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

Percentage Accurate: 58.1% → 97.0%

Time: 17.5s

Alternatives: 12

Speedup: 3.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+59} \lor \neg \left(z \leq 6.5 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.7e+59) (not (<= z 6.5e+16)))
   (+
    x
    (+
     (/
      y
      (+
       (/ 3.7269864963038164 z)
       (- 0.31942702700572795 (/ 3.241970391368047 (* z z)))))
     (* 0.10203362558171805 (* 9.800690647801265 (* t (/ y (* z z)))))))
   (+
    (/
     (*
      y
      (+
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))
       b))
     (+
      (* z (+ (* z (+ (* 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 <= -6.7e+59) || !(z <= 6.5e+16)) {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	} else {
		tmp = ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.7d+59)) .or. (.not. (z <= 6.5d+16))) then
        tmp = x + ((y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - (3.241970391368047d0 / (z * z))))) + (0.10203362558171805d0 * (9.800690647801265d0 * (t * (y / (z * z))))))
    else
        tmp = ((y * ((z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))) + b)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.7e+59) || !(z <= 6.5e+16)) {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	} else {
		tmp = ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.7e+59) or not (z <= 6.5e+16):
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))))
	else:
		tmp = ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / ((z * ((z * ((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 <= -6.7e+59) || !(z <= 6.5e+16))
		tmp = Float64(x + Float64(Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(3.241970391368047 / Float64(z * z))))) + Float64(0.10203362558171805 * Float64(9.800690647801265 * Float64(t * Float64(y / Float64(z * z)))))));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.7e+59) || ~((z <= 6.5e+16)))
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	else
		tmp = ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.7e+59], N[Not[LessEqual[z, 6.5e+16]], $MachinePrecision]], N[(x + N[(N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(3.241970391368047 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.10203362558171805 * N[(9.800690647801265 * N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7000000000000004e59 or 6.5e16 < z

   1. Initial program 10.8%

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

      1. associate-/l* 15.3%

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

      2. fma-def 15.3%

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

      3. fma-def 15.3%

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

      4. fma-def 15.3%

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

      5. fma-def 15.3%

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

      6. fma-def 15.3%

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

      7. fma-def 15.3%

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

      8. fma-def 15.3%

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

   3. Simplified 15.3%

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

   4. Taylor expanded in z around inf 89.9%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.9%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 89.9%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 89.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 89.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 89.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 89.9%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around 0 79.0%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 79.0%

         \[\leadsto x + \left(\frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      2. associate-*r/ 79.0%

         \[\leadsto x + \left(\frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      3. metadata-eval 79.0%

         \[\leadsto x + \left(\frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      4. associate-*r/ 79.0%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \color{blue}{\frac{3.241970391368047 \cdot 1}{{z}^{2}}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      5. metadata-eval 79.0%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{\color{blue}{3.241970391368047}}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      6. unpow2 79.0%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{\color{blue}{z \cdot z}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      7. times-frac 96.0%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)}\right) \]

      8. unpow2 96.0%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)\right) \]

   9. Simplified 96.0%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{z \cdot z} \cdot \frac{t}{{\left(\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)\right)}^{2}}\right)\right)} \]

   10. Taylor expanded in z around inf 79.0%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \frac{y \cdot t}{{z}^{2}}\right)}\right) \]
   11. Step-by-step derivation

       1. associate-*l/ 96.0%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot t\right)}\right)\right) \]

       2. unpow2 96.0%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot t\right)\right)\right) \]

       3. *-commutative 96.0%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(t \cdot \frac{y}{z \cdot z}\right)}\right)\right) \]

   12. Simplified 96.0%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)}\right) \]

   if -6.7000000000000004e59 < z < 6.5e16

   1. Initial program 98.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+59} \lor \neg \left(z \leq 6.5 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \]

Alternative 2: 97.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot \left(t_2 + b\right)}{t_1} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
   (if (<= (/ (* y (+ t_2 b)) t_1) INFINITY)
     (+ (* y (+ (/ b t_1) (/ t_2 t_1))) x)
     (+
      x
      (+
       (/
        y
        (+
         (/ 3.7269864963038164 z)
         (- 0.31942702700572795 (/ 3.241970391368047 (* z z)))))
       (* 0.10203362558171805 (* 9.800690647801265 (* t (/ y (* z z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= ((double) INFINITY)) {
		tmp = (y * ((b / t_1) + (t_2 / t_1))) + x;
	} else {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = (y * ((b / t_1) + (t_2 / t_1))) + x;
	} else {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	t_2 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))
	tmp = 0
	if ((y * (t_2 + b)) / t_1) <= math.inf:
		tmp = (y * ((b / t_1) + (t_2 / t_1))) + x
	else:
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623)))))))
	tmp = 0.0
	if (Float64(Float64(y * Float64(t_2 + b)) / t_1) <= Inf)
		tmp = Float64(Float64(y * Float64(Float64(b / t_1) + Float64(t_2 / t_1))) + x);
	else
		tmp = Float64(x + Float64(Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(3.241970391368047 / Float64(z * z))))) + Float64(0.10203362558171805 * Float64(9.800690647801265 * Float64(t * Float64(y / Float64(z * z)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	t_2 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	tmp = 0.0;
	if (((y * (t_2 + b)) / t_1) <= Inf)
		tmp = (y * ((b / t_1) + (t_2 / t_1))) + x;
	else
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(t$95$2 + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(3.241970391368047 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.10203362558171805 * N[(9.800690647801265 * N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

      4. fma-def 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in y around 0 95.5%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. fma-def 0.0%

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

      3. fma-def 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 0.0%

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

      6. fma-def 0.0%

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

      7. fma-def 0.0%

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

      8. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 96.8%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 96.8%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 96.8%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 96.8%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 96.8%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 96.8%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 96.8%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around 0 80.7%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 80.7%

         \[\leadsto x + \left(\frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      2. associate-*r/ 80.7%

         \[\leadsto x + \left(\frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      3. metadata-eval 80.7%

         \[\leadsto x + \left(\frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      4. associate-*r/ 80.7%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \color{blue}{\frac{3.241970391368047 \cdot 1}{{z}^{2}}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      5. metadata-eval 80.7%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{\color{blue}{3.241970391368047}}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      6. unpow2 80.7%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{\color{blue}{z \cdot z}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      7. times-frac 99.5%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)}\right) \]

      8. unpow2 99.5%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)\right) \]

   9. Simplified 99.5%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{z \cdot z} \cdot \frac{t}{{\left(\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)\right)}^{2}}\right)\right)} \]

   10. Taylor expanded in z around inf 80.7%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \frac{y \cdot t}{{z}^{2}}\right)}\right) \]
   11. Step-by-step derivation

       1. associate-*l/ 99.5%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot t\right)}\right)\right) \]

       2. unpow2 99.5%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot t\right)\right)\right) \]

       3. *-commutative 99.5%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(t \cdot \frac{y}{z \cdot z}\right)}\right)\right) \]

   12. Simplified 99.5%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;y \cdot \left(\frac{b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \end{array} \]

Alternative 3: 96.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+18} \lor \neg \left(z \leq 2 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4e+18) (not (<= z 2e+16)))
   (+
    x
    (+
     (/
      y
      (+
       (/ 3.7269864963038164 z)
       (- 0.31942702700572795 (/ 3.241970391368047 (* z z)))))
     (* 0.10203362558171805 (* 9.800690647801265 (* t (/ y (* z z)))))))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))
       b))
     (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e+18) || !(z <= 2e+16)) {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	} else {
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	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 <= (-4d+18)) .or. (.not. (z <= 2d+16))) then
        tmp = x + ((y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - (3.241970391368047d0 / (z * z))))) + (0.10203362558171805d0 * (9.800690647801265d0 * (t * (y / (z * z))))))
    else
        tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))) + b)) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    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 <= -4e+18) || !(z <= 2e+16)) {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	} else {
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4e+18) or not (z <= 2e+16):
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))))
	else:
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4e+18) || !(z <= 2e+16))
		tmp = Float64(x + Float64(Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(3.241970391368047 / Float64(z * z))))) + Float64(0.10203362558171805 * Float64(9.800690647801265 * Float64(t * Float64(y / Float64(z * z)))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))) + b)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4e+18) || ~((z <= 2e+16)))
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	else
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4e+18], N[Not[LessEqual[z, 2e+16]], $MachinePrecision]], N[(x + N[(N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(3.241970391368047 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.10203362558171805 * N[(9.800690647801265 * N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e18 or 2e16 < z

   1. Initial program 15.4%

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

      1. associate-/l* 20.3%

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

      2. fma-def 20.3%

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

      3. fma-def 20.3%

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

      4. fma-def 20.3%

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

      5. fma-def 20.3%

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

      6. fma-def 20.3%

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

      7. fma-def 20.3%

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

      8. fma-def 20.3%

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

   3. Simplified 20.3%

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

   4. Taylor expanded in z around inf 87.6%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 87.6%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 87.6%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 87.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 87.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 87.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 87.6%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around 0 77.3%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 77.3%

         \[\leadsto x + \left(\frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      2. associate-*r/ 77.3%

         \[\leadsto x + \left(\frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      3. metadata-eval 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      4. associate-*r/ 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \color{blue}{\frac{3.241970391368047 \cdot 1}{{z}^{2}}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      5. metadata-eval 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{\color{blue}{3.241970391368047}}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      6. unpow2 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{\color{blue}{z \cdot z}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      7. times-frac 93.4%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)}\right) \]

      8. unpow2 93.4%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)\right) \]

   9. Simplified 93.4%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{z \cdot z} \cdot \frac{t}{{\left(\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)\right)}^{2}}\right)\right)} \]

   10. Taylor expanded in z around inf 77.3%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \frac{y \cdot t}{{z}^{2}}\right)}\right) \]
   11. Step-by-step derivation

       1. associate-*l/ 93.4%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot t\right)}\right)\right) \]

       2. unpow2 93.4%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot t\right)\right)\right) \]

       3. *-commutative 93.4%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(t \cdot \frac{y}{z \cdot z}\right)}\right)\right) \]

   12. Simplified 93.4%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)}\right) \]

   if -4e18 < z < 2e16

   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. Taylor expanded in z around 0 97.1%

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

      1. *-commutative 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+18} \lor \neg \left(z \leq 2 \cdot 10^{+16}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]

Alternative 4: 91.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+67} \lor \neg \left(z \leq 1.45 \cdot 10^{-27}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.5e+67) (not (<= z 1.45e-27)))
   (+
    x
    (+
     (/
      y
      (+
       (/ 3.7269864963038164 z)
       (- 0.31942702700572795 (/ 3.241970391368047 (* z z)))))
     (* 0.10203362558171805 (* 9.800690647801265 (* t (/ y (* z z)))))))
   (+
    x
    (/
     (* y (+ b (* z a)))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.5e+67) || !(z <= 1.45e-27)) {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	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 <= (-6.5d+67)) .or. (.not. (z <= 1.45d-27))) then
        tmp = x + ((y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - (3.241970391368047d0 / (z * z))))) + (0.10203362558171805d0 * (9.800690647801265d0 * (t * (y / (z * z))))))
    else
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    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 <= -6.5e+67) || !(z <= 1.45e-27)) {
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.5e+67) or not (z <= 1.45e-27):
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))))
	else:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.5e+67) || !(z <= 1.45e-27))
		tmp = Float64(x + Float64(Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(3.241970391368047 / Float64(z * z))))) + Float64(0.10203362558171805 * Float64(9.800690647801265 * Float64(t * Float64(y / Float64(z * z)))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.5e+67) || ~((z <= 1.45e-27)))
		tmp = x + ((y / ((3.7269864963038164 / z) + (0.31942702700572795 - (3.241970391368047 / (z * z))))) + (0.10203362558171805 * (9.800690647801265 * (t * (y / (z * z))))));
	else
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.5e+67], N[Not[LessEqual[z, 1.45e-27]], $MachinePrecision]], N[(x + N[(N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(3.241970391368047 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.10203362558171805 * N[(9.800690647801265 * N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999995e67 or 1.45000000000000002e-27 < z

   1. Initial program 14.4%

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

      1. associate-/l* 18.0%

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

      2. fma-def 18.0%

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

      3. fma-def 18.0%

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

      4. fma-def 18.0%

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

      5. fma-def 18.0%

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

      6. fma-def 18.0%

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

      7. fma-def 18.0%

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

      8. fma-def 18.0%

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

   3. Simplified 18.0%

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

   4. Taylor expanded in z around inf 86.4%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 86.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 86.4%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 86.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 86.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 86.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 86.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around 0 77.3%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)} \]
   8. Step-by-step derivation

      1. associate--l+ 77.3%

         \[\leadsto x + \left(\frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      2. associate-*r/ 77.3%

         \[\leadsto x + \left(\frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      3. metadata-eval 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      4. associate-*r/ 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \color{blue}{\frac{3.241970391368047 \cdot 1}{{z}^{2}}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      5. metadata-eval 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{\color{blue}{3.241970391368047}}{{z}^{2}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      6. unpow2 77.3%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{\color{blue}{z \cdot z}}\right)} + 0.10203362558171805 \cdot \frac{y \cdot t}{{z}^{2} \cdot {\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right) \]

      7. times-frac 93.2%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)}\right) \]

      8. unpow2 93.2%

         \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot \frac{t}{{\left(\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 3.241970391368047 \cdot \frac{1}{{z}^{2}}\right)}^{2}}\right)\right) \]

   9. Simplified 93.2%

      \[\leadsto x + \color{blue}{\left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(\frac{y}{z \cdot z} \cdot \frac{t}{{\left(\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)\right)}^{2}}\right)\right)} \]

   10. Taylor expanded in z around inf 77.4%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \frac{y \cdot t}{{z}^{2}}\right)}\right) \]
   11. Step-by-step derivation

       1. associate-*l/ 94.0%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(\frac{y}{{z}^{2}} \cdot t\right)}\right)\right) \]

       2. unpow2 94.0%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(\frac{y}{\color{blue}{z \cdot z}} \cdot t\right)\right)\right) \]

       3. *-commutative 94.0%

          \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \color{blue}{\left(t \cdot \frac{y}{z \cdot z}\right)}\right)\right) \]

   12. Simplified 94.0%

       \[\leadsto x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \color{blue}{\left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)}\right) \]

   if -6.4999999999999995e67 < z < 1.45000000000000002e-27

   1. Initial program 96.7%

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

   2. Taylor expanded in z around 0 91.6%

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

      1. +-commutative 89.4%

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

      2. associate-*r* 86.0%

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

      3. *-commutative 86.0%

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

      4. associate-*r* 90.6%

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

      5. distribute-lft-out 92.2%

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

      6. *-commutative 92.2%

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

   4. Simplified 94.4%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+67} \lor \neg \left(z \leq 1.45 \cdot 10^{-27}\right):\\ \;\;\;\;x + \left(\frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047}{z \cdot z}\right)} + 0.10203362558171805 \cdot \left(9.800690647801265 \cdot \left(t \cdot \frac{y}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 5: 90.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.5e+67)
   (+
    x
    (/
     y
     (+
      (+ (/ 3.7269864963038164 z) 0.31942702700572795)
      (* -0.10203362558171805 (/ t (* z z))))))
   (if (<= z 1.7e+16)
     (+
      x
      (/
       (* y (+ b (* z a)))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.5e+67) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 1.7e+16) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} 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 <= (-6.5d+67)) then
        tmp = x + (y / (((3.7269864963038164d0 / z) + 0.31942702700572795d0) + ((-0.10203362558171805d0) * (t / (z * z)))))
    else if (z <= 1.7d+16) then
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    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 <= -6.5e+67) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 1.7e+16) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.5e+67:
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))))
	elif z <= 1.7e+16:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.5e+67)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(3.7269864963038164 / z) + 0.31942702700572795) + Float64(-0.10203362558171805 * Float64(t / Float64(z * z))))));
	elseif (z <= 1.7e+16)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.5e+67)
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	elseif (z <= 1.7e+16)
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.5e+67], N[(x + N[(y / N[(N[(N[(3.7269864963038164 / z), $MachinePrecision] + 0.31942702700572795), $MachinePrecision] + N[(-0.10203362558171805 * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+16], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999995e67

   1. Initial program 0.2%

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

      1. associate-/l* 0.2%

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

      2. fma-def 0.2%

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

      3. fma-def 0.2%

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

      4. fma-def 0.2%

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

      5. fma-def 0.2%

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

      6. fma-def 0.2%

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

      7. fma-def 0.2%

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

      8. fma-def 0.2%

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

   3. Simplified 0.2%

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

   4. Taylor expanded in z around inf 93.1%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 93.1%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 93.1%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 93.1%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 93.1%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 93.1%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 93.1%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around inf 93.1%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{0.10203362558171805 \cdot \frac{t}{{z}^{2}}}\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r/ 93.1%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{{z}^{2}}}\right)\right)} \]

      2. unpow2 93.1%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{0.10203362558171805 \cdot t}{\color{blue}{z \cdot z}}\right)\right)} \]

   9. Simplified 93.1%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{z \cdot z}}\right)\right)} \]

   10. Taylor expanded in y around 0 93.1%

       \[\leadsto x + \color{blue}{\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 0.10203362558171805 \cdot \frac{t}{{z}^{2}}}} \]
   11. Step-by-step derivation

       1. cancel-sign-sub-inv 93.1%

          \[\leadsto x + \frac{y}{\color{blue}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}}} \]

       2. associate-*r/ 93.1%

          \[\leadsto x + \frac{y}{\left(\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       3. metadata-eval 93.1%

          \[\leadsto x + \frac{y}{\left(\frac{\color{blue}{3.7269864963038164}}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       4. metadata-eval 93.1%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + \color{blue}{-0.10203362558171805} \cdot \frac{t}{{z}^{2}}} \]

       5. unpow2 93.1%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{\color{blue}{z \cdot z}}} \]

   12. Simplified 93.1%

       \[\leadsto x + \color{blue}{\frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}} \]

   if -6.4999999999999995e67 < z < 1.7e16

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 89.8%

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

      1. +-commutative 87.7%

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

      2. associate-*r* 84.4%

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

      3. *-commutative 84.4%

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

      4. associate-*r* 88.9%

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

      5. distribute-lft-out 90.4%

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

      6. *-commutative 90.4%

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

   4. Simplified 92.5%

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

   if 1.7e16 < z

   1. Initial program 17.9%

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

      1. +-commutative 17.9%

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

      2. associate-*l/ 23.9%

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

      3. *-commutative 23.9%

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

      4. fma-def 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in z around inf 87.3%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+67}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 6: 83.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + \left(z + 15.234687407\right) \cdot \left(z \cdot z\right)\right)}{b}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8e+47)
   (+
    x
    (/
     y
     (+
      (+ (/ 3.7269864963038164 z) 0.31942702700572795)
      (* -0.10203362558171805 (/ t (* z z))))))
   (if (<= z 1.25e+16)
     (+
      x
      (/
       y
       (/
        (+
         0.607771387771
         (* z (+ 11.9400905721 (* (+ z 15.234687407) (* z z)))))
        b)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8e+47) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 1.25e+16) {
		tmp = x + (y / ((0.607771387771 + (z * (11.9400905721 + ((z + 15.234687407) * (z * z))))) / 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 <= (-8d+47)) then
        tmp = x + (y / (((3.7269864963038164d0 / z) + 0.31942702700572795d0) + ((-0.10203362558171805d0) * (t / (z * z)))))
    else if (z <= 1.25d+16) then
        tmp = x + (y / ((0.607771387771d0 + (z * (11.9400905721d0 + ((z + 15.234687407d0) * (z * z))))) / 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 <= -8e+47) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 1.25e+16) {
		tmp = x + (y / ((0.607771387771 + (z * (11.9400905721 + ((z + 15.234687407) * (z * z))))) / b));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8e+47:
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))))
	elif z <= 1.25e+16:
		tmp = x + (y / ((0.607771387771 + (z * (11.9400905721 + ((z + 15.234687407) * (z * z))))) / b))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8e+47)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(3.7269864963038164 / z) + 0.31942702700572795) + Float64(-0.10203362558171805 * Float64(t / Float64(z * z))))));
	elseif (z <= 1.25e+16)
		tmp = Float64(x + Float64(y / Float64(Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(Float64(z + 15.234687407) * Float64(z * z))))) / 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 <= -8e+47)
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	elseif (z <= 1.25e+16)
		tmp = x + (y / ((0.607771387771 + (z * (11.9400905721 + ((z + 15.234687407) * (z * z))))) / b));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8e+47], N[(x + N[(y / N[(N[(N[(3.7269864963038164 / z), $MachinePrecision] + 0.31942702700572795), $MachinePrecision] + N[(-0.10203362558171805 * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+16], N[(x + N[(y / N[(N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(N[(z + 15.234687407), $MachinePrecision] * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000004e47

   1. Initial program 7.0%

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

      1. associate-/l* 10.2%

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

      2. fma-def 10.2%

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

      3. fma-def 10.2%

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

      4. fma-def 10.2%

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

      5. fma-def 10.2%

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

      6. fma-def 10.2%

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

      7. fma-def 10.2%

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

      8. fma-def 10.2%

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

   3. Simplified 10.2%

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

   4. Taylor expanded in z around inf 90.7%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 90.7%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 90.7%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 90.7%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 90.7%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 90.7%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 90.7%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around inf 90.7%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{0.10203362558171805 \cdot \frac{t}{{z}^{2}}}\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r/ 90.7%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{{z}^{2}}}\right)\right)} \]

      2. unpow2 90.7%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{0.10203362558171805 \cdot t}{\color{blue}{z \cdot z}}\right)\right)} \]

   9. Simplified 90.7%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{z \cdot z}}\right)\right)} \]

   10. Taylor expanded in y around 0 90.7%

       \[\leadsto x + \color{blue}{\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 0.10203362558171805 \cdot \frac{t}{{z}^{2}}}} \]
   11. Step-by-step derivation

       1. cancel-sign-sub-inv 90.7%

          \[\leadsto x + \frac{y}{\color{blue}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}}} \]

       2. associate-*r/ 90.7%

          \[\leadsto x + \frac{y}{\left(\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       3. metadata-eval 90.7%

          \[\leadsto x + \frac{y}{\left(\frac{\color{blue}{3.7269864963038164}}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       4. metadata-eval 90.7%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + \color{blue}{-0.10203362558171805} \cdot \frac{t}{{z}^{2}}} \]

       5. unpow2 90.7%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{\color{blue}{z \cdot z}}} \]

   12. Simplified 90.7%

       \[\leadsto x + \color{blue}{\frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}} \]

   if -8.0000000000000004e47 < z < 1.25e16

   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. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.7%

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

      6. fma-def 99.7%

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

      7. fma-def 99.7%

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

      8. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 78.7%

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

   5. Taylor expanded in z around inf 78.7%

      \[\leadsto x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + \color{blue}{\left({z}^{3} + 15.234687407 \cdot {z}^{2}\right)}\right)}{b}} \]
   6. Step-by-step derivation

      1. cube-mult 78.7%

         \[\leadsto x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + \left(\color{blue}{z \cdot \left(z \cdot z\right)} + 15.234687407 \cdot {z}^{2}\right)\right)}{b}} \]

      2. unpow2 78.7%

         \[\leadsto x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + \left(z \cdot \color{blue}{{z}^{2}} + 15.234687407 \cdot {z}^{2}\right)\right)}{b}} \]

      3. distribute-rgt-out 78.7%

         \[\leadsto x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + \color{blue}{{z}^{2} \cdot \left(z + 15.234687407\right)}\right)}{b}} \]

      4. unpow2 78.7%

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

   7. Simplified 78.7%

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

   if 1.25e16 < z

   1. Initial program 17.9%

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

      1. +-commutative 17.9%

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

      2. associate-*l/ 23.9%

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

      3. *-commutative 23.9%

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

      4. fma-def 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in z around inf 87.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + \left(z + 15.234687407\right) \cdot \left(z \cdot z\right)\right)}{b}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 7: 90.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.4e+16)
   (+
    x
    (/
     y
     (+
      (+ (/ 3.7269864963038164 z) 0.31942702700572795)
      (* -0.10203362558171805 (/ t (* z z))))))
   (if (<= z 2.7e+15)
     (+
      x
      (/
       (* y (+ b (* z a)))
       (+ 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 <= -5.4e+16) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 2.7e+15) {
		tmp = x + ((y * (b + (z * a))) / (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 <= (-5.4d+16)) then
        tmp = x + (y / (((3.7269864963038164d0 / z) + 0.31942702700572795d0) + ((-0.10203362558171805d0) * (t / (z * z)))))
    else if (z <= 2.7d+15) then
        tmp = x + ((y * (b + (z * a))) / (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 <= -5.4e+16) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 2.7e+15) {
		tmp = x + ((y * (b + (z * a))) / (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 <= -5.4e+16:
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))))
	elif z <= 2.7e+15:
		tmp = x + ((y * (b + (z * a))) / (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 <= -5.4e+16)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(3.7269864963038164 / z) + 0.31942702700572795) + Float64(-0.10203362558171805 * Float64(t / Float64(z * z))))));
	elseif (z <= 2.7e+15)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / 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 <= -5.4e+16)
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	elseif (z <= 2.7e+15)
		tmp = x + ((y * (b + (z * a))) / (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, -5.4e+16], N[(x + N[(y / N[(N[(N[(3.7269864963038164 / z), $MachinePrecision] + 0.31942702700572795), $MachinePrecision] + N[(-0.10203362558171805 * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+15], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $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 < -5.4e16

   1. Initial program 14.0%

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

      1. associate-/l* 17.0%

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

      2. fma-def 17.0%

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

      3. fma-def 17.0%

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

      4. fma-def 17.0%

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

      5. fma-def 17.0%

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

      6. fma-def 17.0%

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

      7. fma-def 17.0%

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

      8. fma-def 17.0%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in z around inf 86.9%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 86.9%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 86.9%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 86.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 86.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 86.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 86.9%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around inf 86.9%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{0.10203362558171805 \cdot \frac{t}{{z}^{2}}}\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r/ 86.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{{z}^{2}}}\right)\right)} \]

      2. unpow2 86.9%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{0.10203362558171805 \cdot t}{\color{blue}{z \cdot z}}\right)\right)} \]

   9. Simplified 86.9%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{z \cdot z}}\right)\right)} \]

   10. Taylor expanded in y around 0 86.9%

       \[\leadsto x + \color{blue}{\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 0.10203362558171805 \cdot \frac{t}{{z}^{2}}}} \]
   11. Step-by-step derivation

       1. cancel-sign-sub-inv 86.9%

          \[\leadsto x + \frac{y}{\color{blue}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}}} \]

       2. associate-*r/ 86.9%

          \[\leadsto x + \frac{y}{\left(\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       3. metadata-eval 86.9%

          \[\leadsto x + \frac{y}{\left(\frac{\color{blue}{3.7269864963038164}}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       4. metadata-eval 86.9%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + \color{blue}{-0.10203362558171805} \cdot \frac{t}{{z}^{2}}} \]

       5. unpow2 86.9%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{\color{blue}{z \cdot z}}} \]

   12. Simplified 86.9%

       \[\leadsto x + \color{blue}{\frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}} \]

   if -5.4e16 < z < 2.7e15

   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. Taylor expanded in z around 0 97.1%

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

      1. *-commutative 97.1%

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

   4. Simplified 97.1%

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

   5. Taylor expanded in z around 0 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-*r* 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*r* 92.5%

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

      5. distribute-lft-out 94.1%

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

      6. *-commutative 94.1%

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

   7. Simplified 94.1%

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

   if 2.7e15 < z

   1. Initial program 17.9%

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

      1. +-commutative 17.9%

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

      2. associate-*l/ 23.9%

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

      3. *-commutative 23.9%

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

      4. fma-def 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in z around inf 87.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+16}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 8: 83.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.2e+18)
   (+
    x
    (/
     y
     (+
      (+ (/ 3.7269864963038164 z) 0.31942702700572795)
      (* -0.10203362558171805 (/ t (* z z))))))
   (if (<= z 7.5e+15)
     (+ x (* y (* b 1.6453555072203998)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e+18) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 7.5e+15) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-6.2d+18)) then
        tmp = x + (y / (((3.7269864963038164d0 / z) + 0.31942702700572795d0) + ((-0.10203362558171805d0) * (t / (z * z)))))
    else if (z <= 7.5d+15) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.2e+18) {
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	} else if (z <= 7.5e+15) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.2e+18:
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))))
	elif z <= 7.5e+15:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.2e+18)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(3.7269864963038164 / z) + 0.31942702700572795) + Float64(-0.10203362558171805 * Float64(t / Float64(z * z))))));
	elseif (z <= 7.5e+15)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.2e+18)
		tmp = x + (y / (((3.7269864963038164 / z) + 0.31942702700572795) + (-0.10203362558171805 * (t / (z * z)))));
	elseif (z <= 7.5e+15)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.2e+18], N[(x + N[(y / N[(N[(N[(3.7269864963038164 / z), $MachinePrecision] + 0.31942702700572795), $MachinePrecision] + N[(-0.10203362558171805 * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+15], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e18

   1. Initial program 12.7%

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

      1. associate-/l* 15.7%

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

      2. fma-def 15.7%

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

      3. fma-def 15.7%

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

      4. fma-def 15.7%

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

      5. fma-def 15.7%

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

      6. fma-def 15.7%

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

      7. fma-def 15.7%

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

      8. fma-def 15.7%

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

   3. Simplified 15.7%

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

   4. Taylor expanded in z around inf 88.2%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 88.2%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 88.2%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 88.2%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 88.2%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 88.2%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 88.2%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   7. Taylor expanded in t around inf 88.2%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{0.10203362558171805 \cdot \frac{t}{{z}^{2}}}\right)\right)} \]
   8. Step-by-step derivation

      1. associate-*r/ 88.2%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{{z}^{2}}}\right)\right)} \]

      2. unpow2 88.2%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{0.10203362558171805 \cdot t}{\color{blue}{z \cdot z}}\right)\right)} \]

   9. Simplified 88.2%

      \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\color{blue}{\frac{0.10203362558171805 \cdot t}{z \cdot z}}\right)\right)} \]

   10. Taylor expanded in y around 0 88.2%

       \[\leadsto x + \color{blue}{\frac{y}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - 0.10203362558171805 \cdot \frac{t}{{z}^{2}}}} \]
   11. Step-by-step derivation

       1. cancel-sign-sub-inv 88.2%

          \[\leadsto x + \frac{y}{\color{blue}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}}} \]

       2. associate-*r/ 88.2%

          \[\leadsto x + \frac{y}{\left(\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       3. metadata-eval 88.2%

          \[\leadsto x + \frac{y}{\left(\frac{\color{blue}{3.7269864963038164}}{z} + 0.31942702700572795\right) + \left(-0.10203362558171805\right) \cdot \frac{t}{{z}^{2}}} \]

       4. metadata-eval 88.2%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + \color{blue}{-0.10203362558171805} \cdot \frac{t}{{z}^{2}}} \]

       5. unpow2 88.2%

          \[\leadsto x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{\color{blue}{z \cdot z}}} \]

   12. Simplified 88.2%

       \[\leadsto x + \color{blue}{\frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}} \]

   if -6.2e18 < z < 7.5e15

   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. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.7%

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

      6. fma-def 99.7%

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

      7. fma-def 99.7%

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

      8. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 79.6%

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

   5. Taylor expanded in z around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l* 78.9%

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

   7. Simplified 78.9%

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

   if 7.5e15 < z

   1. Initial program 17.9%

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

      1. +-commutative 17.9%

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

      2. associate-*l/ 23.9%

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

      3. *-commutative 23.9%

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

      4. fma-def 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in z around inf 87.3%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y}{\left(\frac{3.7269864963038164}{z} + 0.31942702700572795\right) + -0.10203362558171805 \cdot \frac{t}{z \cdot z}}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9: 63.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(y \cdot b\right)\\ t_2 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 1.6453555072203998 (* y b))) (t_2 (+ x (* y 3.13060547623))))
   (if (<= z -1.22e-18)
     t_2
     (if (<= z -4e-181)
       t_1
       (if (<= z -5e-245) x (if (<= z 1.3e-49) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (y * b);
	double t_2 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.22e-18) {
		tmp = t_2;
	} else if (z <= -4e-181) {
		tmp = t_1;
	} else if (z <= -5e-245) {
		tmp = x;
	} else if (z <= 1.3e-49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.6453555072203998d0 * (y * b)
    t_2 = x + (y * 3.13060547623d0)
    if (z <= (-1.22d-18)) then
        tmp = t_2
    else if (z <= (-4d-181)) then
        tmp = t_1
    else if (z <= (-5d-245)) then
        tmp = x
    else if (z <= 1.3d-49) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (y * b);
	double t_2 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.22e-18) {
		tmp = t_2;
	} else if (z <= -4e-181) {
		tmp = t_1;
	} else if (z <= -5e-245) {
		tmp = x;
	} else if (z <= 1.3e-49) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.6453555072203998 * (y * b)
	t_2 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.22e-18:
		tmp = t_2
	elif z <= -4e-181:
		tmp = t_1
	elif z <= -5e-245:
		tmp = x
	elif z <= 1.3e-49:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.6453555072203998 * Float64(y * b))
	t_2 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.22e-18)
		tmp = t_2;
	elseif (z <= -4e-181)
		tmp = t_1;
	elseif (z <= -5e-245)
		tmp = x;
	elseif (z <= 1.3e-49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.6453555072203998 * (y * b);
	t_2 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -1.22e-18)
		tmp = t_2;
	elseif (z <= -4e-181)
		tmp = t_1;
	elseif (z <= -5e-245)
		tmp = x;
	elseif (z <= 1.3e-49)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e-18], t$95$2, If[LessEqual[z, -4e-181], t$95$1, If[LessEqual[z, -5e-245], x, If[LessEqual[z, 1.3e-49], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2200000000000001e-18 or 1.29999999999999997e-49 < z

   1. Initial program 24.8%

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

      1. +-commutative 24.8%

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

      2. associate-*l/ 28.9%

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

      3. *-commutative 28.9%

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

      4. fma-def 28.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in z around inf 81.8%

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

   if -1.2200000000000001e-18 < z < -4.00000000000000019e-181 or -4.9999999999999997e-245 < z < 1.29999999999999997e-49

   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. Step-by-step derivation

      1. +-commutative 99.7%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. fma-def 99.7%

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

   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. Taylor expanded in z around 0 82.3%

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

      1. fma-def 82.3%

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

   6. Simplified 82.3%

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

   7. Taylor expanded in y around inf 54.2%

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

   if -4.00000000000000019e-181 < z < -4.9999999999999997e-245

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 77.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{-18}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-181}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-49}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 10: 83.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.35 \cdot 10^{+18} \lor \neg \left(z \leq 4.6 \cdot 10^{+14}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.35e+18) (not (<= z 4.6e+14)))
   (+ 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 <= -4.35e+18) || !(z <= 4.6e+14)) {
		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 <= (-4.35d+18)) .or. (.not. (z <= 4.6d+14))) 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 <= -4.35e+18) || !(z <= 4.6e+14)) {
		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 <= -4.35e+18) or not (z <= 4.6e+14):
		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 <= -4.35e+18) || !(z <= 4.6e+14))
		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 <= -4.35e+18) || ~((z <= 4.6e+14)))
		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, -4.35e+18], N[Not[LessEqual[z, 4.6e+14]], $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 < -4.35e18 or 4.6e14 < z

   1. Initial program 15.4%

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

      1. +-commutative 15.4%

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

      2. associate-*l/ 19.4%

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

      3. *-commutative 19.4%

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

      4. fma-def 19.4%

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

   3. Simplified 19.4%

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

   4. Taylor expanded in z around inf 87.4%

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

   if -4.35e18 < z < 4.6e14

   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. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.7%

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

      6. fma-def 99.7%

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

      7. fma-def 99.7%

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

      8. fma-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in b around inf 79.6%

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

   5. Taylor expanded in z around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l* 78.9%

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

   7. Simplified 78.9%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.35 \cdot 10^{+18} \lor \neg \left(z \leq 4.6 \cdot 10^{+14}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 11: 48.3% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+214} \lor \neg \left(y \leq 5500000000\right):\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e+214) (not (<= y 5500000000.0)))
   (* 1.6453555072203998 (* y b))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+214) || !(y <= 5500000000.0)) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.3d+214)) .or. (.not. (y <= 5500000000.0d0))) then
        tmp = 1.6453555072203998d0 * (y * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+214) || !(y <= 5500000000.0)) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e+214) or not (y <= 5500000000.0):
		tmp = 1.6453555072203998 * (y * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e+214) || !(y <= 5500000000.0))
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e+214) || ~((y <= 5500000000.0)))
		tmp = 1.6453555072203998 * (y * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e+214], N[Not[LessEqual[y, 5500000000.0]], $MachinePrecision]], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000011e214 or 5.5e9 < y

   1. Initial program 60.2%

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

      1. +-commutative 60.2%

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

      2. associate-*l/ 63.5%

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

      3. *-commutative 63.5%

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

      4. fma-def 63.5%

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

   3. Simplified 63.5%

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

   4. Taylor expanded in z around 0 43.6%

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

      1. fma-def 43.6%

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

   6. Simplified 43.6%

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

   7. Taylor expanded in y around inf 36.9%

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

   if -3.30000000000000011e214 < y < 5.5e9

   1. Initial program 52.8%

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

      1. +-commutative 52.8%

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

      2. associate-*l/ 54.8%

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

      3. *-commutative 54.8%

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

      4. fma-def 54.8%

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

   3. Simplified 54.8%

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

   4. Taylor expanded in y around 0 51.4%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+214} \lor \neg \left(y \leq 5500000000\right):\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 44.3% 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 55.2%

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

   1. +-commutative 55.2%

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

   2. associate-*l/ 57.7%

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

   3. *-commutative 57.7%

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

   4. fma-def 57.7%

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

3. Simplified 57.7%

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

4. Taylor expanded in y around 0 37.5%

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

5. Final simplification 37.5%

   \[\leadsto x \]

Developer target: 98.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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