color{blue}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z} + \frac{607771387771}{1000000000000}}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\frac{y}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right), \color{blue}{\left(\frac{y}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto x + \color{blue}{\left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+62}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{+43}:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (* -36.52704169880642 (/ y z))
          (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z))))))))
   (if (<= z -6.5e+22)
     t_1
     (if (<= z 10000.0)
       (+
        x
        (/
         (*
          y
          (+
           b
           (*
            z
            (+ a (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t))))))
         (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -6.5e+22) {
		tmp = t_1;
	} else if (z <= 10000.0) {
		tmp = x + ((y * (b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} 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 = ((-36.52704169880642d0) * (y / z)) + (x + (y * (3.13060547623d0 + ((t + 457.9610022158428d0) / (z * z)))))
    if (z <= (-6.5d+22)) then
        tmp = t_1
    else if (z <= 10000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    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 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -6.5e+22) {
		tmp = t_1;
	} else if (z <= 10000.0) {
		tmp = x + ((y * (b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	tmp = 0
	if z <= -6.5e+22:
		tmp = t_1
	elif z <= 10000.0:
		tmp = x + ((y * (b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -6.5e+22)
		tmp = t_1;
	elseif (z <= 10000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	tmp = 0.0;
	if (z <= -6.5e+22)
		tmp = t_1;
	elseif (z <= 10000.0)
		tmp = x + ((y * (b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+22], t$95$1, If[LessEqual[z, 10000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.49999999999999979e22 or 1e4 < z

   1. Initial program 15.8%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 65.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 65.8%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 96.1%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 96.1%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]

   if -6.49999999999999979e22 < z < 1e4

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z\right)\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z\right)\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(\frac{314690115749}{10000000000} \cdot z\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot \frac{314690115749}{10000000000}\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. *-lowering-*.f64 96.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \frac{314690115749}{10000000000}\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 96.3%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)} + 0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+22}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 10000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 80000:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right) \cdot \left(y \cdot \frac{1}{0.607771387771 + z \cdot 11.9400905721}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (* -36.52704169880642 (/ y z))
          (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z))))))))
   (if (<= z -0.05)
     t_1
     (if (<= z 80000.0)
       (+
        x
        (*
         (+
          b
          (* z (+ a (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)))))
         (* y (/ 1.0 (+ 0.607771387771 (* z 11.9400905721))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 80000.0) {
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y * (1.0 / (0.607771387771 + (z * 11.9400905721)))));
	} 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 = ((-36.52704169880642d0) * (y / z)) + (x + (y * (3.13060547623d0 + ((t + 457.9610022158428d0) / (z * z)))))
    if (z <= (-0.05d0)) then
        tmp = t_1
    else if (z <= 80000.0d0) then
        tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t))))) * (y * (1.0d0 / (0.607771387771d0 + (z * 11.9400905721d0)))))
    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 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 80000.0) {
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y * (1.0 / (0.607771387771 + (z * 11.9400905721)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	tmp = 0
	if z <= -0.05:
		tmp = t_1
	elif z <= 80000.0:
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y * (1.0 / (0.607771387771 + (z * 11.9400905721)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 80000.0)
		tmp = Float64(x + Float64(Float64(b + Float64(z * Float64(a + Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t))))) * Float64(y * Float64(1.0 / Float64(0.607771387771 + Float64(z * 11.9400905721))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	tmp = 0.0;
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 80000.0)
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y * (1.0 / (0.607771387771 + (z * 11.9400905721)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.05], t$95$1, If[LessEqual[z, 80000.0], N[(x + N[(N[(b + N[(z * N[(a + N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * N[(1.0 / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.050000000000000003 or 8e4 < z

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 64.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 93.5%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 93.5%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]

   if -0.050000000000000003 < z < 8e4

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.8%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{z \cdot 11.9400905721} + 0.607771387771} \]
   6. Step-by-step derivation

      1. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\right) \cdot \color{blue}{\frac{1}{z \cdot \frac{119400905721}{10000000000} + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y\right) \cdot \frac{\color{blue}{1}}{z \cdot \frac{119400905721}{10000000000} + \frac{607771387771}{1000000000000}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\left(y \cdot \frac{1}{z \cdot \frac{119400905721}{10000000000} + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right), \color{blue}{\left(y \cdot \frac{1}{z \cdot \frac{119400905721}{10000000000} + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

   7. Applied egg-rr 98.9%

      \[\leadsto x + \color{blue}{\left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \left(y \cdot \frac{1}{0.607771387771 + z \cdot 11.9400905721}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 80000:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right) \cdot \left(y \cdot \frac{1}{0.607771387771 + z \cdot 11.9400905721}\right)\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 66000:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (* -36.52704169880642 (/ y z))
          (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z))))))))
   (if (<= z -0.05)
     t_1
     (if (<= z 66000.0)
       (+
        x
        (*
         (+
          b
          (* z (+ a (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)))))
         (/ y (+ 0.607771387771 (* z 11.9400905721)))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 66000.0) {
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * 11.9400905721))));
	} 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 = ((-36.52704169880642d0) * (y / z)) + (x + (y * (3.13060547623d0 + ((t + 457.9610022158428d0) / (z * z)))))
    if (z <= (-0.05d0)) then
        tmp = t_1
    else if (z <= 66000.0d0) then
        tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t))))) * (y / (0.607771387771d0 + (z * 11.9400905721d0))))
    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 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 66000.0) {
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * 11.9400905721))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	tmp = 0
	if z <= -0.05:
		tmp = t_1
	elif z <= 66000.0:
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * 11.9400905721))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 66000.0)
		tmp = Float64(x + Float64(Float64(b + Float64(z * Float64(a + Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t))))) * Float64(y / Float64(0.607771387771 + Float64(z * 11.9400905721)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	tmp = 0.0;
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 66000.0)
		tmp = x + ((b + (z * (a + (z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t))))) * (y / (0.607771387771 + (z * 11.9400905721))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.05], t$95$1, If[LessEqual[z, 66000.0], N[(x + N[(N[(b + N[(z * N[(a + N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.050000000000000003 or 66000 < z

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 64.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 93.5%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 93.5%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]

   if -0.050000000000000003 < z < 66000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.8%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{z \cdot 11.9400905721} + 0.607771387771} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y}{\color{blue}{z \cdot \frac{119400905721}{10000000000}} + \frac{607771387771}{1000000000000}}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\frac{y}{z \cdot \frac{119400905721}{10000000000} + \frac{607771387771}{1000000000000}}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right), \color{blue}{\left(\frac{y}{z \cdot \frac{119400905721}{10000000000} + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

   7. Applied egg-rr 98.8%

      \[\leadsto x + \color{blue}{\left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot 11.9400905721}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 66000:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right)\right)\right) \cdot \frac{y}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 72000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (* -36.52704169880642 (/ y z))
          (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z))))))))
   (if (<= z -0.05)
     t_1
     (if (<= z 72000.0)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
         (+ 0.607771387771 (* z 11.9400905721))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 72000.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 = ((-36.52704169880642d0) * (y / z)) + (x + (y * (3.13060547623d0 + ((t + 457.9610022158428d0) / (z * z)))))
    if (z <= (-0.05d0)) then
        tmp = t_1
    else if (z <= 72000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 72000.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	tmp = 0
	if z <= -0.05:
		tmp = t_1
	elif z <= 72000.0:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 72000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	tmp = 0.0;
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 72000.0)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.05], t$95$1, If[LessEqual[z, 72000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.050000000000000003 or 72000 < z

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 64.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 93.5%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 93.5%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]

   if -0.050000000000000003 < z < 72000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{55833770631}{5000000000} \cdot z\right)}, t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{55833770631}{5000000000}\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{55833770631}{5000000000}\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 98.5%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\color{blue}{z \cdot 11.1667541262} + t\right) \cdot z + a\right) \cdot z + b\right)}{z \cdot 11.9400905721 + 0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 72000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 55000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (* -36.52704169880642 (/ y z))
          (+ x (* y (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z))))))))
   (if (<= z -0.05)
     t_1
     (if (<= z 55000.0)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z t)))))
         (+ 0.607771387771 (* z 11.9400905721))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 55000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 = ((-36.52704169880642d0) * (y / z)) + (x + (y * (3.13060547623d0 + ((t + 457.9610022158428d0) / (z * z)))))
    if (z <= (-0.05d0)) then
        tmp = t_1
    else if (z <= 55000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	double tmp;
	if (z <= -0.05) {
		tmp = t_1;
	} else if (z <= 55000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))))
	tmp = 0
	if z <= -0.05:
		tmp = t_1
	elif z <= 55000.0:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 55000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (-36.52704169880642 * (y / z)) + (x + (y * (3.13060547623 + ((t + 457.9610022158428) / (z * z)))));
	tmp = 0.0;
	if (z <= -0.05)
		tmp = t_1;
	elseif (z <= 55000.0)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(x + N[(y * N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.05], t$95$1, If[LessEqual[z, 55000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.050000000000000003 or 55000 < z

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 92.7%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + \left(y \cdot \frac{t}{z \cdot z} + \left(\left(\frac{y \cdot -47.69379582500642}{z} + \frac{y}{z \cdot z} \cdot -98.5170599679272\right) + \frac{y \cdot 556.47806218377}{z \cdot z}\right)\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \color{blue}{\left(\frac{\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)}{{z}^{2}}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + \left(t \cdot y + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right)\right), \color{blue}{\left({z}^{2}\right)}\right)\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      3. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right) + z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \left(\frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y + t \cdot y\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({\color{blue}{z}}^{2}\right)\right)\right) \]

      5. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} \cdot y + \frac{55647806218377003596563527016327}{100000000000000000000000000000} \cdot y\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t \cdot y\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + y \cdot t\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      8. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right) + t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{-98517059967927196814627}{1000000000000000000000} + \frac{55647806218377003596563527016327}{100000000000000000000000000000}\right), t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \left(z \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(\frac{-4769379582500641883561}{100000000000000000000} \cdot y + \frac{55833770631}{5000000000} \cdot y\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      13. distribute-rgt-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      14. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \left(\frac{-4769379582500641883561}{100000000000000000000} + \frac{55833770631}{5000000000}\right)\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left({z}^{2}\right)\right)\right) \]

      16. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \left(z \cdot \color{blue}{z}\right)\right)\right) \]

      17. *-lowering-*.f64 64.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \frac{-3652704169880641883561}{100000000000000000000}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right)\right) \]

   8. Simplified 64.6%

      \[\leadsto \left(x + y \cdot 3.13060547623\right) + \color{blue}{\frac{y \cdot \left(457.9610022158428 + t\right) + z \cdot \left(y \cdot -36.52704169880642\right)}{z \cdot z}} \]

   9. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right)} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)\right) + \color{blue}{x} \]

       2. associate-+l+ N/A

          \[\leadsto \frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)} \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z}\right), \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right) + x\right)}\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \left(\frac{y}{z}\right)\right), \left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right)} + x\right)\right) \]

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \left(\left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}}\right) + x\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), \color{blue}{x}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + \frac{y \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)}{{z}^{2}}\right), x\right)\right) \]

       8. associate-/l* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000} + y \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right), x\right)\right) \]

       9. distribute-lft-out N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       10. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{313060547623}{100000000000} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right), x\right)\right) \]

       11. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}}\right)\right)\right), x\right)\right) \]

       12. /-lowering-/.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left({z}^{2}\right)\right)\right)\right), x\right)\right) \]

       14. unpow2 N/A

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \left(z \cdot z\right)\right)\right)\right), x\right)\right) \]

       15. *-lowering-*.f64 93.5%

           \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{-3652704169880641883561}{100000000000000000000}, \mathsf{/.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, t\right), \mathsf{*.f64}\left(z, z\right)\right)\right)\right), x\right)\right) \]

   11. Simplified 93.5%

       \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot \left(3.13060547623 + \frac{457.9610022158428 + t}{z \cdot z}\right) + x\right)} \]

   if -0.050000000000000003 < z < 55000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + z \cdot \left(t \cdot z + a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(z \cdot \left(t \cdot z\right) + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(z \cdot \left(z \cdot t\right) + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(\left(z \cdot z\right) \cdot t + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left({z}^{2} \cdot t + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(t \cdot {z}^{2} + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(t \cdot {z}^{2} + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(t \cdot {z}^{2} + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left({z}^{2} \cdot t + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(\left(z \cdot z\right) \cdot t + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(z \cdot t\right) + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(t \cdot z\right) + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(t \cdot z\right) + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(t \cdot z + a\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(z \cdot t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      19. *-lowering-*.f64 96.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 96.6%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \mathbf{elif}\;z \leq 55000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;-36.52704169880642 \cdot \frac{y}{z} + \left(x + y \cdot \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.05)
   (+ x (+ (* y 3.13060547623) (/ (* y -36.52704169880642) z)))
   (if (<= z 105000.0)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z t)))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.05) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 105000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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) :: tmp
    if (z <= (-0.05d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y * (-36.52704169880642d0)) / z))
    else if (z <= 105000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.05) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 105000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.05:
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z))
	elif z <= 105000.0:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.05)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y * -36.52704169880642) / z)));
	elseif (z <= 105000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.05)
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	elseif (z <= 105000.0)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.05], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.050000000000000003

   1. Initial program 25.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{-3652704169880641883561}{100000000000000000000} + \frac{313060547623}{100000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{3652704169880641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      8. times-frac N/A

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

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{313060547623}{100000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{313060547623}{100000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

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

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)}\right) \]

   5. Simplified 85.8%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)} \]

   if -0.050000000000000003 < z < 105000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + z \cdot \left(t \cdot z + a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(z \cdot \left(t \cdot z\right) + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(z \cdot \left(z \cdot t\right) + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(\left(z \cdot z\right) \cdot t + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left({z}^{2} \cdot t + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(t \cdot {z}^{2} + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(t \cdot {z}^{2} + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(t \cdot {z}^{2} + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left({z}^{2} \cdot t + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      10. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(\left(z \cdot z\right) \cdot t + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(z \cdot t\right) + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(t \cdot z\right) + a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      13. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(t \cdot z\right) + z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      14. distribute-lft-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(t \cdot z + a\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      15. +-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      17. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(z \cdot t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      19. *-lowering-*.f64 96.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 96.6%

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

   if 105000 < z

   1. Initial program 14.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 86.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 86.6%

      \[\leadsto \color{blue}{x + y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 58000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6500.0)
   (+ x (+ (* y 3.13060547623) (/ (* y -36.52704169880642) z)))
   (if (<= z 1.5e-94)
     (+ x (* y (* b 1.6453555072203998)))
     (if (<= z 58000.0)
       (+ x (/ (* y (* z a)) (+ 0.607771387771 (* z 11.9400905721))))
       (+ x (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6500.0) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 1.5e-94) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 58000.0) {
		tmp = x + ((y * (z * a)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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) :: tmp
    if (z <= (-6500.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y * (-36.52704169880642d0)) / z))
    else if (z <= 1.5d-94) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else if (z <= 58000.0d0) then
        tmp = x + ((y * (z * a)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6500.0) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 1.5e-94) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 58000.0) {
		tmp = x + ((y * (z * a)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6500.0:
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z))
	elif z <= 1.5e-94:
		tmp = x + (y * (b * 1.6453555072203998))
	elif z <= 58000.0:
		tmp = x + ((y * (z * a)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6500.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y * -36.52704169880642) / z)));
	elseif (z <= 1.5e-94)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	elseif (z <= 58000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z * a)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6500.0)
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	elseif (z <= 1.5e-94)
		tmp = x + (y * (b * 1.6453555072203998));
	elseif (z <= 58000.0)
		tmp = x + ((y * (z * a)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6500.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-94], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 58000.0], N[(x + N[(N[(y * N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6500

   1. Initial program 23.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{-3652704169880641883561}{100000000000000000000} + \frac{313060547623}{100000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{3652704169880641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      8. times-frac N/A

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

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{313060547623}{100000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{313060547623}{100000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

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

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)}\right) \]

   5. Simplified 87.1%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)} \]

   if -6500 < z < 1.5000000000000001e-94

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. 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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot \color{blue}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(b \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

      6. *-lowering-*.f64 83.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 83.3%

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

   if 1.5000000000000001e-94 < z < 58000

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 95.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 95.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(a \cdot \left(y \cdot z\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(a \cdot y\right) \cdot z\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y \cdot a\right) \cdot z\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot z\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(a \cdot z\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. *-lowering-*.f64 82.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{*.f64}\left(a, z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 82.0%

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

   if 58000 < z

   1. Initial program 14.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 86.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 86.6%

      \[\leadsto \color{blue}{x + y \cdot 3.13060547623} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-94}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 58000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7200:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + z \cdot \left(a \cdot 1.6453555072203998 + b \cdot -32.324150453290734\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.55e+18)
     t_1
     (if (<= z 7200.0)
       (+
        x
        (*
         y
         (+
          (* b 1.6453555072203998)
          (* z (+ (* a 1.6453555072203998) (* b -32.324150453290734))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.55e+18) {
		tmp = t_1;
	} else if (z <= 7200.0) {
		tmp = x + (y * ((b * 1.6453555072203998) + (z * ((a * 1.6453555072203998) + (b * -32.324150453290734)))));
	} 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 + (y * 3.13060547623d0)
    if (z <= (-1.55d+18)) then
        tmp = t_1
    else if (z <= 7200.0d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) + (z * ((a * 1.6453555072203998d0) + (b * (-32.324150453290734d0))))))
    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 + (y * 3.13060547623);
	double tmp;
	if (z <= -1.55e+18) {
		tmp = t_1;
	} else if (z <= 7200.0) {
		tmp = x + (y * ((b * 1.6453555072203998) + (z * ((a * 1.6453555072203998) + (b * -32.324150453290734)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.55e+18:
		tmp = t_1
	elif z <= 7200.0:
		tmp = x + (y * ((b * 1.6453555072203998) + (z * ((a * 1.6453555072203998) + (b * -32.324150453290734)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.55e+18)
		tmp = t_1;
	elseif (z <= 7200.0)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(z * Float64(Float64(a * 1.6453555072203998) + Float64(b * -32.324150453290734))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -1.55e+18)
		tmp = t_1;
	elseif (z <= 7200.0)
		tmp = x + (y * ((b * 1.6453555072203998) + (z * ((a * 1.6453555072203998) + (b * -32.324150453290734)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e+18], t$95$1, If[LessEqual[z, 7200.0], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(z * N[(N[(a * 1.6453555072203998), $MachinePrecision] + N[(b * -32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e18 or 7200 < z

   1. Initial program 17.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 88.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 88.4%

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

   if -1.55e18 < z < 7200

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(a \cdot \left(y \cdot z\right) + b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(b \cdot y + a \cdot \left(y \cdot z\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(b \cdot y\right), \left(a \cdot \left(y \cdot z\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot b\right), \left(a \cdot \left(y \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right)}, z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(a \cdot \left(y \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right)}, z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\left(a \cdot y\right) \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\left(y \cdot a\right) \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(y \cdot \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(y, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(y, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      10. *-lowering-*.f64 91.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 91.2%

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

      1. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot b + y \cdot \left(z \cdot a\right)\right) \cdot \color{blue}{\frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. distribute-lft-out N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot \left(b + z \cdot a\right)\right) \cdot \frac{\color{blue}{1}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\left(b + z \cdot a\right) \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\left(b + z \cdot a\right) \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(b + z \cdot a\right), \color{blue}{\left(\frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \left(z \cdot a\right)\right), \left(\frac{\color{blue}{1}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \left(\frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{/.f64}\left(1, \color{blue}{\left(\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}\right)}\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z\right), \color{blue}{\frac{607771387771}{1000000000000}}\right)\right)\right)\right)\right) \]

   7. Applied egg-rr 91.3%

      \[\leadsto x + \color{blue}{y \cdot \left(\left(b + z \cdot a\right) \cdot \frac{1}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right)} \]

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b + z \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot b\right), \color{blue}{\left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(b \cdot \frac{1000000000000}{607771387771}\right), \left(\color{blue}{z} \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \left(\color{blue}{z} \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \left(\frac{1000000000000}{607771387771} \cdot a + \color{blue}{\left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)}\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot a\right), \color{blue}{\left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)}\right)\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(a \cdot \frac{1000000000000}{607771387771}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441} \cdot b}\right)\right)\right)\right)\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(\mathsf{neg}\left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441} \cdot b}\right)\right)\right)\right)\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(\mathsf{neg}\left(b \cdot \frac{11940090572100000000000000}{369386059793087248348441}\right)\right)\right)\right)\right)\right)\right) \]

      10. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441}\right)\right)}\right)\right)\right)\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(b, \color{blue}{\left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441}\right)\right)}\right)\right)\right)\right)\right)\right) \]

      12. metadata-eval 90.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(b, \frac{-11940090572100000000000000}{369386059793087248348441}\right)\right)\right)\right)\right)\right) \]

   10. Simplified 90.5%

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

Alternative 11: 90.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.05)
   (+ x (+ (* y 3.13060547623) (/ (* y -36.52704169880642) z)))
   (if (<= z 105000.0)
     (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.05) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 105000.0) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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) :: tmp
    if (z <= (-0.05d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y * (-36.52704169880642d0)) / z))
    else if (z <= 105000.0d0) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.05) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 105000.0) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.05:
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z))
	elif z <= 105000.0:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.05)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y * -36.52704169880642) / z)));
	elseif (z <= 105000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.05)
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	elseif (z <= 105000.0)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.05], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105000.0], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.050000000000000003

   1. Initial program 25.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{-3652704169880641883561}{100000000000000000000} + \frac{313060547623}{100000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{3652704169880641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      8. times-frac N/A

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

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{313060547623}{100000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{313060547623}{100000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

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

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)}\right) \]

   5. Simplified 85.8%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)} \]

   if -0.050000000000000003 < z < 105000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 98.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(a \cdot \left(y \cdot z\right) + b \cdot y\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot \left(z \cdot y\right) + b \cdot y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(a \cdot z\right) \cdot y + b \cdot y\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{z}, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(a \cdot z + b\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(b + a \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + a \cdot z\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. *-lowering-*.f64 92.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(a, z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 92.6%

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

   if 105000 < z

   1. Initial program 14.4%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 86.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 86.6%

      \[\leadsto \color{blue}{x + y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.05:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -720:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -720.0)
   (+ x (+ (* y 3.13060547623) (/ (* y -36.52704169880642) z)))
   (if (<= z 1.3e-14)
     (+ x (* y (* b 1.6453555072203998)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -720.0) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 1.3e-14) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	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) :: tmp
    if (z <= (-720.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((y * (-36.52704169880642d0)) / z))
    else if (z <= 1.3d-14) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -720.0) {
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	} else if (z <= 1.3e-14) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -720.0:
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z))
	elif z <= 1.3e-14:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -720.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y * -36.52704169880642) / z)));
	elseif (z <= 1.3e-14)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -720.0)
		tmp = x + ((y * 3.13060547623) + ((y * -36.52704169880642) / z));
	elseif (z <= 1.3e-14)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -720.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-14], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -720

   1. Initial program 23.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

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

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

      5. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{-3652704169880641883561}{100000000000000000000} + \frac{313060547623}{100000000000} \cdot y\right) \]

      6. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{3652704169880641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      7. metadata-eval N/A

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) \]

      8. times-frac N/A

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

      9. *-commutative N/A

         \[\leadsto x + \left(\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

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

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{-1 \cdot z} + \frac{313060547623}{100000000000} \cdot y\right) \]

      11. mul-1-neg N/A

          \[\leadsto x + \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{\mathsf{neg}\left(z\right)} + \frac{313060547623}{100000000000} \cdot y\right) \]

      12. distribute-neg-frac2 N/A

          \[\leadsto x + \left(\left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) + \color{blue}{\frac{313060547623}{100000000000}} \cdot y\right) \]

      13. mul-1-neg N/A

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

      14. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)}\right) \]

   5. Simplified 87.1%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 + \frac{y \cdot -36.52704169880642}{z}\right)} \]

   if -720 < z < 1.29999999999999998e-14

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. 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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot \color{blue}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(b \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

      6. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 78.1%

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

   if 1.29999999999999998e-14 < z

   1. Initial program 20.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 84.4%

      \[\leadsto \color{blue}{x + y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 82.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -400:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -400.0)
     t_1
     (if (<= z 1.3e-14) (+ x (* y (* b 1.6453555072203998))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -400.0) {
		tmp = t_1;
	} else if (z <= 1.3e-14) {
		tmp = x + (y * (b * 1.6453555072203998));
	} 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 + (y * 3.13060547623d0)
    if (z <= (-400.0d0)) then
        tmp = t_1
    else if (z <= 1.3d-14) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    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 + (y * 3.13060547623);
	double tmp;
	if (z <= -400.0) {
		tmp = t_1;
	} else if (z <= 1.3e-14) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -400.0:
		tmp = t_1
	elif z <= 1.3e-14:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -400.0)
		tmp = t_1;
	elseif (z <= 1.3e-14)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -400.0)
		tmp = t_1;
	elseif (z <= 1.3e-14)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -400.0], t$95$1, If[LessEqual[z, 1.3e-14], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -400 or 1.29999999999999998e-14 < z

   1. Initial program 21.8%

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

   3. Taylor expanded in z around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 85.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 85.6%

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

   if -400 < z < 1.29999999999999998e-14

   1. Initial program 99.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. 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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot \color{blue}{y}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(b \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

      6. *-lowering-*.f64 78.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(b, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 78.1%

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

Alternative 14: 82.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -60:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -60.0)
     t_1
     (if (<= z 1.3e-14) (+ x (* 1.6453555072203998 (* y b))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -60.0) {
		tmp = t_1;
	} else if (z <= 1.3e-14) {
		tmp = x + (1.6453555072203998 * (y * 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 + (y * 3.13060547623d0)
    if (z <= (-60.0d0)) then
        tmp = t_1
    else if (z <= 1.3d-14) then
        tmp = x + (1.6453555072203998d0 * (y * 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 + (y * 3.13060547623);
	double tmp;
	if (z <= -60.0) {
		tmp = t_1;
	} else if (z <= 1.3e-14) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -60.0:
		tmp = t_1
	elif z <= 1.3e-14:
		tmp = x + (1.6453555072203998 * (y * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -60.0)
		tmp = t_1;
	elseif (z <= 1.3e-14)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -60.0)
		tmp = t_1;
	elseif (z <= 1.3e-14)
		tmp = x + (1.6453555072203998 * (y * 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[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -60.0], t$95$1, If[LessEqual[z, 1.3e-14], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -60 or 1.29999999999999998e-14 < z

   1. Initial program 21.8%

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

   3. Taylor expanded in z around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 85.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 85.6%

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

   if -60 < z < 1.29999999999999998e-14

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\color{blue}{\left(b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)\right)}, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(b \cdot y\right), \left(z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(y \cdot b\right), \left(z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right)}, z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right)}, z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(a \cdot y\right), \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(y \cdot a\right), \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      8. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \left(\left(t \cdot y\right) \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \left(\left(y \cdot t\right) \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      10. associate-*l* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \left(y \cdot \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \mathsf{*.f64}\left(y, \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \mathsf{*.f64}\left(y, \left(z \cdot t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      13. *-lowering-*.f64 93.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, a\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 93.0%

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

   6. Taylor expanded in z around 0

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \color{blue}{\left(b \cdot y\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \left(y \cdot \color{blue}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 78.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \mathsf{*.f64}\left(y, \color{blue}{b}\right)\right)\right) \]

   8. Simplified 78.0%

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

Alternative 15: 63.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -7.5e-36) t_1 (if (<= z 3.5e-119) x t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -7.5e-36) {
		tmp = t_1;
	} else if (z <= 3.5e-119) {
		tmp = x;
	} 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 + (y * 3.13060547623d0)
    if (z <= (-7.5d-36)) then
        tmp = t_1
    else if (z <= 3.5d-119) then
        tmp = x
    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 + (y * 3.13060547623);
	double tmp;
	if (z <= -7.5e-36) {
		tmp = t_1;
	} else if (z <= 3.5e-119) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -7.5e-36:
		tmp = t_1
	elif z <= 3.5e-119:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -7.5e-36)
		tmp = t_1;
	elseif (z <= 3.5e-119)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -7.5e-36)
		tmp = t_1;
	elseif (z <= 3.5e-119)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e-36], t$95$1, If[LessEqual[z, 3.5e-119], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999972e-36 or 3.5e-119 < z

   1. Initial program 37.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 75.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 75.2%

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

   if -7.49999999999999972e-36 < z < 3.5e-119

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 50.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 49.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+131}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.5e+131)
   (* y 3.13060547623)
   (if (<= y 1.3e+104) x (* y 3.13060547623))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.5e+131) {
		tmp = y * 3.13060547623;
	} else if (y <= 1.3e+104) {
		tmp = x;
	} else {
		tmp = y * 3.13060547623;
	}
	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) :: tmp
    if (y <= (-5.5d+131)) then
        tmp = y * 3.13060547623d0
    else if (y <= 1.3d+104) then
        tmp = x
    else
        tmp = y * 3.13060547623d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.5e+131) {
		tmp = y * 3.13060547623;
	} else if (y <= 1.3e+104) {
		tmp = x;
	} else {
		tmp = y * 3.13060547623;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.5e+131:
		tmp = y * 3.13060547623
	elif y <= 1.3e+104:
		tmp = x
	else:
		tmp = y * 3.13060547623
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.5e+131)
		tmp = Float64(y * 3.13060547623);
	elseif (y <= 1.3e+104)
		tmp = x;
	else
		tmp = Float64(y * 3.13060547623);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.5e+131)
		tmp = y * 3.13060547623;
	elseif (y <= 1.3e+104)
		tmp = x;
	else
		tmp = y * 3.13060547623;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.5e+131], N[(y * 3.13060547623), $MachinePrecision], If[LessEqual[y, 1.3e+104], x, N[(y * 3.13060547623), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999971e131 or 1.3e104 < y

   1. Initial program 49.5%

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

   3. Taylor expanded in z around inf

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 46.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 46.2%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 40.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{313060547623}{100000000000}, \color{blue}{y}\right) \]

   8. Simplified 40.2%

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

   if -5.49999999999999971e131 < y < 1.3e104

   1. Initial program 61.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 62.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+131}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+104}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.9% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 57.7%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 45.2%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 98.5% 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 2024191 
(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))))