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

Percentage Accurate: 57.9% → 99.1%

Time: 23.3s

Alternatives: 15

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.9% 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: 99.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+30} \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e+30) (not (<= z 5.8e+32)))
   (fma
    y
    (-
     3.13060547623
     (/
      (-
       36.52704169880642
       (/
        (+
         457.9610022158428
         (+ t (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) z)))
        z))
      z))
    x)
   (fma
    (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
    (/
     y
     (fma
      z
      (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
      0.607771387771))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e+30) || !(z <= 5.8e+32)) {
		tmp = fma(y, (3.13060547623 - ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (-5864.8025282699045 + (t * -15.234687407))) / z))) / z)) / z)), x);
	} else {
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), (y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e+30) || !(z <= 5.8e+32))
		tmp = fma(y, Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407))) / z))) / z)) / z)), x);
	else
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e+30], N[Not[LessEqual[z, 5.8e+32]], $MachinePrecision]], N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999999e30 or 5.80000000000000006e32 < z

   1. Initial program 10.1%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in z around -inf 98.2%

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

   7. Simplified 98.2%

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

   if -4.7999999999999999e30 < z < 5.80000000000000006e32

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+30} \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+33}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1e+33)
   (+
    x
    (+
     (* y (/ (- (/ (+ 457.9610022158428 t) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (if (<= z 5.8e+32)
     (+
      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)))))))))
     (fma
      y
      (-
       3.13060547623
       (/
        (-
         36.52704169880642
         (/
          (+
           457.9610022158428
           (+ t (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) z)))
          z))
        z))
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1e+33) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else if (z <= 5.8e+32) {
		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))))))));
	} else {
		tmp = fma(y, (3.13060547623 - ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (-5864.8025282699045 + (t * -15.234687407))) / z))) / z)) / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1e+33)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + t) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	elseif (z <= 5.8e+32)
		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)))))))));
	else
		tmp = fma(y, Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407))) / z))) / z)) / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1e+33], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+32], 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], N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999995e32

   1. Initial program 9.5%

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

   3. Taylor expanded in z around -inf 84.1%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   4. Taylor expanded in y around 0 91.3%

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

      1. associate-/l* 96.4%

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

      2. mul-1-neg 96.4%

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

      3. unsub-neg 96.4%

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

      4. +-commutative 96.4%

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

   6. Simplified 96.4%

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

   if -9.9999999999999995e32 < z < 5.80000000000000006e32

   1. Initial program 99.7%

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

   if 5.80000000000000006e32 < z

   1. Initial program 9.1%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in z around -inf 99.8%

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

   7. Simplified 99.8%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t - \frac{\left(-a\right) - \left(-5864.8025282699045 + -15.234687407 \cdot t\right)}{z}\right)}{z}}{z}}, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+33}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34} \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.65e+34) (not (<= z 6.12e+32)))
   (+
    x
    (+
     (* y (/ (- (/ (+ 457.9610022158428 t) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    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 <= -1.65e+34) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} 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 <= (-1.65d+34)) .or. (.not. (z <= 6.12d+32))) then
        tmp = x + ((y * ((((457.9610022158428d0 + t) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    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 <= -1.65e+34) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} 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 <= -1.65e+34) or not (z <= 6.12e+32):
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	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 <= -1.65e+34) || !(z <= 6.12e+32))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + t) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	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 <= -1.65e+34) || ~((z <= 6.12e+32)))
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	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, -1.65e+34], N[Not[LessEqual[z, 6.12e+32]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $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 < -1.64999999999999994e34 or 6.1200000000000003e32 < z

   1. Initial program 9.3%

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

   3. Taylor expanded in z around -inf 83.7%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   4. Taylor expanded in y around 0 93.9%

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

      1. associate-/l* 97.1%

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

      2. mul-1-neg 97.1%

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

      3. unsub-neg 97.1%

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

      4. +-commutative 97.1%

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

   6. Simplified 97.1%

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

   if -1.64999999999999994e34 < z < 6.1200000000000003e32

   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. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34} \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+33} \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e+33) (not (<= z 6.12e+32)))
   (+
    x
    (+
     (* y (/ (- (/ (+ 457.9610022158428 t) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+
      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 <= -8e+33) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= (-8d+33)) .or. (.not. (z <= 6.12d+32))) then
        tmp = x + ((y * ((((457.9610022158428d0 + t) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= -8e+33) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= -8e+33) or not (z <= 6.12e+32):
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= -8e+33) || !(z <= 6.12e+32))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + t) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / 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 <= -8e+33) || ~((z <= 6.12e+32)))
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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, -8e+33], N[Not[LessEqual[z, 6.12e+32]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $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 < -7.9999999999999996e33 or 6.1200000000000003e32 < z

   1. Initial program 9.3%

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

   3. Taylor expanded in z around -inf 83.7%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   4. Taylor expanded in y around 0 93.9%

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

      1. associate-/l* 97.1%

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

      2. mul-1-neg 97.1%

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

      3. unsub-neg 97.1%

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

      4. +-commutative 97.1%

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

   6. Simplified 97.1%

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

   if -7.9999999999999996e33 < z < 6.1200000000000003e32

   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 88.9%

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

   4. Taylor expanded in y around 0 97.7%

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

      1. *-commutative 97.7%

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

   6. Simplified 97.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+33} \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9500000 \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9500000.0) (not (<= z 6.12e+32)))
   (+
    x
    (+
     (* y (/ (- (/ (+ 457.9610022158428 t) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9500000.0) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	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 <= (-9500000.0d0)) .or. (.not. (z <= 6.12d+32))) then
        tmp = x + ((y * ((((457.9610022158428d0 + t) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -9500000.0) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9500000.0) or not (z <= 6.12e+32):
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9500000.0) || !(z <= 6.12e+32))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + t) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	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 * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9500000.0) || ~((z <= 6.12e+32)))
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9500000.0], N[Not[LessEqual[z, 6.12e+32]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $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 * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e6 or 6.1200000000000003e32 < z

   1. Initial program 14.6%

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

   3. Taylor expanded in z around -inf 82.3%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   4. Taylor expanded in y around 0 91.9%

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

      1. associate-/l* 94.9%

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

      2. mul-1-neg 94.9%

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

      3. unsub-neg 94.9%

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

      4. +-commutative 94.9%

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

   6. Simplified 94.9%

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

   if -9.5e6 < z < 6.1200000000000003e32

   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 96.1%

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

      1. *-commutative 77.6%

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

   5. Simplified 96.1%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9500000 \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+28} \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+28) (not (<= z 6.12e+32)))
   (+ x (* y 3.13060547623))
   (+
    x
    (*
     1.6453555072203998
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+28) || !(z <= 6.12e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))));
	}
	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 <= (-1.15d+28)) .or. (.not. (z <= 6.12d+32))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))))
    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 <= -1.15e+28) || !(z <= 6.12e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.15e+28) or not (z <= 6.12e+32):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+28) || !(z <= 6.12e+32))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.15e+28) || ~((z <= 6.12e+32)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+28], N[Not[LessEqual[z, 6.12e+32]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999992e28 or 6.1200000000000003e32 < z

   1. Initial program 10.1%

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

   3. Simplified 13.4%

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

   5. Taylor expanded in z around inf 90.1%

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

      1. +-commutative 90.1%

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

      2. *-commutative 90.1%

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

   7. Simplified 90.1%

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

   if -1.14999999999999992e28 < z < 6.1200000000000003e32

   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%

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

   5. Taylor expanded in x around inf 83.1%

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

   6. Taylor expanded in z around 0 80.2%

      \[\leadsto x \cdot \left(1 + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)}{\color{blue}{0.607771387771 \cdot x}}\right) \]

   7. Taylor expanded in x around 0 93.7%

      \[\leadsto \color{blue}{x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)\right)} \]

   8. Taylor expanded in z around 0 93.7%

      \[\leadsto x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \color{blue}{11.1667541262 \cdot z}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative 93.7%

         \[\leadsto x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \color{blue}{z \cdot 11.1667541262}\right)\right)\right)\right) \]

   10. Simplified 93.7%

       \[\leadsto x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \color{blue}{z \cdot 11.1667541262}\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+28} \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1660000000000 \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1660000000000.0) (not (<= z 6.12e+32)))
   (+
    x
    (+
     (* y (/ (- (/ (+ 457.9610022158428 t) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (*
     1.6453555072203998
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1660000000000.0) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))));
	}
	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 <= (-1660000000000.0d0)) .or. (.not. (z <= 6.12d+32))) then
        tmp = x + ((y * ((((457.9610022158428d0 + t) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + (1.6453555072203998d0 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))))
    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 <= -1660000000000.0) || !(z <= 6.12e+32)) {
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1660000000000.0) or not (z <= 6.12e+32):
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1660000000000.0) || !(z <= 6.12e+32))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + t) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1660000000000.0) || ~((z <= 6.12e+32)))
		tmp = x + ((y * ((((457.9610022158428 + t) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + (1.6453555072203998 * (y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1660000000000.0], N[Not[LessEqual[z, 6.12e+32]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.66e12 or 6.1200000000000003e32 < z

   1. Initial program 13.1%

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

   3. Taylor expanded in z around -inf 82.8%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   4. Taylor expanded in y around 0 92.6%

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

      1. associate-/l* 95.7%

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

      2. mul-1-neg 95.7%

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

      3. unsub-neg 95.7%

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

      4. +-commutative 95.7%

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

   6. Simplified 95.7%

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

   if -1.66e12 < z < 6.1200000000000003e32

   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%

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

   5. Taylor expanded in x around inf 83.3%

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

   6. Taylor expanded in z around 0 81.0%

      \[\leadsto x \cdot \left(1 + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)}{\color{blue}{0.607771387771 \cdot x}}\right) \]

   7. Taylor expanded in x around 0 94.9%

      \[\leadsto \color{blue}{x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)\right)} \]

   8. Taylor expanded in z around 0 94.9%

      \[\leadsto x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \color{blue}{11.1667541262 \cdot z}\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative 94.9%

         \[\leadsto x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \color{blue}{z \cdot 11.1667541262}\right)\right)\right)\right) \]

   10. Simplified 94.9%

       \[\leadsto x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + \color{blue}{z \cdot 11.1667541262}\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1660000000000 \lor \neg \left(z \leq 6.12 \cdot 10^{+32}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + t}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5500000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5500000000.0)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 5.8e+32)
     (+
      x
      (/
       (* y b)
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5500000000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 5.8e+32) {
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-5500000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 5.8d+32) then
        tmp = x + ((y * b) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5500000000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 5.8e+32) {
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5500000000.0:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 5.8e+32:
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5500000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 5.8e+32)
		tmp = Float64(x + Float64(Float64(y * b) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5500000000.0)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 5.8e+32)
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5500000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+32], N[(x + N[(N[(y * b), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5e9

   1. Initial program 18.5%

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

   3. Taylor expanded in z around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. *-commutative 83.1%

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

      5. distribute-rgt-out-- 83.1%

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

      6. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

   if -5.5e9 < z < 5.80000000000000006e32

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 78.8%

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

      1. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in z around 0 77.9%

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

      1. *-commutative 77.9%

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

   8. Simplified 77.9%

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

   if 5.80000000000000006e32 < z

   1. Initial program 9.1%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in z around inf 91.6%

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

      1. +-commutative 91.6%

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

      2. *-commutative 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5500000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1700000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6.12 \cdot 10^{+32}:\\ \;\;\;\;x + b \cdot \left(-32.324150453290734 \cdot \left(z \cdot y\right) + y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1700000000.0)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 6.12e+32)
     (+ x (* b (+ (* -32.324150453290734 (* z y)) (* y 1.6453555072203998))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1700000000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 6.12e+32) {
		tmp = x + (b * ((-32.324150453290734 * (z * y)) + (y * 1.6453555072203998)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1700000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 6.12d+32) then
        tmp = x + (b * (((-32.324150453290734d0) * (z * y)) + (y * 1.6453555072203998d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1700000000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 6.12e+32) {
		tmp = x + (b * ((-32.324150453290734 * (z * y)) + (y * 1.6453555072203998)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1700000000.0:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 6.12e+32:
		tmp = x + (b * ((-32.324150453290734 * (z * y)) + (y * 1.6453555072203998)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1700000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 6.12e+32)
		tmp = Float64(x + Float64(b * Float64(Float64(-32.324150453290734 * Float64(z * y)) + Float64(y * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1700000000.0)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 6.12e+32)
		tmp = x + (b * ((-32.324150453290734 * (z * y)) + (y * 1.6453555072203998)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1700000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.12e+32], N[(x + N[(b * N[(N[(-32.324150453290734 * N[(z * y), $MachinePrecision]), $MachinePrecision] + N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e9

   1. Initial program 18.5%

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

   3. Taylor expanded in z around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. *-commutative 83.1%

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

      5. distribute-rgt-out-- 83.1%

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

      6. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

   if -1.7e9 < z < 6.1200000000000003e32

   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 78.3%

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

      1. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in z around 0 75.7%

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

   7. Taylor expanded in b around 0 77.1%

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

   if 6.1200000000000003e32 < z

   1. Initial program 9.1%

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

   3. Simplified 15.4%

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

   5. Taylor expanded in z around inf 93.1%

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

      1. +-commutative 93.1%

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

      2. *-commutative 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1700000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6.12 \cdot 10^{+32}:\\ \;\;\;\;x + b \cdot \left(-32.324150453290734 \cdot \left(z \cdot y\right) + y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 82.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+80} \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e+80) (not (<= z 5.8e+32)))
   (+ x (* y 3.13060547623))
   (+ x (/ (* y b) (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e+80) || !(z <= 5.8e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	}
	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+80)) .or. (.not. (z <= 5.8d+32))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * b) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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+80) || !(z <= 5.8e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e+80) or not (z <= 5.8e+32):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e+80) || !(z <= 5.8e+32))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * b) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e+80) || ~((z <= 5.8e+32)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e+80], N[Not[LessEqual[z, 5.8e+32]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999976e80 or 5.80000000000000006e32 < z

   1. Initial program 5.3%

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

   3. Simplified 9.9%

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

   5. Taylor expanded in z around inf 94.0%

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

      1. +-commutative 94.0%

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

      2. *-commutative 94.0%

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

   7. Simplified 94.0%

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

   if -6.19999999999999976e80 < z < 5.80000000000000006e32

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 76.6%

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

      1. *-commutative 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around 0 74.4%

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

      1. *-commutative 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+80} \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -31500000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -31500000000.0) (not (<= z 5.8e+32)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -31500000000.0) || !(z <= 5.8e+32)) {
		tmp = x + (y * 3.13060547623);
	} 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 <= (-31500000000.0d0)) .or. (.not. (z <= 5.8d+32))) then
        tmp = x + (y * 3.13060547623d0)
    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 <= -31500000000.0) || !(z <= 5.8e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -31500000000.0) or not (z <= 5.8e+32):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -31500000000.0) || !(z <= 5.8e+32))
		tmp = Float64(x + Float64(y * 3.13060547623));
	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 <= -31500000000.0) || ~((z <= 5.8e+32)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -31500000000.0], N[Not[LessEqual[z, 5.8e+32]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.15e10 or 5.80000000000000006e32 < z

   1. Initial program 13.8%

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

   3. Simplified 17.7%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -3.15e10 < z < 5.80000000000000006e32

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 77.5%

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

      1. associate-*r* 77.5%

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

      2. *-commutative 77.5%

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

   5. Simplified 77.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31500000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -370000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -370000000.0) (not (<= z 5.8e+32)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -370000000.0) || !(z <= 5.8e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	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 <= (-370000000.0d0)) .or. (.not. (z <= 5.8d+32))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * b))
    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 <= -370000000.0) || !(z <= 5.8e+32)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -370000000.0) or not (z <= 5.8e+32):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -370000000.0) || !(z <= 5.8e+32))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -370000000.0) || ~((z <= 5.8e+32)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -370000000.0], N[Not[LessEqual[z, 5.8e+32]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7e8 or 5.80000000000000006e32 < z

   1. Initial program 13.8%

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

   3. Simplified 17.7%

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

   5. Taylor expanded in z around inf 87.3%

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

      1. +-commutative 87.3%

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

      2. *-commutative 87.3%

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

   7. Simplified 87.3%

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

   if -3.7e8 < z < 5.80000000000000006e32

   1. Initial program 99.7%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -370000000 \lor \neg \left(z \leq 5.8 \cdot 10^{+32}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -360000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -360000000.0)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 5.8e+32)
     (+ x (* 1.6453555072203998 (* y b)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -360000000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 5.8e+32) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-360000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 5.8d+32) then
        tmp = x + (1.6453555072203998d0 * (y * b))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -360000000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 5.8e+32) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -360000000.0:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 5.8e+32:
		tmp = x + (1.6453555072203998 * (y * b))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -360000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 5.8e+32)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -360000000.0)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 5.8e+32)
		tmp = x + (1.6453555072203998 * (y * b));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -360000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+32], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e8

   1. Initial program 18.5%

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

   3. Taylor expanded in z around -inf 83.1%

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

      1. +-commutative 83.1%

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

      2. mul-1-neg 83.1%

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

      3. unsub-neg 83.1%

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

      4. *-commutative 83.1%

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

      5. distribute-rgt-out-- 83.1%

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

      6. metadata-eval 83.1%

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

   5. Simplified 83.1%

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

   if -3.6e8 < z < 5.80000000000000006e32

   1. Initial program 99.7%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 77.5%

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

      1. +-commutative 77.5%

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

      2. *-commutative 77.5%

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

   7. Simplified 77.5%

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

   if 5.80000000000000006e32 < z

   1. Initial program 9.1%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in z around inf 91.6%

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

      1. +-commutative 91.6%

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

      2. *-commutative 91.6%

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

   7. Simplified 91.6%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -360000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+32}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.4% accurate, 7.4× speedup

Math

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

FPCore

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

C

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

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 * 3.13060547623d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.4%

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

3. Simplified 61.2%

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

5. Taylor expanded in z around inf 60.0%

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

   1. +-commutative 60.0%

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

   2. *-commutative 60.0%

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

7. Simplified 60.0%

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

8. Final simplification 60.0%

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

Alternative 15: 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 59.4%

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

3. Simplified 61.2%

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

5. Taylor expanded in y around 0 41.9%

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

6. Final simplification 41.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (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))))