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

Percentage Accurate: 57.5% → 99.0%

Time: 22.2s

Alternatives: 16

Speedup: 7.4×

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: 57.5% 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: 99.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+27} \lor \neg \left(z \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623 + \left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{t_1} + \left(\frac{z \cdot a}{t_1} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)}{t_1}\right), y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
   (if (or (<= z -1.8e+27) (not (<= z 1.9e+16)))
     (fma
      (+
       3.13060547623
       (+
        (+
         (+ (/ 457.9610022158428 (pow z 2.0)) (/ t (pow z 2.0)))
         (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
        (/ -36.52704169880642 z)))
      y
      x)
     (fma
      (+
       (/ b t_1)
       (+
        (/ (* z a) t_1)
        (/
         (* (pow z 2.0) (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))
         t_1)))
      y
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double tmp;
	if ((z <= -1.8e+27) || !(z <= 1.9e+16)) {
		tmp = fma((3.13060547623 + ((((457.9610022158428 / pow(z, 2.0)) + (t / pow(z, 2.0))) + ((a + (-5864.8025282699045 + (t * -15.234687407))) / pow(z, 3.0))) + (-36.52704169880642 / z))), y, x);
	} else {
		tmp = fma(((b / t_1) + (((z * a) / t_1) + ((pow(z, 2.0) * (t + (z * (11.1667541262 + (z * 3.13060547623))))) / t_1))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	tmp = 0.0
	if ((z <= -1.8e+27) || !(z <= 1.9e+16))
		tmp = fma(Float64(3.13060547623 + Float64(Float64(Float64(Float64(457.9610022158428 / (z ^ 2.0)) + Float64(t / (z ^ 2.0))) + Float64(Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407))) / (z ^ 3.0))) + Float64(-36.52704169880642 / z))), y, x);
	else
		tmp = fma(Float64(Float64(b / t_1) + Float64(Float64(Float64(z * a) / t_1) + Float64(Float64((z ^ 2.0) * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))) / t_1))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.8e+27], N[Not[LessEqual[z, 1.9e+16]], $MachinePrecision]], N[(N[(3.13060547623 + N[(N[(N[(N[(457.9610022158428 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(N[(b / t$95$1), $MachinePrecision] + N[(N[(N[(z * a), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(N[Power[z, 2.0], $MachinePrecision] * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999991e27 or 1.9e16 < z

   1. Initial program 12.2%

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

   3. Simplified 13.5%

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

   4. Taylor expanded in z around -inf 99.9%

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

   6. Simplified 99.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{3.13060547623 + \left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) - \frac{\left(-a\right) - \left(-5864.8025282699045 + -15.234687407 \cdot t\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right)}, y, x\right) \]

   if -1.79999999999999991e27 < z < 1.9e16

   1. Initial program 98.9%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+27} \lor \neg \left(z \leq 1.9 \cdot 10^{+16}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623 + \left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \left(\frac{z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\right), y, x\right)\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot t_1\right)\right)}{t_2} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{t_2} + \left(\frac{z \cdot a}{t_2} + \frac{{z}^{2} \cdot t_1}{t_2}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623 + \left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) - \frac{36.52704169880642}{z}\right), y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))
        (t_2
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
   (if (<= (/ (* y (+ b (* z (+ a (* z t_1))))) t_2) INFINITY)
     (fma (+ (/ b t_2) (+ (/ (* z a) t_2) (/ (* (pow z 2.0) t_1) t_2))) y x)
     (fma
      (+
       3.13060547623
       (-
        (+ (/ 457.9610022158428 (pow z 2.0)) (/ t (pow z 2.0)))
        (/ 36.52704169880642 z)))
      y
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (z * (11.1667541262 + (z * 3.13060547623)));
	double t_2 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double tmp;
	if (((y * (b + (z * (a + (z * t_1))))) / t_2) <= ((double) INFINITY)) {
		tmp = fma(((b / t_2) + (((z * a) / t_2) + ((pow(z, 2.0) * t_1) / t_2))), y, x);
	} else {
		tmp = fma((3.13060547623 + (((457.9610022158428 / pow(z, 2.0)) + (t / pow(z, 2.0))) - (36.52704169880642 / z))), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))
	t_2 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	tmp = 0.0
	if (Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t_1))))) / t_2) <= Inf)
		tmp = fma(Float64(Float64(b / t_2) + Float64(Float64(Float64(z * a) / t_2) + Float64(Float64((z ^ 2.0) * t_1) / t_2))), y, x);
	else
		tmp = fma(Float64(3.13060547623 + Float64(Float64(Float64(457.9610022158428 / (z ^ 2.0)) + Float64(t / (z ^ 2.0))) - Float64(36.52704169880642 / z))), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(b + N[(z * N[(a + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], Infinity], N[(N[(N[(b / t$95$2), $MachinePrecision] + N[(N[(N[(z * a), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(N[Power[z, 2.0], $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(3.13060547623 + N[(N[(N[(457.9610022158428 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.8%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 95.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \left(\frac{a \cdot z}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)}, y, x\right) \]

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 99.1%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. associate--l+ 99.1%

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

      2. associate-*r/ 99.1%

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

      3. metadata-eval 99.1%

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

      4. associate-*r/ 99.1%

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

      5. metadata-eval 99.1%

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

   6. Simplified 99.1%

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

4. Final simplification 97.2%

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

Alternative 3: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot t_1\right)\right)}{t_2} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{t_2} + \left(\frac{z \cdot a}{t_2} + \frac{{z}^{2} \cdot t_1}{t_2}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))
        (t_2
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
   (if (<= (/ (* y (+ b (* z (+ a (* z t_1))))) t_2) INFINITY)
     (fma (+ (/ b t_2) (+ (/ (* z a) t_2) (/ (* (pow z 2.0) t_1) t_2))) y x)
     (+ x (* 3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t + (z * (11.1667541262 + (z * 3.13060547623)));
	double t_2 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double tmp;
	if (((y * (b + (z * (a + (z * t_1))))) / t_2) <= ((double) INFINITY)) {
		tmp = fma(((b / t_2) + (((z * a) / t_2) + ((pow(z, 2.0) * t_1) / t_2))), y, x);
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))
	t_2 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	tmp = 0.0
	if (Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t_1))))) / t_2) <= Inf)
		tmp = fma(Float64(Float64(b / t_2) + Float64(Float64(Float64(z * a) / t_2) + Float64(Float64((z ^ 2.0) * t_1) / t_2))), y, x);
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(b + N[(z * N[(a + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], Infinity], N[(N[(N[(b / t$95$2), $MachinePrecision] + N[(N[(N[(z * a), $MachinePrecision] / t$95$2), $MachinePrecision] + N[(N[(N[Power[z, 2.0], $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.8%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in a around 0 95.8%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \left(\frac{a \cdot z}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)}, y, x\right) \]

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 95.6%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 95.6%

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

      2. *-commutative 95.6%

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

   6. Simplified 95.6%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \left(\frac{z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 4: 95.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 95.6%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 95.6%

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

      2. *-commutative 95.6%

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

   6. Simplified 95.6%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

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

Alternative 5: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+69} \lor \neg \left(z \leq 1.55 \cdot 10^{+49}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.32e+69) (not (<= z 1.55e+49)))
   (+ x (* 3.13060547623 y))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+
      0.607771387771
      (*
       z
       (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.32e+69) || !(z <= 1.55e+49)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	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 <= (-1.32d+69)) .or. (.not. (z <= 1.55d+49))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 <= -1.32e+69) || !(z <= 1.55e+49)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.32e+69) or not (z <= 1.55e+49):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.32e+69) || !(z <= 1.55e+49))
		tmp = Float64(x + Float64(3.13060547623 * y));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.32e+69) || ~((z <= 1.55e+49)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.32e+69], N[Not[LessEqual[z, 1.55e+49]], $MachinePrecision]], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.32e69 or 1.54999999999999996e49 < z

   1. Initial program 1.8%

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

   3. Simplified 1.8%

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

   4. Taylor expanded in z around inf 93.3%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 93.3%

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

      2. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   if -1.32e69 < z < 1.54999999999999996e49

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 94.1%

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

      1. *-commutative 86.0%

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

   4. Simplified 94.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+69} \lor \neg \left(z \leq 1.55 \cdot 10^{+49}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]

Alternative 6: 93.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -30000.0)
   (+ x (- (* 3.13060547623 y) (/ (* y 36.52704169880642) z)))
   (if (<= z 6.0)
     (+
      x
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* 3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -30000.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 6.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (3.13060547623 * y);
	}
	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 <= (-30000.0d0)) then
        tmp = x + ((3.13060547623d0 * y) - ((y * 36.52704169880642d0) / z))
    else if (z <= 6.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (3.13060547623d0 * y)
    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 <= -30000.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 6.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -30000.0:
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z))
	elif z <= 6.0:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (3.13060547623 * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -30000.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 * y) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 6.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -30000.0)
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	elseif (z <= 6.0)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (3.13060547623 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -30000.0], N[(x + N[(N[(3.13060547623 * y), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e4

   1. Initial program 19.8%

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

   3. Simplified 22.4%

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

   4. Taylor expanded in z around -inf 83.4%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]
   5. Step-by-step derivation

      1. +-commutative 83.4%

         \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y + -1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} \]

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. *-commutative 83.4%

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

      5. cancel-sign-sub-inv 83.4%

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

      6. metadata-eval 83.4%

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

      7. distribute-rgt-out 83.4%

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

      8. metadata-eval 83.4%

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

   6. Simplified 83.4%

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

   if -3e4 < z < 6

   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. Taylor expanded in z around 0 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   if 6 < z

   1. Initial program 12.3%

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

   3. Simplified 10.9%

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

   4. Taylor expanded in z around inf 89.1%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 89.1%

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

      2. *-commutative 89.1%

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

   6. Simplified 89.1%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 7: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -30000:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -30000.0)
   (+ x (- (* 3.13060547623 y) (/ (* y 36.52704169880642) z)))
   (if (<= z 6.0)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* 3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -30000.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 6.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (3.13060547623 * y);
	}
	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 <= (-30000.0d0)) then
        tmp = x + ((3.13060547623d0 * y) - ((y * 36.52704169880642d0) / z))
    else if (z <= 6.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (3.13060547623d0 * y)
    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 <= -30000.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 6.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -30000.0:
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z))
	elif z <= 6.0:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (3.13060547623 * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -30000.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 * y) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 6.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -30000.0)
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	elseif (z <= 6.0)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (3.13060547623 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -30000.0], N[(x + N[(N[(3.13060547623 * y), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e4

   1. Initial program 19.8%

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

   3. Simplified 22.4%

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

   4. Taylor expanded in z around -inf 83.4%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]
   5. Step-by-step derivation

      1. +-commutative 83.4%

         \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y + -1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} \]

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. *-commutative 83.4%

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

      5. cancel-sign-sub-inv 83.4%

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

      6. metadata-eval 83.4%

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

      7. distribute-rgt-out 83.4%

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

      8. metadata-eval 83.4%

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

   6. Simplified 83.4%

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

   if -3e4 < z < 6

   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. Taylor expanded in z around 0 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in z around 0 98.9%

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

      1. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if 6 < z

   1. Initial program 12.3%

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

   3. Simplified 10.9%

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

   4. Taylor expanded in z around inf 89.1%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 89.1%

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

      2. *-commutative 89.1%

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

   6. Simplified 89.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -30000:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 8: 81.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-91}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-144}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-41}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -6.5e+33)
     t_1
     (if (<= z -1.56e-91)
       (+ x (* 1.6453555072203998 (* z (* a y))))
       (if (<= z 3.8e-144)
         (+ x (* b (* y 1.6453555072203998)))
         (if (<= z 1.4e-41)
           (+ x (* 1.6453555072203998 (* a (* z y))))
           (if (<= z 8.2e-8)
             (+ x (/ (* y b) (+ 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 + (3.13060547623 * y);
	double tmp;
	if (z <= -6.5e+33) {
		tmp = t_1;
	} else if (z <= -1.56e-91) {
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	} else if (z <= 3.8e-144) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 1.4e-41) {
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	} else if (z <= 8.2e-8) {
		tmp = x + ((y * b) / (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 + (3.13060547623d0 * y)
    if (z <= (-6.5d+33)) then
        tmp = t_1
    else if (z <= (-1.56d-91)) then
        tmp = x + (1.6453555072203998d0 * (z * (a * y)))
    else if (z <= 3.8d-144) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 1.4d-41) then
        tmp = x + (1.6453555072203998d0 * (a * (z * y)))
    else if (z <= 8.2d-8) then
        tmp = x + ((y * b) / (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 + (3.13060547623 * y);
	double tmp;
	if (z <= -6.5e+33) {
		tmp = t_1;
	} else if (z <= -1.56e-91) {
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	} else if (z <= 3.8e-144) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 1.4e-41) {
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	} else if (z <= 8.2e-8) {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -6.5e+33:
		tmp = t_1
	elif z <= -1.56e-91:
		tmp = x + (1.6453555072203998 * (z * (a * y)))
	elif z <= 3.8e-144:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 1.4e-41:
		tmp = x + (1.6453555072203998 * (a * (z * y)))
	elif z <= 8.2e-8:
		tmp = x + ((y * b) / (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(3.13060547623 * y))
	tmp = 0.0
	if (z <= -6.5e+33)
		tmp = t_1;
	elseif (z <= -1.56e-91)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(z * Float64(a * y))));
	elseif (z <= 3.8e-144)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 1.4e-41)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(a * Float64(z * y))));
	elseif (z <= 8.2e-8)
		tmp = Float64(x + Float64(Float64(y * b) / 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 + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -6.5e+33)
		tmp = t_1;
	elseif (z <= -1.56e-91)
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	elseif (z <= 3.8e-144)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 1.4e-41)
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	elseif (z <= 8.2e-8)
		tmp = x + ((y * b) / (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[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+33], t$95$1, If[LessEqual[z, -1.56e-91], N[(x + N[(1.6453555072203998 * N[(z * N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-144], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-41], N[(x + N[(1.6453555072203998 * N[(a * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x + N[(N[(y * b), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.49999999999999993e33 or 8.20000000000000063e-8 < z

   1. Initial program 12.9%

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

   3. Simplified 12.7%

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

   4. Taylor expanded in z around inf 88.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -6.49999999999999993e33 < z < -1.5599999999999999e-91

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 64.7%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around 0 64.6%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -1.5599999999999999e-91 < z < 3.79999999999999993e-144

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in b around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 89.5%

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

   9. Simplified 89.5%

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

   if 3.79999999999999993e-144 < z < 1.4000000000000001e-41

   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. Taylor expanded in a around inf 80.3%

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

      1. associate-*r* 80.3%

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

      2. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in z around 0 80.3%

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

   if 1.4000000000000001e-41 < z < 8.20000000000000063e-8

   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. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around 0 83.7%

      \[\leadsto x + \frac{\color{blue}{b \cdot y}}{z \cdot 11.9400905721 + 0.607771387771} \]
   6. Step-by-step derivation

      1. *-commutative 83.7%

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

   7. Simplified 83.7%

      \[\leadsto x + \frac{\color{blue}{y \cdot b}}{z \cdot 11.9400905721 + 0.607771387771} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+33}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-91}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-144}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-41}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 9: 81.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot 11.9400905721\\ t_2 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-142}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{a \cdot \left(z \cdot y\right)}{t_1}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 0.607771387771 (* z 11.9400905721)))
        (t_2 (+ x (* 3.13060547623 y))))
   (if (<= z -6.2e+33)
     t_2
     (if (<= z -3.4e-91)
       (+ x (* 1.6453555072203998 (* z (* a y))))
       (if (<= z 3.8e-142)
         (+ x (* b (* y 1.6453555072203998)))
         (if (<= z 4.6e-39)
           (+ x (/ (* a (* z y)) t_1))
           (if (<= z 8.2e-8) (+ x (/ (* y b) t_1)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * 11.9400905721);
	double t_2 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -6.2e+33) {
		tmp = t_2;
	} else if (z <= -3.4e-91) {
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	} else if (z <= 3.8e-142) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 4.6e-39) {
		tmp = x + ((a * (z * y)) / t_1);
	} else if (z <= 8.2e-8) {
		tmp = x + ((y * b) / 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 = 0.607771387771d0 + (z * 11.9400905721d0)
    t_2 = x + (3.13060547623d0 * y)
    if (z <= (-6.2d+33)) then
        tmp = t_2
    else if (z <= (-3.4d-91)) then
        tmp = x + (1.6453555072203998d0 * (z * (a * y)))
    else if (z <= 3.8d-142) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 4.6d-39) then
        tmp = x + ((a * (z * y)) / t_1)
    else if (z <= 8.2d-8) then
        tmp = x + ((y * b) / 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 = 0.607771387771 + (z * 11.9400905721);
	double t_2 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -6.2e+33) {
		tmp = t_2;
	} else if (z <= -3.4e-91) {
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	} else if (z <= 3.8e-142) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 4.6e-39) {
		tmp = x + ((a * (z * y)) / t_1);
	} else if (z <= 8.2e-8) {
		tmp = x + ((y * b) / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * 11.9400905721)
	t_2 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -6.2e+33:
		tmp = t_2
	elif z <= -3.4e-91:
		tmp = x + (1.6453555072203998 * (z * (a * y)))
	elif z <= 3.8e-142:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 4.6e-39:
		tmp = x + ((a * (z * y)) / t_1)
	elif z <= 8.2e-8:
		tmp = x + ((y * b) / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * 11.9400905721))
	t_2 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -6.2e+33)
		tmp = t_2;
	elseif (z <= -3.4e-91)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(z * Float64(a * y))));
	elseif (z <= 3.8e-142)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 4.6e-39)
		tmp = Float64(x + Float64(Float64(a * Float64(z * y)) / t_1));
	elseif (z <= 8.2e-8)
		tmp = Float64(x + Float64(Float64(y * b) / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * 11.9400905721);
	t_2 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -6.2e+33)
		tmp = t_2;
	elseif (z <= -3.4e-91)
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	elseif (z <= 3.8e-142)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 4.6e-39)
		tmp = x + ((a * (z * y)) / t_1);
	elseif (z <= 8.2e-8)
		tmp = x + ((y * b) / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+33], t$95$2, If[LessEqual[z, -3.4e-91], N[(x + N[(1.6453555072203998 * N[(z * N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-142], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-39], N[(x + N[(N[(a * N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x + N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.2e33 or 8.20000000000000063e-8 < z

   1. Initial program 12.9%

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

   3. Simplified 12.7%

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

   4. Taylor expanded in z around inf 88.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -6.2e33 < z < -3.40000000000000027e-91

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 64.7%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around 0 64.6%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -3.40000000000000027e-91 < z < 3.79999999999999972e-142

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in b around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 89.5%

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

   9. Simplified 89.5%

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

   if 3.79999999999999972e-142 < z < 4.60000000000000016e-39

   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. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in a around inf 80.3%

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

   if 4.60000000000000016e-39 < z < 8.20000000000000063e-8

   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. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around 0 83.7%

      \[\leadsto x + \frac{\color{blue}{b \cdot y}}{z \cdot 11.9400905721 + 0.607771387771} \]
   6. Step-by-step derivation

      1. *-commutative 83.7%

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

   7. Simplified 83.7%

      \[\leadsto x + \frac{\color{blue}{y \cdot b}}{z \cdot 11.9400905721 + 0.607771387771} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+33}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-142}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{a \cdot \left(z \cdot y\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 10: 89.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+33} \lor \neg \left(z \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + \left(a \cdot 1.6453555072203998\right) \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e+33) (not (<= z 8.2e-8)))
   (+ x (* 3.13060547623 y))
   (+
    x
    (+ (* 1.6453555072203998 (* y b)) (* (* a 1.6453555072203998) (* z y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+33) || !(z <= 8.2e-8)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((1.6453555072203998 * (y * b)) + ((a * 1.6453555072203998) * (z * y)));
	}
	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 <= (-2.8d+33)) .or. (.not. (z <= 8.2d-8))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + ((1.6453555072203998d0 * (y * b)) + ((a * 1.6453555072203998d0) * (z * y)))
    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 <= -2.8e+33) || !(z <= 8.2e-8)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((1.6453555072203998 * (y * b)) + ((a * 1.6453555072203998) * (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e+33) or not (z <= 8.2e-8):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + ((1.6453555072203998 * (y * b)) + ((a * 1.6453555072203998) * (z * y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e+33) || !(z <= 8.2e-8))
		tmp = Float64(x + Float64(3.13060547623 * y));
	else
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(Float64(a * 1.6453555072203998) * Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e+33) || ~((z <= 8.2e-8)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + ((1.6453555072203998 * (y * b)) + ((a * 1.6453555072203998) * (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e+33], N[Not[LessEqual[z, 8.2e-8]], $MachinePrecision]], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 1.6453555072203998), $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e33 or 8.20000000000000063e-8 < z

   1. Initial program 12.9%

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

   3. Simplified 12.7%

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

   4. Taylor expanded in z around inf 88.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -2.8000000000000001e33 < z < 8.20000000000000063e-8

   1. Initial program 98.2%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 85.0%

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

   5. Taylor expanded in a around inf 89.4%

      \[\leadsto x + \left(1.6453555072203998 \cdot \left(b \cdot y\right) + \color{blue}{1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)}\right) \]
   6. Step-by-step derivation

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+33} \lor \neg \left(z \leq 8.2 \cdot 10^{-8}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + \left(a \cdot 1.6453555072203998\right) \cdot \left(z \cdot y\right)\right)\\ \end{array} \]

Alternative 11: 80.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-67}:\\ \;\;\;\;x + 0.031777292960723624 \cdot \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-142}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -4.1e+86)
     t_1
     (if (<= z -2.05e-67)
       (+ x (* 0.031777292960723624 (/ a (/ z y))))
       (if (<= z 3.8e-142)
         (+ x (* b (* y 1.6453555072203998)))
         (if (<= z 2.8e-41)
           (+ x (* 1.6453555072203998 (* a (* z y))))
           (if (<= z 8.2e-8) (+ x (* y (* b 1.6453555072203998))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -4.1e+86) {
		tmp = t_1;
	} else if (z <= -2.05e-67) {
		tmp = x + (0.031777292960723624 * (a / (z / y)));
	} else if (z <= 3.8e-142) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 2.8e-41) {
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	} else if (z <= 8.2e-8) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-4.1d+86)) then
        tmp = t_1
    else if (z <= (-2.05d-67)) then
        tmp = x + (0.031777292960723624d0 * (a / (z / y)))
    else if (z <= 3.8d-142) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 2.8d-41) then
        tmp = x + (1.6453555072203998d0 * (a * (z * y)))
    else if (z <= 8.2d-8) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -4.1e+86) {
		tmp = t_1;
	} else if (z <= -2.05e-67) {
		tmp = x + (0.031777292960723624 * (a / (z / y)));
	} else if (z <= 3.8e-142) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 2.8e-41) {
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	} else if (z <= 8.2e-8) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -4.1e+86:
		tmp = t_1
	elif z <= -2.05e-67:
		tmp = x + (0.031777292960723624 * (a / (z / y)))
	elif z <= 3.8e-142:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 2.8e-41:
		tmp = x + (1.6453555072203998 * (a * (z * y)))
	elif z <= 8.2e-8:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -4.1e+86)
		tmp = t_1;
	elseif (z <= -2.05e-67)
		tmp = Float64(x + Float64(0.031777292960723624 * Float64(a / Float64(z / y))));
	elseif (z <= 3.8e-142)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 2.8e-41)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(a * Float64(z * y))));
	elseif (z <= 8.2e-8)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -4.1e+86)
		tmp = t_1;
	elseif (z <= -2.05e-67)
		tmp = x + (0.031777292960723624 * (a / (z / y)));
	elseif (z <= 3.8e-142)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 2.8e-41)
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	elseif (z <= 8.2e-8)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+86], t$95$1, If[LessEqual[z, -2.05e-67], N[(x + N[(0.031777292960723624 * N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-142], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e-41], N[(x + N[(1.6453555072203998 * N[(a * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.0999999999999999e86 or 8.20000000000000063e-8 < z

   1. Initial program 8.2%

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

   3. Simplified 7.4%

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

   4. Taylor expanded in z around inf 91.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 91.0%

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

      2. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   if -4.0999999999999999e86 < z < -2.0499999999999999e-67

   1. Initial program 81.9%

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

   2. Taylor expanded in a around inf 63.9%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in z around inf 63.9%

      \[\leadsto x + \color{blue}{0.031777292960723624 \cdot \frac{a \cdot y}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 66.8%

         \[\leadsto x + 0.031777292960723624 \cdot \color{blue}{\frac{a}{\frac{z}{y}}} \]

   10. Simplified 66.8%

       \[\leadsto x + \color{blue}{0.031777292960723624 \cdot \frac{a}{\frac{z}{y}}} \]

   if -2.0499999999999999e-67 < z < 3.79999999999999972e-142

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 86.6%

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

      1. associate-*r* 86.5%

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

      2. *-commutative 86.5%

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

   6. Simplified 86.5%

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

   7. Taylor expanded in b around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. associate-*r* 86.6%

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

   9. Simplified 86.6%

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

   if 3.79999999999999972e-142 < z < 2.8000000000000002e-41

   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. Taylor expanded in a around inf 80.3%

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

      1. associate-*r* 80.3%

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

      2. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in z around 0 80.3%

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

   if 2.8000000000000002e-41 < z < 8.20000000000000063e-8

   1. Initial program 99.7%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

      \[\leadsto x + \color{blue}{\left(b \cdot 1.6453555072203998\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-67}:\\ \;\;\;\;x + 0.031777292960723624 \cdot \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-142}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-41}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 12: 81.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-92}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-146}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-40}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -2.8e+33)
     t_1
     (if (<= z -7.2e-92)
       (+ x (* 1.6453555072203998 (* z (* a y))))
       (if (<= z 4.5e-146)
         (+ x (* b (* y 1.6453555072203998)))
         (if (<= z 4.5e-40)
           (+ x (* 1.6453555072203998 (* a (* z y))))
           (if (<= z 8.2e-8) (+ x (* y (* b 1.6453555072203998))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -2.8e+33) {
		tmp = t_1;
	} else if (z <= -7.2e-92) {
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	} else if (z <= 4.5e-146) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 4.5e-40) {
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	} else if (z <= 8.2e-8) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-2.8d+33)) then
        tmp = t_1
    else if (z <= (-7.2d-92)) then
        tmp = x + (1.6453555072203998d0 * (z * (a * y)))
    else if (z <= 4.5d-146) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 4.5d-40) then
        tmp = x + (1.6453555072203998d0 * (a * (z * y)))
    else if (z <= 8.2d-8) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -2.8e+33) {
		tmp = t_1;
	} else if (z <= -7.2e-92) {
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	} else if (z <= 4.5e-146) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 4.5e-40) {
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	} else if (z <= 8.2e-8) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -2.8e+33:
		tmp = t_1
	elif z <= -7.2e-92:
		tmp = x + (1.6453555072203998 * (z * (a * y)))
	elif z <= 4.5e-146:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 4.5e-40:
		tmp = x + (1.6453555072203998 * (a * (z * y)))
	elif z <= 8.2e-8:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -2.8e+33)
		tmp = t_1;
	elseif (z <= -7.2e-92)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(z * Float64(a * y))));
	elseif (z <= 4.5e-146)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 4.5e-40)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(a * Float64(z * y))));
	elseif (z <= 8.2e-8)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -2.8e+33)
		tmp = t_1;
	elseif (z <= -7.2e-92)
		tmp = x + (1.6453555072203998 * (z * (a * y)));
	elseif (z <= 4.5e-146)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 4.5e-40)
		tmp = x + (1.6453555072203998 * (a * (z * y)));
	elseif (z <= 8.2e-8)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+33], t$95$1, If[LessEqual[z, -7.2e-92], N[(x + N[(1.6453555072203998 * N[(z * N[(a * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-146], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-40], N[(x + N[(1.6453555072203998 * N[(a * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.8000000000000001e33 or 8.20000000000000063e-8 < z

   1. Initial program 12.9%

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

   3. Simplified 12.7%

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

   4. Taylor expanded in z around inf 88.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -2.8000000000000001e33 < z < -7.20000000000000032e-92

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 64.7%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around 0 64.6%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

   7. Simplified 71.2%

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

   if -7.20000000000000032e-92 < z < 4.5000000000000001e-146

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. associate-*r* 89.4%

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

      2. *-commutative 89.4%

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

   6. Simplified 89.4%

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

   7. Taylor expanded in b around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 89.5%

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

   9. Simplified 89.5%

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

   if 4.5000000000000001e-146 < z < 4.5000000000000001e-40

   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. Taylor expanded in a around inf 80.3%

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

      1. associate-*r* 80.3%

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

      2. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in z around 0 80.3%

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

   if 4.5000000000000001e-40 < z < 8.20000000000000063e-8

   1. Initial program 99.7%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   6. Simplified 81.8%

      \[\leadsto x + \color{blue}{\left(b \cdot 1.6453555072203998\right) \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-92}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(z \cdot \left(a \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-146}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-40}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(z \cdot y\right)\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 13: 81.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-68}:\\ \;\;\;\;x + 0.031777292960723624 \cdot \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -4.1e+86)
     t_1
     (if (<= z -4.7e-68)
       (+ x (* 0.031777292960723624 (/ a (/ z y))))
       (if (<= z 8.2e-8) (+ x (* b (* y 1.6453555072203998))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -4.1e+86) {
		tmp = t_1;
	} else if (z <= -4.7e-68) {
		tmp = x + (0.031777292960723624 * (a / (z / y)));
	} else if (z <= 8.2e-8) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-4.1d+86)) then
        tmp = t_1
    else if (z <= (-4.7d-68)) then
        tmp = x + (0.031777292960723624d0 * (a / (z / y)))
    else if (z <= 8.2d-8) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -4.1e+86) {
		tmp = t_1;
	} else if (z <= -4.7e-68) {
		tmp = x + (0.031777292960723624 * (a / (z / y)));
	} else if (z <= 8.2e-8) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -4.1e+86:
		tmp = t_1
	elif z <= -4.7e-68:
		tmp = x + (0.031777292960723624 * (a / (z / y)))
	elif z <= 8.2e-8:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -4.1e+86)
		tmp = t_1;
	elseif (z <= -4.7e-68)
		tmp = Float64(x + Float64(0.031777292960723624 * Float64(a / Float64(z / y))));
	elseif (z <= 8.2e-8)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -4.1e+86)
		tmp = t_1;
	elseif (z <= -4.7e-68)
		tmp = x + (0.031777292960723624 * (a / (z / y)));
	elseif (z <= 8.2e-8)
		tmp = x + (b * (y * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+86], t$95$1, If[LessEqual[z, -4.7e-68], N[(x + N[(0.031777292960723624 * N[(a / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-8], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0999999999999999e86 or 8.20000000000000063e-8 < z

   1. Initial program 8.2%

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

   3. Simplified 7.4%

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

   4. Taylor expanded in z around inf 91.0%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 91.0%

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

      2. *-commutative 91.0%

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

   6. Simplified 91.0%

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

   if -4.0999999999999999e86 < z < -4.69999999999999988e-68

   1. Initial program 81.9%

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

   2. Taylor expanded in a around inf 63.9%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in z around 0 66.7%

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

      1. *-commutative 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in z around inf 63.9%

      \[\leadsto x + \color{blue}{0.031777292960723624 \cdot \frac{a \cdot y}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 66.8%

         \[\leadsto x + 0.031777292960723624 \cdot \color{blue}{\frac{a}{\frac{z}{y}}} \]

   10. Simplified 66.8%

       \[\leadsto x + \color{blue}{0.031777292960723624 \cdot \frac{a}{\frac{z}{y}}} \]

   if -4.69999999999999988e-68 < z < 8.20000000000000063e-8

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. associate-*r* 81.0%

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

      2. *-commutative 81.0%

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

   6. Simplified 81.0%

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

   7. Taylor expanded in b around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-*r* 81.1%

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

   9. Simplified 81.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+86}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-68}:\\ \;\;\;\;x + 0.031777292960723624 \cdot \frac{a}{\frac{z}{y}}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-8}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]

Alternative 14: 83.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1020000 \lor \neg \left(z \leq 2.7 \cdot 10^{-8}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1020000.0) (not (<= z 2.7e-8)))
   (+ x (* 3.13060547623 y))
   (+ x (* b (* y 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1020000.0) || !(z <= 2.7e-8)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	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 <= (-1020000.0d0)) .or. (.not. (z <= 2.7d-8))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + (b * (y * 1.6453555072203998d0))
    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 <= -1020000.0) || !(z <= 2.7e-8)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1020000.0) or not (z <= 2.7e-8):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + (b * (y * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1020000.0) || !(z <= 2.7e-8))
		tmp = Float64(x + Float64(3.13060547623 * y));
	else
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1020000.0) || ~((z <= 2.7e-8)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + (b * (y * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1020000.0], N[Not[LessEqual[z, 2.7e-8]], $MachinePrecision]], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02e6 or 2.70000000000000002e-8 < z

   1. Initial program 16.4%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in z around inf 85.6%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 85.6%

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

      2. *-commutative 85.6%

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

   6. Simplified 85.6%

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

   if -1.02e6 < z < 2.70000000000000002e-8

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 78.3%

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

      1. associate-*r* 78.3%

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

      2. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in b around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-*r* 78.3%

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

   9. Simplified 78.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020000 \lor \neg \left(z \leq 2.7 \cdot 10^{-8}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 15: 63.0% accurate, 7.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 53.5%

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

3. Simplified 53.8%

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

4. Taylor expanded in z around inf 66.3%

   \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
5. Step-by-step derivation

   1. +-commutative 66.3%

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

   2. *-commutative 66.3%

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

6. Simplified 66.3%

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

7. Final simplification 66.3%

   \[\leadsto x + 3.13060547623 \cdot y \]

Alternative 16: 44.9% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 53.5%

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

3. Simplified 53.8%

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

4. Taylor expanded in y around 0 47.8%

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

5. Final simplification 47.8%

   \[\leadsto x \]

Developer target: 98.5% accurate, 0.9× 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 2023322 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0)))))

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