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

Percentage Accurate: 58.5% → 99.2%

Time: 21.3s

Alternatives: 17

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: 58.5% 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: 99.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+24} \lor \neg \left(z \leq 1.55 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.6e+24) (not (<= z 1.55e+35)))
   (fma
    (+
     (+
      (+ (/ 457.9610022158428 (pow z 2.0)) (/ t (pow z 2.0)))
      (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
     (+ 3.13060547623 (/ -36.52704169880642 z)))
    y
    x)
   (+
    x
    (*
     (/
      y
      (fma
       z
       (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
       0.607771387771))
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.6e+24) || !(z <= 1.55e+35)) {
		tmp = fma(((((457.9610022158428 / pow(z, 2.0)) + (t / pow(z, 2.0))) + ((a + (-5864.8025282699045 + (t * -15.234687407))) / pow(z, 3.0))) + (3.13060547623 + (-36.52704169880642 / z))), y, x);
	} else {
		tmp = x + ((y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)) * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.6e+24) || !(z <= 1.55e+35))
		tmp = fma(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(3.13060547623 + Float64(-36.52704169880642 / z))), y, x);
	else
		tmp = Float64(x + Float64(Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)) * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.6e+24], N[Not[LessEqual[z, 1.55e+35]], $MachinePrecision]], N[(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[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5999999999999998e24 or 1.54999999999999993e35 < z

   1. Initial program 7.9%

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

   3. Simplified 14.5%

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

   5. Taylor expanded in z around -inf 99.2%

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

   7. Simplified 99.2%

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

   if -4.5999999999999998e24 < z < 1.54999999999999993e35

   1. Initial program 99.0%

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

   3. Simplified 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. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+24} \lor \neg \left(z \leq 1.55 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+28} \lor \neg \left(z \leq 6.2 \cdot 10^{+37}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{-0.607771387771 - z \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.25e+28) (not (<= z 6.2e+37)))
   (fma
    (+
     (+
      (+ (/ 457.9610022158428 (pow z 2.0)) (/ t (pow z 2.0)))
      (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
     (+ 3.13060547623 (/ -36.52704169880642 z)))
    y
    x)
   (+
    x
    (/
     -1.0
     (/
      (/
       (-
        -0.607771387771
        (* z (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)))
       (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b))
      y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.25e+28) || !(z <= 6.2e+37)) {
		tmp = fma(((((457.9610022158428 / pow(z, 2.0)) + (t / pow(z, 2.0))) + ((a + (-5864.8025282699045 + (t * -15.234687407))) / pow(z, 3.0))) + (3.13060547623 + (-36.52704169880642 / z))), y, x);
	} else {
		tmp = x + (-1.0 / (((-0.607771387771 - (z * fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721))) / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)) / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.25e+28) || !(z <= 6.2e+37))
		tmp = fma(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(3.13060547623 + Float64(-36.52704169880642 / z))), y, x);
	else
		tmp = Float64(x + Float64(-1.0 / Float64(Float64(Float64(-0.607771387771 - Float64(z * fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721))) / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.25e+28], N[Not[LessEqual[z, 6.2e+37]], $MachinePrecision]], N[(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[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(-1.0 / N[(N[(N[(-0.607771387771 - N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.24999999999999985e28 or 6.2000000000000004e37 < z

   1. Initial program 7.1%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in z around -inf 99.2%

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

   7. Simplified 99.2%

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

   if -2.24999999999999985e28 < z < 6.2000000000000004e37

   1. Initial program 99.0%

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

   3. Simplified 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. Add Preprocessing

   6. Applied egg-rr 99.0%

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

   8. Simplified 99.7%

      \[\leadsto x + \color{blue}{\frac{-1}{\frac{\frac{-0.607771387771 - z \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}{y}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+28} \lor \neg \left(z \leq 6.2 \cdot 10^{+37}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{\frac{-0.607771387771 - z \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;z \leq -4100000000000 \lor \neg \left(z \leq 5 \cdot 10^{+34}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{t_1} + \left(\frac{z \cdot a}{t_1} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)}{t_1}\right), y, x\right)\\ \end{array} \end{array} \]

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 -4100000000000.0) (not (<= z 5e+34)))
     (fma
      (+
       (+
        (+ (/ 457.9610022158428 (pow z 2.0)) (/ t (pow z 2.0)))
        (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) (pow z 3.0)))
       (+ 3.13060547623 (/ -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 <= -4100000000000.0) || !(z <= 5e+34)) {
		tmp = fma(((((457.9610022158428 / pow(z, 2.0)) + (t / pow(z, 2.0))) + ((a + (-5864.8025282699045 + (t * -15.234687407))) / pow(z, 3.0))) + (3.13060547623 + (-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 <= -4100000000000.0) || !(z <= 5e+34))
		tmp = fma(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(3.13060547623 + 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, -4100000000000.0], N[Not[LessEqual[z, 5e+34]], $MachinePrecision]], N[(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[(3.13060547623 + 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 < -4.1e12 or 4.9999999999999998e34 < z

   1. Initial program 9.3%

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

   3. Simplified 15.8%

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

   5. Taylor expanded in z around -inf 99.2%

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

   7. Simplified 99.2%

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

   if -4.1e12 < z < 4.9999999999999998e34

   1. Initial program 99.0%

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

   3. Simplified 99.6%

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

   5. 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 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4100000000000 \lor \neg \left(z \leq 5 \cdot 10^{+34}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(\left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{{z}^{3}}\right) + \left(3.13060547623 + \frac{-36.52704169880642}{z}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \left(\frac{z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\right), y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot t_1\right)\right)}{t_2} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{t_2} + \left(\frac{z \cdot a}{t_2} + \frac{{z}^{2} \cdot t_1}{t_2}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(3.13060547623 + \frac{457.9610022158428 + t}{{z}^{2}}\right) + 36.52704169880642 \cdot \frac{-1}{z}, y, x\right)\\ \end{array} \end{array} \]

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 t) (pow z 2.0)))
       (* 36.52704169880642 (/ -1.0 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 + t) / pow(z, 2.0))) + (36.52704169880642 * (-1.0 / 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(Float64(3.13060547623 + Float64(Float64(457.9610022158428 + t) / (z ^ 2.0))) + Float64(36.52704169880642 * Float64(-1.0 / 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[(N[(3.13060547623 + N[(N[(457.9610022158428 + t), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(36.52704169880642 * N[(-1.0 / 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 90.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in a around 0 95.9%

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

   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. Add Preprocessing

   5. Taylor expanded in b around 0 0.0%

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

   6. Taylor expanded in z around -inf 100.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \left(\frac{z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \frac{{z}^{2} \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\right), y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(3.13060547623 + \frac{457.9610022158428 + t}{{z}^{2}}\right) + 36.52704169880642 \cdot \frac{-1}{z}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+28} \lor \neg \left(z \leq 6.5 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(3.13060547623 + \frac{457.9610022158428 + t}{{z}^{2}}\right) + 36.52704169880642 \cdot \frac{-1}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(z \cdot \left(z \cdot 3.13060547623\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.9e+28) (not (<= z 6.5e+35)))
   (fma
    (+
     (+ 3.13060547623 (/ (+ 457.9610022158428 t) (pow z 2.0)))
     (* 36.52704169880642 (/ -1.0 z)))
    y
    x)
   (+
    x
    (/
     (*
      y
      (+
       b
       (*
        z
        (+ a (* z (+ t (+ (* z (* z 3.13060547623)) (* 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 <= -2.9e+28) || !(z <= 6.5e+35)) {
		tmp = fma(((3.13060547623 + ((457.9610022158428 + t) / pow(z, 2.0))) + (36.52704169880642 * (-1.0 / z))), y, x);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= -2.9e+28) || !(z <= 6.5e+35))
		tmp = fma(Float64(Float64(3.13060547623 + Float64(Float64(457.9610022158428 + t) / (z ^ 2.0))) + Float64(36.52704169880642 * Float64(-1.0 / z))), y, x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(Float64(z * Float64(z * 3.13060547623)) + 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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.9e+28], N[Not[LessEqual[z, 6.5e+35]], $MachinePrecision]], N[(N[(N[(3.13060547623 + N[(N[(457.9610022158428 + t), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(36.52704169880642 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(N[(z * N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(z * 11.1667541262), $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]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e28 or 6.5000000000000003e35 < z

   1. Initial program 7.1%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in b around 0 13.1%

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

   6. Taylor expanded in z around -inf 96.4%

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

   if -2.9000000000000001e28 < z < 6.5000000000000003e35

   1. Initial program 99.0%

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

      1. *-commutative 93.5%

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

      2. distribute-lft-in 93.5%

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

   4. Applied egg-rr 99.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+28} \lor \neg \left(z \leq 6.5 \cdot 10^{+35}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(3.13060547623 + \frac{457.9610022158428 + t}{{z}^{2}}\right) + 36.52704169880642 \cdot \frac{-1}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(z \cdot \left(z \cdot 3.13060547623\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 6.1 \cdot 10^{+59}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(z \cdot \left(z \cdot 3.13060547623\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+30) (not (<= z 6.1e+59)))
   (+ x (* 3.13060547623 y))
   (+
    x
    (/
     (*
      y
      (+
       b
       (*
        z
        (+ a (* z (+ t (+ (* z (* z 3.13060547623)) (* 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 <= -4.5e+30) || !(z <= 6.1e+59)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= (-4.5d+30)) .or. (.not. (z <= 6.1d+59))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623d0)) + (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 <= -4.5e+30) || !(z <= 6.1e+59)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= -4.5e+30) or not (z <= 6.1e+59):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= -4.5e+30) || !(z <= 6.1e+59))
		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(Float64(z * Float64(z * 3.13060547623)) + 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 <= -4.5e+30) || ~((z <= 6.1e+59)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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, -4.5e+30], N[Not[LessEqual[z, 6.1e+59]], $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[(N[(z * N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(z * 11.1667541262), $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]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999995e30 or 6.09999999999999973e59 < z

   1. Initial program 3.1%

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

   3. Simplified 7.1%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   if -4.49999999999999995e30 < z < 6.09999999999999973e59

   1. Initial program 95.8%

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

      1. *-commutative 88.5%

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

      2. distribute-lft-in 88.5%

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

   4. Applied egg-rr 95.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 6.1 \cdot 10^{+59}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(z \cdot \left(z \cdot 3.13060547623\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+30} \lor \neg \left(z \leq 2.9 \cdot 10^{+60}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+30) (not (<= z 2.9e+60)))
   (+ x (* 3.13060547623 y))
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+
      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 <= -1.3e+30) || !(z <= 2.9e+60)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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 <= (-1.3d+30)) .or. (.not. (z <= 2.9d+60))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (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 <= -1.3e+30) || !(z <= 2.9e+60)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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 <= -1.3e+30) or not (z <= 2.9e+60):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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 <= -1.3e+30) || !(z <= 2.9e+60))
		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 * 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)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.3e+30) || ~((z <= 2.9e+60)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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, -1.3e+30], N[Not[LessEqual[z, 2.9e+60]], $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 * 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]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.29999999999999994e30 or 2.9e60 < z

   1. Initial program 3.1%

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

   3. Simplified 7.1%

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

   5. Taylor expanded in z around inf 93.9%

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

      1. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   if -1.29999999999999994e30 < z < 2.9e60

   1. Initial program 95.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+30} \lor \neg \left(z \leq 2.9 \cdot 10^{+60}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+27} \lor \neg \left(z \leq 6.5 \cdot 10^{+34}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e+27) (not (<= z 6.5e+34)))
   (+ 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 <= -6.2e+27) || !(z <= 6.5e+34)) {
		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 <= (-6.2d+27)) .or. (.not. (z <= 6.5d+34))) 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 <= -6.2e+27) || !(z <= 6.5e+34)) {
		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 <= -6.2e+27) or not (z <= 6.5e+34):
		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 <= -6.2e+27) || !(z <= 6.5e+34))
		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 <= -6.2e+27) || ~((z <= 6.5e+34)))
		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, -6.2e+27], N[Not[LessEqual[z, 6.5e+34]], $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 < -6.19999999999999992e27 or 6.50000000000000017e34 < z

   1. Initial program 7.9%

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

   3. Simplified 14.4%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

   7. Simplified 90.7%

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

   if -6.19999999999999992e27 < z < 6.50000000000000017e34

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 97.4%

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

      1. *-commutative 94.1%

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

   5. Simplified 97.4%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+27} \lor \neg \left(z \leq 6.5 \cdot 10^{+34}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(z \cdot \left(z \cdot 3.13060547623\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+ x (- (* 3.13060547623 y) (/ (* y 36.52704169880642) z)))
   (if (<= z 1.85e+34)
     (+
      x
      (/
       (*
        y
        (+
         b
         (*
          z
          (+
           a
           (* z (+ t (+ (* z (* z 3.13060547623)) (* 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 <= -13.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 1.85e+34) {
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= (-13.0d0)) then
        tmp = x + ((3.13060547623d0 * y) - ((y * 36.52704169880642d0) / z))
    else if (z <= 1.85d+34) then
        tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623d0)) + (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 <= -13.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 1.85e+34) {
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= -13.0:
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z))
	elif z <= 1.85e+34:
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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 <= -13.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 * y) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 1.85e+34)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(Float64(z * Float64(z * 3.13060547623)) + 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 <= -13.0)
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	elseif (z <= 1.85e+34)
		tmp = x + ((y * (b + (z * (a + (z * (t + ((z * (z * 3.13060547623)) + (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, -13.0], N[(x + N[(N[(3.13060547623 * y), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.85e+34], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(N[(z * N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(z * 11.1667541262), $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 < -13

   1. Initial program 13.1%

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

   3. Simplified 20.2%

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

   5. Taylor expanded in z around -inf 86.4%

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

      1. +-commutative 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

      4. *-commutative 86.4%

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

      5. distribute-rgt-out-- 86.4%

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

      6. metadata-eval 86.4%

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

   7. Simplified 86.4%

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

   if -13 < z < 1.85000000000000004e34

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 96.4%

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

      1. *-commutative 96.4%

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

   5. Simplified 96.4%

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

      1. *-commutative 96.4%

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

      2. distribute-lft-in 96.4%

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

   7. Applied egg-rr 96.4%

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

   if 1.85000000000000004e34 < z

   1. Initial program 8.3%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

   7. Simplified 91.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+34}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \left(z \cdot \left(z \cdot 3.13060547623\right) + z \cdot 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+ x (- (* 3.13060547623 y) (/ (* y 36.52704169880642) z)))
   (if (<= z 8.2e+33)
     (+
      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 <= -13.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 8.2e+33) {
		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 <= (-13.0d0)) then
        tmp = x + ((3.13060547623d0 * y) - ((y * 36.52704169880642d0) / z))
    else if (z <= 8.2d+33) 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 <= -13.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 8.2e+33) {
		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 <= -13.0:
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z))
	elif z <= 8.2e+33:
		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 <= -13.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 * y) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 8.2e+33)
		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 <= -13.0)
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	elseif (z <= 8.2e+33)
		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, -13.0], N[(x + N[(N[(3.13060547623 * y), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+33], 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 < -13

   1. Initial program 13.1%

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

   3. Simplified 20.2%

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

   5. Taylor expanded in z around -inf 86.4%

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

      1. +-commutative 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

      4. *-commutative 86.4%

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

      5. distribute-rgt-out-- 86.4%

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

      6. metadata-eval 86.4%

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

   7. Simplified 86.4%

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

   if -13 < z < 8.1999999999999999e33

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 96.4%

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

      1. *-commutative 96.4%

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

   5. Simplified 96.4%

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

   if 8.1999999999999999e33 < z

   1. Initial program 8.3%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

   7. Simplified 91.9%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+ x (- (* 3.13060547623 y) (/ (* y 36.52704169880642) z)))
   (if (<= z 9.5e+33)
     (+
      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 <= -13.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 9.5e+33) {
		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 <= (-13.0d0)) then
        tmp = x + ((3.13060547623d0 * y) - ((y * 36.52704169880642d0) / z))
    else if (z <= 9.5d+33) 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 <= -13.0) {
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	} else if (z <= 9.5e+33) {
		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 <= -13.0:
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z))
	elif z <= 9.5e+33:
		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 <= -13.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 * y) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 9.5e+33)
		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 <= -13.0)
		tmp = x + ((3.13060547623 * y) - ((y * 36.52704169880642) / z));
	elseif (z <= 9.5e+33)
		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, -13.0], N[(x + N[(N[(3.13060547623 * y), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+33], 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 < -13

   1. Initial program 13.1%

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

   3. Simplified 20.2%

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

   5. Taylor expanded in z around -inf 86.4%

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

      1. +-commutative 86.4%

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

      2. mul-1-neg 86.4%

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

      3. unsub-neg 86.4%

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

      4. *-commutative 86.4%

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

      5. distribute-rgt-out-- 86.4%

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

      6. metadata-eval 86.4%

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

   7. Simplified 86.4%

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

   if -13 < z < 9.5000000000000003e33

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 96.4%

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

      1. *-commutative 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in z around 0 96.2%

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

      1. *-commutative 96.2%

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

   8. Simplified 96.2%

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

   if 9.5000000000000003e33 < z

   1. Initial program 8.3%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

   7. Simplified 91.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(3.13060547623 \cdot y - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19} \lor \neg \left(z \leq 1.35 \cdot 10^{+34}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e+19) (not (<= z 1.35e+34)))
   (+ x (* 3.13060547623 y))
   (+
    x
    (/
     (* y b)
     (+
      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 <= -1.9e+19) || !(z <= 1.35e+34)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * b) / (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 <= (-1.9d+19)) .or. (.not. (z <= 1.35d+34))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + ((y * b) / (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 <= -1.9e+19) || !(z <= 1.35e+34)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * b) / (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 <= -1.9e+19) or not (z <= 1.35e+34):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + ((y * b) / (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 <= -1.9e+19) || !(z <= 1.35e+34))
		tmp = Float64(x + Float64(3.13060547623 * y));
	else
		tmp = Float64(x + Float64(Float64(y * b) / 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 <= -1.9e+19) || ~((z <= 1.35e+34)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + ((y * b) / (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, -1.9e+19], N[Not[LessEqual[z, 1.35e+34]], $MachinePrecision]], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $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 < -1.9e19 or 1.35e34 < z

   1. Initial program 7.9%

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

   3. Simplified 14.4%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

   7. Simplified 90.7%

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

   if -1.9e19 < z < 1.35e34

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 83.6%

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

      1. *-commutative 83.6%

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

   5. Simplified 83.6%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19} \lor \neg \left(z \leq 1.35 \cdot 10^{+34}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 84.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+17} \lor \neg \left(z \leq 6.2 \cdot 10^{+35}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e+17) (not (<= z 6.2e+35)))
   (+ x (* 3.13060547623 y))
   (+ x (* (* y b) 1.6453555072203998))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e+17) || !(z <= 6.2e+35)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * b) * 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 <= (-1.8d+17)) .or. (.not. (z <= 6.2d+35))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + ((y * b) * 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 <= -1.8e+17) || !(z <= 6.2e+35)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + ((y * b) * 1.6453555072203998);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e+17) or not (z <= 6.2e+35):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + ((y * b) * 1.6453555072203998)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e+17) || !(z <= 6.2e+35))
		tmp = Float64(x + Float64(3.13060547623 * y));
	else
		tmp = Float64(x + Float64(Float64(y * b) * 1.6453555072203998));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.8e+17) || ~((z <= 6.2e+35)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + ((y * b) * 1.6453555072203998);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e+17], N[Not[LessEqual[z, 6.2e+35]], $MachinePrecision]], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e17 or 6.19999999999999973e35 < z

   1. Initial program 7.9%

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

   3. Simplified 14.4%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

   7. Simplified 90.7%

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

   if -1.8e17 < z < 6.19999999999999973e35

   1. Initial program 99.0%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in z around 0 83.0%

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

      1. *-commutative 83.0%

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

   7. Simplified 83.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+17} \lor \neg \left(z \leq 6.2 \cdot 10^{+35}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+19} \lor \neg \left(z \leq 5.6 \cdot 10^{+33}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.5e+19) (not (<= z 5.6e+33)))
   (+ x (* 3.13060547623 y))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.5e+19) || !(z <= 5.6e+33)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + (y * (b * 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 <= (-2.5d+19)) .or. (.not. (z <= 5.6d+33))) then
        tmp = x + (3.13060547623d0 * y)
    else
        tmp = x + (y * (b * 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 <= -2.5e+19) || !(z <= 5.6e+33)) {
		tmp = x + (3.13060547623 * y);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.5e+19) or not (z <= 5.6e+33):
		tmp = x + (3.13060547623 * y)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.5e+19) || !(z <= 5.6e+33))
		tmp = Float64(x + Float64(3.13060547623 * y));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.5e+19) || ~((z <= 5.6e+33)))
		tmp = x + (3.13060547623 * y);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.5e+19], N[Not[LessEqual[z, 5.6e+33]], $MachinePrecision]], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e19 or 5.6000000000000002e33 < z

   1. Initial program 7.9%

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

   3. Simplified 14.4%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

   7. Simplified 90.7%

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

   if -2.5e19 < z < 5.6000000000000002e33

   1. Initial program 99.0%

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

   3. Simplified 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. Add Preprocessing

   5. Taylor expanded in z around 0 83.0%

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

      1. *-commutative 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in y around 0 83.0%

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

      1. *-commutative 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-*l* 83.0%

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

      4. *-commutative 83.0%

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

   10. Simplified 83.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+19} \lor \neg \left(z \leq 5.6 \cdot 10^{+33}\right):\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.8% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+110} \lor \neg \left(y \leq 3700000\right):\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.25e+110) (not (<= y 3700000.0))) (* 3.13060547623 y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.25e+110) || !(y <= 3700000.0)) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.25d+110)) .or. (.not. (y <= 3700000.0d0))) then
        tmp = 3.13060547623d0 * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.25e+110) || !(y <= 3700000.0)) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.25e+110) or not (y <= 3700000.0):
		tmp = 3.13060547623 * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.25e+110) || !(y <= 3700000.0))
		tmp = Float64(3.13060547623 * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.25e+110) || ~((y <= 3700000.0)))
		tmp = 3.13060547623 * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.25e+110], N[Not[LessEqual[y, 3700000.0]], $MachinePrecision]], N[(3.13060547623 * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.2500000000000001e110 or 3.7e6 < y

   1. Initial program 46.3%

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

   3. Simplified 54.1%

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

   5. Taylor expanded in z around inf 56.5%

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

      1. *-commutative 56.5%

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

   7. Simplified 56.5%

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

      1. +-commutative 56.5%

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

      2. fma-def 56.5%

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

   9. Applied egg-rr 56.5%

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

   10. Taylor expanded in y around inf 42.4%

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

   if -2.2500000000000001e110 < y < 3.7e6

   1. Initial program 60.9%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in z around inf 75.9%

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

      1. *-commutative 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x around inf 69.2%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+110} \lor \neg \left(y \leq 3700000\right):\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.7% 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 54.1%

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

3. Simplified 57.7%

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

5. Taylor expanded in z around inf 67.0%

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

   1. *-commutative 67.0%

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

7. Simplified 67.0%

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

8. Final simplification 67.0%

   \[\leadsto x + 3.13060547623 \cdot y \]
9. Add Preprocessing

Alternative 17: 45.2% 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 54.1%

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

3. Simplified 57.7%

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

5. Taylor expanded in z around inf 67.0%

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

   1. *-commutative 67.0%

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

7. Simplified 67.0%

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

8. Taylor expanded in x around inf 46.4%

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

9. Final simplification 46.4%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 98.6% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z)))
           (/ y 1.0)))))
   (if (< z -6.499344996252632e+53)
     t_1
     (if (< z 7.066965436914287e+59)
       (+
        x
        (/
         y
         (/
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771)
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))))
       t_1))))

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0))
	tmp = 0
	if z < -6.499344996252632e+53:
		tmp = t_1
	elif z < 7.066965436914287e+59:
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)))
	else:
		tmp = t_1
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	tmp = 0.0;
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(3.13060547623 - N[(36.527041698806414 / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -6.499344996252632e+53], t$95$1, If[Less[z, 7.066965436914287e+59], N[(x + N[(y / N[(N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024020 
(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))))