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

Percentage Accurate: 58.2% → 97.3%

Time: 15.2s

Alternatives: 13

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.2% 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: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + 3.13060547623 \cdot \left(z \cdot z\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) + \frac{457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.35e+50)
   (+
    x
    (*
     y
     (+
      3.13060547623
      (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))
   (if (<= z 3.6e+34)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* 3.13060547623 (* z z))))))))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+
      x
      (*
       y
       (+
        (+ (+ 3.13060547623 (/ t (* z z))) (/ 457.9610022158428 (* z z)))
        (/ -36.52704169880642 z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.35e+50) {
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else if (z <= 3.6e+34) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (3.13060547623 * (z * z)))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)));
	}
	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 <= (-1.35d+50)) then
        tmp = x + (y * (3.13060547623d0 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    else if (z <= 3.6d+34) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (3.13060547623d0 * (z * z)))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y * (((3.13060547623d0 + (t / (z * z))) + (457.9610022158428d0 / (z * z))) + ((-36.52704169880642d0) / z)))
    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 <= -1.35e+50) {
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else if (z <= 3.6e+34) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (3.13060547623 * (z * z)))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.35e+50:
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	elif z <= 3.6e+34:
		tmp = x + ((y * (b + (z * (a + (z * (t + (3.13060547623 * (z * z)))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.35e+50)
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	elseif (z <= 3.6e+34)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(3.13060547623 * Float64(z * z)))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(3.13060547623 + Float64(t / Float64(z * z))) + Float64(457.9610022158428 / Float64(z * z))) + Float64(-36.52704169880642 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.35e+50)
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	elseif (z <= 3.6e+34)
		tmp = x + ((y * (b + (z * (a + (z * (t + (3.13060547623 * (z * z)))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.35e+50], N[(x + N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+34], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(3.13060547623 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[(3.13060547623 + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e50

   1. Initial program 0.2%

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

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

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

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

   4. Applied egg-rr 2.2%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 100.0%

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

   7. Simplified 100.0%

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

   if -1.35e50 < z < 3.6e34

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} \cdot {z}^{2}\right)}, t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{313060547623}{100000000000}, \left({z}^{2}\right)\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. unpow2 N/A

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

      3. *-lowering-*.f64 99.2%

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

   5. Simplified 99.2%

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

   if 3.6e34 < z

   1. Initial program 6.3%

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

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

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

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

   4. Applied egg-rr 9.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) + \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{t}{{z}^{2}} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{313060547623}{100000000000} + \frac{t}{{z}^{2}}\right) + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} + \frac{t}{{z}^{2}}\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{t}{{z}^{2}}\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \left({z}^{2}\right)\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \left(z \cdot z\right)\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \left({z}^{2}\right)\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      11. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \left(z \cdot z\right)\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{z}\right)\right)\right), y\right)\right) \]

      14. metadata-eval N/A

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

      15. distribute-neg-frac N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + 3.13060547623 \cdot \left(z \cdot z\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) + \frac{457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $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$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $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 95.8%

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

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

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

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

   4. Applied egg-rr 98.1%

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

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

   1. Initial program 0.0%

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

      1. 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. *-commutative N/A

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

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

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 98.4%

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

Alternative 3: 95.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) + \frac{457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1e+15)
   (+
    x
    (*
     y
     (+
      3.13060547623
      (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))
   (if (<= z 4.4e+24)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z t)))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+
      x
      (*
       y
       (+
        (+ (+ 3.13060547623 (/ t (* z z))) (/ 457.9610022158428 (* z z)))
        (/ -36.52704169880642 z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+15) {
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else if (z <= 4.4e+24) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)));
	}
	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 <= (-1d+15)) then
        tmp = x + (y * (3.13060547623d0 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    else if (z <= 4.4d+24) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * (((3.13060547623d0 + (t / (z * z))) + (457.9610022158428d0 / (z * z))) + ((-36.52704169880642d0) / z)))
    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 <= -1e+15) {
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else if (z <= 4.4e+24) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1e+15:
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	elif z <= 4.4e+24:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1e+15)
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	elseif (z <= 4.4e+24)
		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 * Float64(Float64(Float64(3.13060547623 + Float64(t / Float64(z * z))) + Float64(457.9610022158428 / Float64(z * z))) + Float64(-36.52704169880642 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1e+15)
		tmp = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	elseif (z <= 4.4e+24)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * (((3.13060547623 + (t / (z * z))) + (457.9610022158428 / (z * z))) + (-36.52704169880642 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1e+15], N[(x + N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+24], 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 * N[(N[(N[(3.13060547623 + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e15

   1. Initial program 18.5%

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

      1. 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. *-commutative N/A

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

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

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

   4. Applied egg-rr 21.7%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 93.7%

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

   7. Simplified 93.7%

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

   if -1e15 < z < 4.40000000000000003e24

   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 97.7%

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

   5. Simplified 97.7%

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

   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. +-lowering-+.f64 N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 98.1%

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

   8. Simplified 98.1%

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

   if 4.40000000000000003e24 < z

   1. Initial program 6.3%

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

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

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

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

   4. Applied egg-rr 9.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) + \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{t}{{z}^{2}} + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      4. associate-+r+ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(\left(\frac{313060547623}{100000000000} + \frac{t}{{z}^{2}}\right) + \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} + \frac{t}{{z}^{2}}\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{t}{{z}^{2}}\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \left({z}^{2}\right)\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \left(z \cdot z\right)\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}}\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \left({z}^{2}\right)\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      11. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \left(z \cdot z\right)\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\mathsf{neg}\left(\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)\right)\right), y\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(z, z\right)\right)\right), \mathsf{/.f64}\left(\frac{45796100221584283915100827016327}{100000000000000000000000000000}, \mathsf{*.f64}\left(z, z\right)\right)\right), \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{z}\right)\right)\right), y\right)\right) \]

      14. metadata-eval N/A

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

      15. distribute-neg-frac N/A

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

      16. metadata-eval N/A

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

      17. /-lowering-/.f64 98.0%

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

   7. Simplified 98.0%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) + \frac{457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           y
           (+
            3.13060547623
            (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))))
   (if (<= z -1e+15)
     t_1
     (if (<= z 2.8e+17)
       (+
        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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -1e+15) {
		tmp = t_1;
	} else if (z <= 2.8e+17) {
		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 = x + (y * (3.13060547623d0 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    if (z <= (-1d+15)) then
        tmp = t_1
    else if (z <= 2.8d+17) 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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -1e+15) {
		tmp = t_1;
	} else if (z <= 2.8e+17) {
		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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	tmp = 0
	if z <= -1e+15:
		tmp = t_1
	elif z <= 2.8e+17:
		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(x + Float64(y * Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))))
	tmp = 0.0
	if (z <= -1e+15)
		tmp = t_1;
	elseif (z <= 2.8e+17)
		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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	tmp = 0.0;
	if (z <= -1e+15)
		tmp = t_1;
	elseif (z <= 2.8e+17)
		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[(x + N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+15], t$95$1, If[LessEqual[z, 2.8e+17], 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 < -1e15 or 2.8e17 < z

   1. Initial program 12.9%

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

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

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

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

   4. Applied egg-rr 16.3%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 95.7%

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

   7. Simplified 95.7%

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

   if -1e15 < z < 2.8e17

   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 97.7%

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

   5. Simplified 97.7%

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

   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. +-lowering-+.f64 N/A

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 98.1%

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

   8. Simplified 98.1%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           y
           (+
            3.13060547623
            (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))))
   (if (<= z -7.5e+18)
     t_1
     (if (<= z 4e+19)
       (+
        x
        (*
         y
         (/
          b
          (+
           0.607771387771
           (* z (+ 11.9400905721 (* z (+ 31.4690115749 (* z z)))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -7.5e+18) {
		tmp = t_1;
	} else if (z <= 4e+19) {
		tmp = x + (y * (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z))))))));
	} 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 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    if (z <= (-7.5d+18)) then
        tmp = t_1
    else if (z <= 4d+19) then
        tmp = x + (y * (b / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * z))))))))
    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 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -7.5e+18) {
		tmp = t_1;
	} else if (z <= 4e+19) {
		tmp = x + (y * (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	tmp = 0
	if z <= -7.5e+18:
		tmp = t_1
	elif z <= 4e+19:
		tmp = x + (y * (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))))
	tmp = 0.0
	if (z <= -7.5e+18)
		tmp = t_1;
	elseif (z <= 4e+19)
		tmp = Float64(x + Float64(y * Float64(b / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * z)))))))));
	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 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	tmp = 0.0;
	if (z <= -7.5e+18)
		tmp = t_1;
	elseif (z <= 4e+19)
		tmp = x + (y * (b / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z))))))));
	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 * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+18], t$95$1, If[LessEqual[z, 4e+19], N[(x + N[(y * N[(b / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e18 or 4e19 < z

   1. Initial program 11.3%

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

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

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

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

   4. Applied egg-rr 14.7%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 97.3%

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

   7. Simplified 97.3%

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

   if -7.5e18 < z < 4e19

   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. 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. *-commutative N/A

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

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

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 83.6%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\color{blue}{\left({z}^{2}\right)}, \frac{314690115749}{10000000000}\right)\right), \frac{119400905721}{10000000000}\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]
   9. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 83.4%

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

   10. Simplified 83.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.78 \cdot 10^{-298}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4:\\ \;\;\;\;\frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6e-191)
     t_1
     (if (<= z -1.78e-298)
       (* 1.6453555072203998 (* y b))
       (if (<= z 1.02e-47)
         x
         (if (<= z 4.0) (/ (* y b) 0.607771387771) 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 <= -6e-191) {
		tmp = t_1;
	} else if (z <= -1.78e-298) {
		tmp = 1.6453555072203998 * (y * b);
	} else if (z <= 1.02e-47) {
		tmp = x;
	} else if (z <= 4.0) {
		tmp = (y * b) / 0.607771387771;
	} 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 <= (-6d-191)) then
        tmp = t_1
    else if (z <= (-1.78d-298)) then
        tmp = 1.6453555072203998d0 * (y * b)
    else if (z <= 1.02d-47) then
        tmp = x
    else if (z <= 4.0d0) then
        tmp = (y * b) / 0.607771387771d0
    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 <= -6e-191) {
		tmp = t_1;
	} else if (z <= -1.78e-298) {
		tmp = 1.6453555072203998 * (y * b);
	} else if (z <= 1.02e-47) {
		tmp = x;
	} else if (z <= 4.0) {
		tmp = (y * b) / 0.607771387771;
	} 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 <= -6e-191:
		tmp = t_1
	elif z <= -1.78e-298:
		tmp = 1.6453555072203998 * (y * b)
	elif z <= 1.02e-47:
		tmp = x
	elif z <= 4.0:
		tmp = (y * b) / 0.607771387771
	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 <= -6e-191)
		tmp = t_1;
	elseif (z <= -1.78e-298)
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	elseif (z <= 1.02e-47)
		tmp = x;
	elseif (z <= 4.0)
		tmp = Float64(Float64(y * b) / 0.607771387771);
	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 <= -6e-191)
		tmp = t_1;
	elseif (z <= -1.78e-298)
		tmp = 1.6453555072203998 * (y * b);
	elseif (z <= 1.02e-47)
		tmp = x;
	elseif (z <= 4.0)
		tmp = (y * b) / 0.607771387771;
	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, -6e-191], t$95$1, If[LessEqual[z, -1.78e-298], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-47], x, If[LessEqual[z, 4.0], N[(N[(y * b), $MachinePrecision] / 0.607771387771), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.0000000000000001e-191 or 4 < z

   1. Initial program 39.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 78.1%

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

   5. Simplified 78.1%

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

   if -6.0000000000000001e-191 < z < -1.7800000000000001e-298

   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 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

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

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 77.0%

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

   8. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}} \]

   9. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. *-lowering-*.f64 77.1%

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

   11. Simplified 77.1%

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

   if -1.7800000000000001e-298 < z < 1.02000000000000002e-47

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 48.1%

      \[\leadsto \color{blue}{x} \]

   if 1.02000000000000002e-47 < z < 4

   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 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

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

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 61.4%

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

   8. Simplified 61.4%

      \[\leadsto \color{blue}{\frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}} \]

   9. Taylor expanded in z around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \color{blue}{\frac{607771387771}{1000000000000}}\right) \]
   10. Step-by-step derivation

   11. Simplified 59.3%

       \[\leadsto \frac{y \cdot b}{\color{blue}{0.607771387771}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-191}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -1.78 \cdot 10^{-298}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4:\\ \;\;\;\;\frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(y \cdot b\right)\\ t_2 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6 \cdot 10^{-190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00019:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 1.6453555072203998 (* y b))) (t_2 (+ x (* y 3.13060547623))))
   (if (<= z -6e-190)
     t_2
     (if (<= z -3.2e-291)
       t_1
       (if (<= z 6.8e-48) x (if (<= z 0.00019) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (y * b);
	double t_2 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -6e-190) {
		tmp = t_2;
	} else if (z <= -3.2e-291) {
		tmp = t_1;
	} else if (z <= 6.8e-48) {
		tmp = x;
	} else if (z <= 0.00019) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 1.6453555072203998d0 * (y * b)
    t_2 = x + (y * 3.13060547623d0)
    if (z <= (-6d-190)) then
        tmp = t_2
    else if (z <= (-3.2d-291)) then
        tmp = t_1
    else if (z <= 6.8d-48) then
        tmp = x
    else if (z <= 0.00019d0) then
        tmp = t_1
    else
        tmp = t_2
    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 = 1.6453555072203998 * (y * b);
	double t_2 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -6e-190) {
		tmp = t_2;
	} else if (z <= -3.2e-291) {
		tmp = t_1;
	} else if (z <= 6.8e-48) {
		tmp = x;
	} else if (z <= 0.00019) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.6453555072203998 * (y * b)
	t_2 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -6e-190:
		tmp = t_2
	elif z <= -3.2e-291:
		tmp = t_1
	elif z <= 6.8e-48:
		tmp = x
	elif z <= 0.00019:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.6453555072203998 * Float64(y * b))
	t_2 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -6e-190)
		tmp = t_2;
	elseif (z <= -3.2e-291)
		tmp = t_1;
	elseif (z <= 6.8e-48)
		tmp = x;
	elseif (z <= 0.00019)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.6453555072203998 * (y * b);
	t_2 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -6e-190)
		tmp = t_2;
	elseif (z <= -3.2e-291)
		tmp = t_1;
	elseif (z <= 6.8e-48)
		tmp = x;
	elseif (z <= 0.00019)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-190], t$95$2, If[LessEqual[z, -3.2e-291], t$95$1, If[LessEqual[z, 6.8e-48], x, If[LessEqual[z, 0.00019], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.9999999999999996e-190 or 1.9000000000000001e-4 < z

   1. Initial program 39.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 78.1%

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

   5. Simplified 78.1%

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

   if -5.9999999999999996e-190 < z < -3.2000000000000002e-291 or 6.80000000000000056e-48 < z < 1.9000000000000001e-4

   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 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

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

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 69.9%

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

   8. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}} \]

   9. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. *-lowering-*.f64 69.0%

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

   11. Simplified 69.0%

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

   if -3.2000000000000002e-291 < z < 6.80000000000000056e-48

   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 x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 48.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-190}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-291}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.00019:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           y
           (+
            3.13060547623
            (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))))
   (if (<= z -7.2e+18)
     t_1
     (if (<= z 2.7e+17)
       (+
        x
        (*
         y
         (/ b (+ 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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -7.2e+18) {
		tmp = t_1;
	} else if (z <= 2.7e+17) {
		tmp = x + (y * (b / (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 = x + (y * (3.13060547623d0 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    if (z <= (-7.2d+18)) then
        tmp = t_1
    else if (z <= 2.7d+17) then
        tmp = x + (y * (b / (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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -7.2e+18) {
		tmp = t_1;
	} else if (z <= 2.7e+17) {
		tmp = x + (y * (b / (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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	tmp = 0
	if z <= -7.2e+18:
		tmp = t_1
	elif z <= 2.7e+17:
		tmp = x + (y * (b / (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(x + Float64(y * Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))))
	tmp = 0.0
	if (z <= -7.2e+18)
		tmp = t_1;
	elseif (z <= 2.7e+17)
		tmp = Float64(x + Float64(y * Float64(b / 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 = x + (y * (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	tmp = 0.0;
	if (z <= -7.2e+18)
		tmp = t_1;
	elseif (z <= 2.7e+17)
		tmp = x + (y * (b / (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[(x + N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e+18], t$95$1, If[LessEqual[z, 2.7e+17], N[(x + N[(y * N[(b / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2e18 or 2.7e17 < z

   1. Initial program 11.3%

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

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

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

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

   4. Applied egg-rr 14.7%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 97.3%

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

   7. Simplified 97.3%

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

   if -7.2e18 < z < 2.7e17

   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. 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. *-commutative N/A

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

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

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 83.6%

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

   8. Taylor expanded in z around 0

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

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

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

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

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 82.2%

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

   10. Simplified 82.2%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;x + y \cdot \frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           y
           (+
            3.13060547623
            (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))))
   (if (<= z -6.2e+18)
     t_1
     (if (<= z 4e+18) (+ 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 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -6.2e+18) {
		tmp = t_1;
	} else if (z <= 4e+18) {
		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 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    if (z <= (-6.2d+18)) then
        tmp = t_1
    else if (z <= 4d+18) 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 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -6.2e+18) {
		tmp = t_1;
	} else if (z <= 4e+18) {
		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 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	tmp = 0
	if z <= -6.2e+18:
		tmp = t_1
	elif z <= 4e+18:
		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 * Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))))
	tmp = 0.0
	if (z <= -6.2e+18)
		tmp = t_1;
	elseif (z <= 4e+18)
		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 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	tmp = 0.0;
	if (z <= -6.2e+18)
		tmp = t_1;
	elseif (z <= 4e+18)
		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 * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+18], t$95$1, If[LessEqual[z, 4e+18], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e18 or 4e18 < z

   1. Initial program 11.3%

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

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

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

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

   4. Applied egg-rr 14.7%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)}, y\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} + \left(\mathsf{neg}\left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right)\right), y\right)\right) \]

      2. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \left(\frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}}{z}\right)\right), y\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{313060547623}{100000000000}, \mathsf{/.f64}\left(\left(\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{z}\right), z\right)\right), y\right)\right) \]

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

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

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

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

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

      9. +-commutative N/A

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

      10. +-lowering-+.f64 97.3%

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

   7. Simplified 97.3%

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

   if -6.2e18 < z < 4e18

   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

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   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. *-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 81.8%

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

   5. Simplified 81.8%

      \[\leadsto \color{blue}{x + 1.6453555072203998 \cdot \left(y \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-259}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.16e-113)
   x
   (if (<= x -2.9e-259)
     (* 1.6453555072203998 (* y b))
     (if (<= x 5.8e-102) (* y 3.13060547623) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.16e-113) {
		tmp = x;
	} else if (x <= -2.9e-259) {
		tmp = 1.6453555072203998 * (y * b);
	} else if (x <= 5.8e-102) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	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 (x <= (-1.16d-113)) then
        tmp = x
    else if (x <= (-2.9d-259)) then
        tmp = 1.6453555072203998d0 * (y * b)
    else if (x <= 5.8d-102) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    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 (x <= -1.16e-113) {
		tmp = x;
	} else if (x <= -2.9e-259) {
		tmp = 1.6453555072203998 * (y * b);
	} else if (x <= 5.8e-102) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.16e-113:
		tmp = x
	elif x <= -2.9e-259:
		tmp = 1.6453555072203998 * (y * b)
	elif x <= 5.8e-102:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.16e-113)
		tmp = x;
	elseif (x <= -2.9e-259)
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	elseif (x <= 5.8e-102)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.16e-113)
		tmp = x;
	elseif (x <= -2.9e-259)
		tmp = 1.6453555072203998 * (y * b);
	elseif (x <= 5.8e-102)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.16e-113], x, If[LessEqual[x, -2.9e-259], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e-102], N[(y * 3.13060547623), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15999999999999999e-113 or 5.79999999999999973e-102 < x

   1. Initial program 62.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 61.2%

      \[\leadsto \color{blue}{x} \]

   if -1.15999999999999999e-113 < x < -2.90000000000000009e-259

   1. Initial program 81.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

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

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

      2. *-commutative N/A

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

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

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 52.9%

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

   8. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}} \]

   9. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

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

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

       3. *-lowering-*.f64 53.1%

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

   11. Simplified 53.1%

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

   if -2.90000000000000009e-259 < x < 5.79999999999999973e-102

   1. Initial program 51.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 49.0%

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

   5. Simplified 49.0%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 47.3%

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

   8. Simplified 47.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-259}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-102}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+20}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.4e+19)
     t_1
     (if (<= z 4e+20) (+ 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 <= -1.4e+19) {
		tmp = t_1;
	} else if (z <= 4e+20) {
		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 <= (-1.4d+19)) then
        tmp = t_1
    else if (z <= 4d+20) 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 <= -1.4e+19) {
		tmp = t_1;
	} else if (z <= 4e+20) {
		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 <= -1.4e+19:
		tmp = t_1
	elif z <= 4e+20:
		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 <= -1.4e+19)
		tmp = t_1;
	elseif (z <= 4e+20)
		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 <= -1.4e+19)
		tmp = t_1;
	elseif (z <= 4e+20)
		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, -1.4e+19], t$95$1, If[LessEqual[z, 4e+20], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e19 or 4e20 < z

   1. Initial program 10.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 92.0%

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

   5. Simplified 92.0%

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

   if -1.4e19 < z < 4e20

   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

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   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. *-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 81.3%

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

   5. Simplified 81.3%

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

Alternative 12: 52.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -9.6e-101) x (if (<= x 9e-106) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -9.6e-101) {
		tmp = x;
	} else if (x <= 9e-106) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	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 (x <= (-9.6d-101)) then
        tmp = x
    else if (x <= 9d-106) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    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 (x <= -9.6e-101) {
		tmp = x;
	} else if (x <= 9e-106) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -9.6e-101:
		tmp = x
	elif x <= 9e-106:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -9.6e-101)
		tmp = x;
	elseif (x <= 9e-106)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -9.6e-101)
		tmp = x;
	elseif (x <= 9e-106)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -9.6e-101], x, If[LessEqual[x, 9e-106], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.6e-101 or 8.99999999999999911e-106 < x

   1. Initial program 62.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 62.1%

      \[\leadsto \color{blue}{x} \]

   if -9.6e-101 < x < 8.99999999999999911e-106

   1. Initial program 60.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 43.5%

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

   5. Simplified 43.5%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 40.3%

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

   8. Simplified 40.3%

      \[\leadsto \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 46.0% 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 62.1%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 44.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 98.7% 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 2024138 
(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))))