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

Percentage Accurate: 58.7% → 97.7%

Time: 18.2s

Alternatives: 16

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% 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: 97.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+30}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, t_1, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, t_1, \frac{\left(y \cdot 36.52704169880642\right) \cdot -15.234687407}{z \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* z z))))
   (if (<= z -3.8e+30)
     (+
      x
      (+
       (* (/ y z) (/ t z))
       (-
        (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642))
        (fma 98.5170599679272 t_1 (/ (* y -556.47806218377) (* z z))))))
     (if (<= z 1.4e+46)
       (+
        (/
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        x)
       (+
        x
        (-
         (-
          (fma y 3.13060547623 (/ y (/ (* z z) t)))
          (/ (* y 36.52704169880642) z))
         (fma
          98.5170599679272
          t_1
          (/ (* (* y 36.52704169880642) -15.234687407) (* z z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (z * z);
	double tmp;
	if (z <= -3.8e+30) {
		tmp = x + (((y / z) * (t / z)) + (((y * 3.13060547623) + ((y / z) * -36.52704169880642)) - fma(98.5170599679272, t_1, ((y * -556.47806218377) / (z * z)))));
	} else if (z <= 1.4e+46) {
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	} else {
		tmp = x + ((fma(y, 3.13060547623, (y / ((z * z) / t))) - ((y * 36.52704169880642) / z)) - fma(98.5170599679272, t_1, (((y * 36.52704169880642) * -15.234687407) / (z * z))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(z * z))
	tmp = 0.0
	if (z <= -3.8e+30)
		tmp = Float64(x + Float64(Float64(Float64(y / z) * Float64(t / z)) + Float64(Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)) - fma(98.5170599679272, t_1, Float64(Float64(y * -556.47806218377) / Float64(z * z))))));
	elseif (z <= 1.4e+46)
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x);
	else
		tmp = Float64(x + Float64(Float64(fma(y, 3.13060547623, Float64(y / Float64(Float64(z * z) / t))) - Float64(Float64(y * 36.52704169880642) / z)) - fma(98.5170599679272, t_1, Float64(Float64(Float64(y * 36.52704169880642) * -15.234687407) / Float64(z * z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+30], N[(x + N[(N[(N[(y / z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * t$95$1 + N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+46], N[(N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $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], N[(x + N[(N[(N[(y * 3.13060547623 + N[(y / N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * t$95$1 + N[(N[(N[(y * 36.52704169880642), $MachinePrecision] * -15.234687407), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000001e30

   1. Initial program 2.8%

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

   2. Taylor expanded in b around 0 2.8%

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

   3. Taylor expanded in z around inf 87.0%

      \[\leadsto x + \color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.0%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot t}{{z}^{2}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right)} \]

      2. unpow2 87.0%

         \[\leadsto x + \left(\frac{y \cdot t}{\color{blue}{z \cdot z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      3. times-frac 99.9%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot \frac{t}{z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      4. fma-def 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\color{blue}{\mathsf{fma}\left(11.1667541262, \frac{y}{z}, 3.13060547623 \cdot y\right)} - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      5. *-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \color{blue}{y \cdot 3.13060547623}\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      6. associate-*r/ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\color{blue}{\frac{47.69379582500642 \cdot y}{z}} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      7. +-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\frac{47.69379582500642 \cdot y}{z} + \color{blue}{\left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right)\right)\right) \]

      8. associate--r+ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \color{blue}{\left(\left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \frac{47.69379582500642 \cdot y}{z}\right) - \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)}\right) \]

   5. Simplified 99.9%

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)} \]

   if -3.8000000000000001e30 < z < 1.40000000000000009e46

   1. Initial program 98.4%

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

   if 1.40000000000000009e46 < z

   1. Initial program 8.5%

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

      1. associate-*l/ 10.0%

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

      2. *-commutative 10.0%

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

      3. fma-def 10.0%

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

      4. *-commutative 10.0%

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

      5. fma-def 10.0%

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

      6. *-commutative 10.0%

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

      7. fma-def 10.0%

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

      8. *-commutative 10.0%

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

      9. fma-def 10.0%

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

   3. Simplified 10.0%

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

   4. Taylor expanded in z around -inf 89.9%

      \[\leadsto x + \color{blue}{\left(\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 89.9%

         \[\leadsto x + \left(\color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) + -1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      2. mul-1-neg 89.9%

         \[\leadsto x + \left(\left(\left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) + \color{blue}{\left(-\frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      3. unsub-neg 89.9%

         \[\leadsto x + \left(\color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      4. +-commutative 89.9%

         \[\leadsto x + \left(\left(\color{blue}{\left(3.13060547623 \cdot y + \frac{y \cdot t}{{z}^{2}}\right)} - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      5. *-commutative 89.9%

         \[\leadsto x + \left(\left(\left(\color{blue}{y \cdot 3.13060547623} + \frac{y \cdot t}{{z}^{2}}\right) - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      6. fma-def 89.9%

         \[\leadsto x + \left(\left(\color{blue}{\mathsf{fma}\left(y, 3.13060547623, \frac{y \cdot t}{{z}^{2}}\right)} - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      7. associate-/l* 98.2%

         \[\leadsto x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \color{blue}{\frac{y}{\frac{{z}^{2}}{t}}}\right) - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      8. unpow2 98.2%

         \[\leadsto x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{\color{blue}{z \cdot z}}{t}}\right) - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      9. distribute-rgt-out-- 98.2%

         \[\leadsto x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      10. metadata-eval 98.2%

          \[\leadsto x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{y \cdot \color{blue}{36.52704169880642}}{z}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      11. +-commutative 98.2%

          \[\leadsto x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \color{blue}{\left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + -15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}}\right)}\right) \]

      12. fma-def 98.2%

          \[\leadsto x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \color{blue}{\mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, -15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}}\right)}\right) \]

   6. Simplified 96.8%

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{\left(y \cdot 36.52704169880642\right) \cdot -15.234687407}{z \cdot z}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+30}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{y}{\frac{z \cdot z}{t}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{\left(y \cdot 36.52704169880642\right) \cdot -15.234687407}{z \cdot z}\right)\right)\\ \end{array} \]

Alternative 2: 98.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (+
    x
    (/
     y
     (/
      (fma
       (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
       z
       0.607771387771)
      (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b))))
   (+
    x
    (+
     (* (/ y z) (/ t z))
     (-
      (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642))
      (fma
       98.5170599679272
       (/ y (* z z))
       (/ (* y -556.47806218377) (* z z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = x + (y / (fma(fma(fma((z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b)));
	} else {
		tmp = x + (((y / z) * (t / z)) + (((y * 3.13060547623) + ((y / z) * -36.52704169880642)) - fma(98.5170599679272, (y / (z * z)), ((y * -556.47806218377) / (z * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = Float64(x + Float64(y / Float64(fma(fma(fma(Float64(z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b))));
	else
		tmp = Float64(x + Float64(Float64(Float64(y / z) * Float64(t / z)) + Float64(Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)) - fma(98.5170599679272, Float64(y / Float64(z * z)), Float64(Float64(y * -556.47806218377) / Float64(z * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $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], Infinity], N[(x + N[(y / N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y / z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $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 93.3%

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

      1. associate-/l* 97.3%

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

      2. fma-def 97.3%

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

      3. fma-def 97.3%

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

      4. fma-def 97.3%

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

      5. fma-def 97.3%

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

      6. fma-def 97.3%

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

      7. fma-def 97.3%

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

      8. fma-def 97.3%

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

   3. Simplified 97.3%

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

   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. Taylor expanded in b around 0 0.0%

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

   3. Taylor expanded in z around inf 87.8%

      \[\leadsto x + \color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.8%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot t}{{z}^{2}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right)} \]

      2. unpow2 87.8%

         \[\leadsto x + \left(\frac{y \cdot t}{\color{blue}{z \cdot z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      3. times-frac 99.9%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot \frac{t}{z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      4. fma-def 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\color{blue}{\mathsf{fma}\left(11.1667541262, \frac{y}{z}, 3.13060547623 \cdot y\right)} - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      5. *-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \color{blue}{y \cdot 3.13060547623}\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      6. associate-*r/ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\color{blue}{\frac{47.69379582500642 \cdot y}{z}} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      7. +-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\frac{47.69379582500642 \cdot y}{z} + \color{blue}{\left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right)\right)\right) \]

      8. associate--r+ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \color{blue}{\left(\left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \frac{47.69379582500642 \cdot y}{z}\right) - \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)}\right) \]

   5. Simplified 99.0%

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \end{array} \]

Alternative 3: 97.8% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (+
    x
    (*
     (/
      y
      (fma
       z
       (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
       0.607771387771))
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)))
   (+
    x
    (+
     (* (/ y z) (/ t z))
     (-
      (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642))
      (fma
       98.5170599679272
       (/ y (* z z))
       (/ (* y -556.47806218377) (* z z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = x + ((y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)) * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b));
	} else {
		tmp = x + (((y / z) * (t / z)) + (((y * 3.13060547623) + ((y / z) * -36.52704169880642)) - fma(98.5170599679272, (y / (z * z)), ((y * -556.47806218377) / (z * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = Float64(x + Float64(Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)) * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y / z) * Float64(t / z)) + Float64(Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)) - fma(98.5170599679272, Float64(y / Float64(z * z)), Float64(Float64(y * -556.47806218377) / Float64(z * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $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], Infinity], N[(x + N[(N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y / z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $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 93.3%

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

      1. associate-*l/ 97.3%

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

      2. *-commutative 97.3%

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

      3. fma-def 97.3%

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

      4. *-commutative 97.3%

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

      5. fma-def 97.3%

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

      6. *-commutative 97.3%

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

      7. fma-def 97.3%

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

      8. *-commutative 97.3%

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

      9. fma-def 97.3%

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

   3. Simplified 97.3%

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

   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. Taylor expanded in b around 0 0.0%

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

   3. Taylor expanded in z around inf 87.8%

      \[\leadsto x + \color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.8%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot t}{{z}^{2}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right)} \]

      2. unpow2 87.8%

         \[\leadsto x + \left(\frac{y \cdot t}{\color{blue}{z \cdot z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      3. times-frac 99.9%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot \frac{t}{z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      4. fma-def 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\color{blue}{\mathsf{fma}\left(11.1667541262, \frac{y}{z}, 3.13060547623 \cdot y\right)} - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      5. *-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \color{blue}{y \cdot 3.13060547623}\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      6. associate-*r/ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\color{blue}{\frac{47.69379582500642 \cdot y}{z}} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      7. +-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\frac{47.69379582500642 \cdot y}{z} + \color{blue}{\left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right)\right)\right) \]

      8. associate--r+ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \color{blue}{\left(\left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \frac{47.69379582500642 \cdot y}{z}\right) - \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)}\right) \]

   5. Simplified 99.0%

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \end{array} \]

Alternative 4: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+29} \lor \neg \left(z \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e+29) (not (<= z 9.2e+75)))
   (+
    x
    (+
     (* (/ y z) (/ t z))
     (-
      (+ (* y 3.13060547623) (* (/ y z) -36.52704169880642))
      (fma
       98.5170599679272
       (/ y (* z z))
       (/ (* y -556.47806218377) (* z z))))))
   (+
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       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 <= -9e+29) || !(z <= 9.2e+75)) {
		tmp = x + (((y / z) * (t / z)) + (((y * 3.13060547623) + ((y / z) * -36.52704169880642)) - fma(98.5170599679272, (y / (z * z)), ((y * -556.47806218377) / (z * z)))));
	} else {
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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 <= -9e+29) || !(z <= 9.2e+75))
		tmp = Float64(x + Float64(Float64(Float64(y / z) * Float64(t / z)) + Float64(Float64(Float64(y * 3.13060547623) + Float64(Float64(y / z) * -36.52704169880642)) - fma(98.5170599679272, Float64(y / Float64(z * z)), Float64(Float64(y * -556.47806218377) / Float64(z * z))))));
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e+29], N[Not[LessEqual[z, 9.2e+75]], $MachinePrecision]], N[(x + N[(N[(N[(y / z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $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 < -9.0000000000000005e29 or 9.1999999999999994e75 < z

   1. Initial program 1.3%

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

   2. Taylor expanded in b around 0 1.3%

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

   3. Taylor expanded in z around inf 87.9%

      \[\leadsto x + \color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 87.9%

         \[\leadsto x + \color{blue}{\left(\frac{y \cdot t}{{z}^{2}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right)} \]

      2. unpow2 87.9%

         \[\leadsto x + \left(\frac{y \cdot t}{\color{blue}{z \cdot z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      3. times-frac 99.9%

         \[\leadsto x + \left(\color{blue}{\frac{y}{z} \cdot \frac{t}{z}} + \left(\left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      4. fma-def 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\color{blue}{\mathsf{fma}\left(11.1667541262, \frac{y}{z}, 3.13060547623 \cdot y\right)} - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      5. *-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, \color{blue}{y \cdot 3.13060547623}\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      6. associate-*r/ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\color{blue}{\frac{47.69379582500642 \cdot y}{z}} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)\right) \]

      7. +-commutative 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \left(\frac{47.69379582500642 \cdot y}{z} + \color{blue}{\left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right)\right)\right) \]

      8. associate--r+ 99.9%

         \[\leadsto x + \left(\frac{y}{z} \cdot \frac{t}{z} + \color{blue}{\left(\left(\mathsf{fma}\left(11.1667541262, \frac{y}{z}, y \cdot 3.13060547623\right) - \frac{47.69379582500642 \cdot y}{z}\right) - \left(15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)}\right) \]

   5. Simplified 99.1%

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)} \]

   if -9.0000000000000005e29 < z < 9.1999999999999994e75

   1. Initial program 97.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+29} \lor \neg \left(z \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \frac{t}{z} + \left(\left(y \cdot 3.13060547623 + \frac{y}{z} \cdot -36.52704169880642\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{z \cdot z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \]

Alternative 5: 95.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $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]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $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 93.3%

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

   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 98.7%

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

      1. associate-*r/ 98.7%

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

      2. metadata-eval 98.7%

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

      3. mul-1-neg 98.7%

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

      4. *-commutative 98.7%

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

      5. unpow2 98.7%

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

   6. Simplified 98.7%

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

4. Final simplification 95.2%

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

Alternative 6: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+53} \lor \neg \left(z \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+53) (not (<= z 9.2e+75)))
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+
      (* 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 <= -4.5e+53) || !(z <= 9.2e+75)) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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 <= (-4.5d+53)) .or. (.not. (z <= 9.2d+75))) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((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 <= -4.5e+53) || !(z <= 9.2e+75)) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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 <= -4.5e+53) or not (z <= 9.2e+75):
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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 <= -4.5e+53) || !(z <= 9.2e+75))
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / 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 <= -4.5e+53) || ~((z <= 9.2e+75)))
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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, -4.5e+53], N[Not[LessEqual[z, 9.2e+75]], $MachinePrecision]], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(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 < -4.5000000000000002e53 or 9.1999999999999994e75 < z

   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* 4.2%

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

      2. fma-def 4.2%

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

      3. fma-def 4.2%

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

      4. fma-def 4.2%

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

      5. fma-def 4.2%

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

      6. fma-def 4.2%

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

      7. fma-def 4.2%

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

      8. fma-def 4.2%

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

   3. Simplified 4.2%

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

   4. Taylor expanded in z around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

      3. mul-1-neg 97.7%

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

      4. *-commutative 97.7%

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

      5. unpow2 97.7%

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

   6. Simplified 97.7%

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

   if -4.5000000000000002e53 < z < 9.1999999999999994e75

   1. Initial program 96.1%

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

   2. Taylor expanded in z around 0 95.4%

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

      1. *-commutative 92.0%

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

   4. Simplified 95.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+53} \lor \neg \left(z \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 7: 94.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+50) (not (<= z 9.2e+75)))
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (+
    x
    (/
     (+ (* y b) (* y (* z (+ a (* z t)))))
     (+
      (* 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 <= -1.3e+50) || !(z <= 9.2e+75)) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else {
		tmp = x + (((y * b) + (y * (z * (a + (z * t))))) / ((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 <= (-1.3d+50)) .or. (.not. (z <= 9.2d+75))) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else
        tmp = x + (((y * b) + (y * (z * (a + (z * t))))) / ((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 <= -1.3e+50) || !(z <= 9.2e+75)) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else {
		tmp = x + (((y * b) + (y * (z * (a + (z * t))))) / ((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 <= -1.3e+50) or not (z <= 9.2e+75):
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	else:
		tmp = x + (((y * b) + (y * (z * (a + (z * t))))) / ((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 <= -1.3e+50) || !(z <= 9.2e+75))
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	else
		tmp = Float64(x + Float64(Float64(Float64(y * b) + Float64(y * Float64(z * Float64(a + Float64(z * t))))) / 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 <= -1.3e+50) || ~((z <= 9.2e+75)))
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	else
		tmp = x + (((y * b) + (y * (z * (a + (z * t))))) / ((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, -1.3e+50], N[Not[LessEqual[z, 9.2e+75]], $MachinePrecision]], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y * b), $MachinePrecision] + N[(y * N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e50 or 9.1999999999999994e75 < z

   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* 4.2%

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

      2. fma-def 4.2%

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

      3. fma-def 4.2%

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

      4. fma-def 4.2%

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

      5. fma-def 4.2%

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

      6. fma-def 4.2%

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

      7. fma-def 4.2%

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

      8. fma-def 4.2%

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

   3. Simplified 4.2%

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

   4. Taylor expanded in z around inf 97.7%

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

      1. associate-*r/ 97.7%

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

      2. metadata-eval 97.7%

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

      3. mul-1-neg 97.7%

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

      4. *-commutative 97.7%

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

      5. unpow2 97.7%

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

   6. Simplified 97.7%

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

   if -1.3000000000000001e50 < z < 9.1999999999999994e75

   1. Initial program 96.1%

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

   2. Taylor expanded in b around 0 94.8%

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

   3. Taylor expanded in z around 0 91.3%

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

      1. associate-*r* 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*r* 91.9%

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

      4. distribute-lft-out 93.8%

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

      5. *-commutative 93.8%

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

      6. unpow2 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in y around 0 93.8%

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

      1. +-commutative 93.8%

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

      2. *-commutative 93.8%

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

      3. unpow2 93.8%

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

      4. associate-*r* 93.8%

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

      5. *-commutative 93.8%

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

      6. distribute-lft-out 93.8%

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

   8. Simplified 93.8%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{+75}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 8: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{+56}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -10000000000.0) (not (<= z 1.25e+56)))
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -10000000000.0) || !(z <= 1.25e+56)) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-10000000000.0d0)) .or. (.not. (z <= 1.25d+56))) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -10000000000.0) || !(z <= 1.25e+56)) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -10000000000.0) or not (z <= 1.25e+56):
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -10000000000.0) || !(z <= 1.25e+56))
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -10000000000.0) || ~((z <= 1.25e+56)))
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -10000000000.0], N[Not[LessEqual[z, 1.25e+56]], $MachinePrecision]], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e10 or 1.25000000000000006e56 < z

   1. Initial program 7.8%

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

      1. associate-/l* 12.1%

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

      2. fma-def 12.1%

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

      3. fma-def 12.1%

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

      4. fma-def 12.1%

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

      5. fma-def 12.1%

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

      6. fma-def 12.1%

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

      7. fma-def 12.1%

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

      8. fma-def 12.1%

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

   3. Simplified 12.1%

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

   4. Taylor expanded in z around inf 94.3%

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

      1. associate-*r/ 94.3%

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

      2. metadata-eval 94.3%

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

      3. mul-1-neg 94.3%

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

      4. *-commutative 94.3%

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

      5. unpow2 94.3%

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

   6. Simplified 94.3%

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

   if -1e10 < z < 1.25000000000000006e56

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 95.0%

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

      1. *-commutative 89.1%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in z around 0 95.3%

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

      1. *-commutative 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{+56}\right):\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 9: 90.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.6e+46)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 1.8e+36)
     (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (/ y 0.31942702700572795)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.6e+46) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 1.8e+36) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.6d+46)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 1.8d+36) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y / 0.31942702700572795d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.6e+46) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 1.8e+36) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.6e+46:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 1.8e+36:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y / 0.31942702700572795)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.6e+46)
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	elseif (z <= 1.8e+36)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.6e+46)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 1.8e+36)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y / 0.31942702700572795);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.6e+46], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+36], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.60000000000000013e46

   1. Initial program 0.6%

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

      1. associate-/l* 9.1%

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

      2. fma-def 9.1%

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

      3. fma-def 9.1%

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

      4. fma-def 9.1%

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

      5. fma-def 9.1%

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

      6. fma-def 9.1%

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

      7. fma-def 9.1%

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

      8. fma-def 9.1%

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

   3. Simplified 9.1%

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

   4. Taylor expanded in z around inf 95.1%

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

      1. associate-*r/ 95.1%

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

      2. metadata-eval 95.1%

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

      3. mul-1-neg 95.1%

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

      4. *-commutative 95.1%

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

      5. unpow2 95.1%

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

   6. Simplified 95.1%

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

   if -2.60000000000000013e46 < z < 1.7999999999999999e36

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 92.0%

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

      1. fma-def 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in z around 0 90.8%

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

      1. *-commutative 90.8%

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

   7. Simplified 90.8%

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

   8. Taylor expanded in y around 0 92.1%

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

   if 1.7999999999999999e36 < 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* 18.2%

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

      2. fma-def 18.2%

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

      3. fma-def 18.2%

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

      4. fma-def 18.2%

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

      5. fma-def 18.2%

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

      6. fma-def 18.2%

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

      7. fma-def 18.2%

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

      8. fma-def 18.2%

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

   3. Simplified 18.2%

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

   4. Taylor expanded in z around inf 89.6%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 10: 90.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+46} \lor \neg \left(z \leq 2.3 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e+46) (not (<= z 2.3e+36)))
   (+ x (/ y 0.31942702700572795))
   (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e+46) || !(z <= 2.3e+36)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.6d+46)) .or. (.not. (z <= 2.3d+36))) then
        tmp = x + (y / 0.31942702700572795d0)
    else
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e+46) || !(z <= 2.3e+36)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.6e+46) or not (z <= 2.3e+36):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e+46) || !(z <= 2.3e+36))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.6e+46) || ~((z <= 2.3e+36)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e+46], N[Not[LessEqual[z, 2.3e+36]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000013e46 or 2.29999999999999996e36 < z

   1. Initial program 9.5%

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

      1. associate-/l* 14.6%

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

      2. fma-def 14.6%

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

      3. fma-def 14.6%

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

      4. fma-def 14.6%

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

      5. fma-def 14.6%

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

      6. fma-def 14.6%

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

      7. fma-def 14.6%

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

      8. fma-def 14.6%

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

   3. Simplified 14.6%

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

   4. Taylor expanded in z around inf 91.5%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

   if -2.60000000000000013e46 < z < 2.29999999999999996e36

   1. Initial program 98.3%

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

   2. Taylor expanded in z around 0 92.0%

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

      1. fma-def 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in z around 0 90.8%

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

      1. *-commutative 90.8%

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

   7. Simplified 90.8%

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

   8. Taylor expanded in y around 0 92.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+46} \lor \neg \left(z \leq 2.3 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 11: 82.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{0.31942702700572795}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-178}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-91}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ y 0.31942702700572795))))
   (if (<= z -8.6e+48)
     t_1
     (if (<= z 8.8e-178)
       (+ x (* (* y b) 1.6453555072203998))
       (if (<= z 4.7e-91)
         (+ x (* 1.6453555072203998 (* a (* y z))))
         (if (<= z 2e+35) (+ x (* b (* y 1.6453555072203998))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / 0.31942702700572795);
	double tmp;
	if (z <= -8.6e+48) {
		tmp = t_1;
	} else if (z <= 8.8e-178) {
		tmp = x + ((y * b) * 1.6453555072203998);
	} else if (z <= 4.7e-91) {
		tmp = x + (1.6453555072203998 * (a * (y * z)));
	} else if (z <= 2e+35) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / 0.31942702700572795d0)
    if (z <= (-8.6d+48)) then
        tmp = t_1
    else if (z <= 8.8d-178) then
        tmp = x + ((y * b) * 1.6453555072203998d0)
    else if (z <= 4.7d-91) then
        tmp = x + (1.6453555072203998d0 * (a * (y * z)))
    else if (z <= 2d+35) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / 0.31942702700572795);
	double tmp;
	if (z <= -8.6e+48) {
		tmp = t_1;
	} else if (z <= 8.8e-178) {
		tmp = x + ((y * b) * 1.6453555072203998);
	} else if (z <= 4.7e-91) {
		tmp = x + (1.6453555072203998 * (a * (y * z)));
	} else if (z <= 2e+35) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y / 0.31942702700572795)
	tmp = 0
	if z <= -8.6e+48:
		tmp = t_1
	elif z <= 8.8e-178:
		tmp = x + ((y * b) * 1.6453555072203998)
	elif z <= 4.7e-91:
		tmp = x + (1.6453555072203998 * (a * (y * z)))
	elif z <= 2e+35:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y / 0.31942702700572795))
	tmp = 0.0
	if (z <= -8.6e+48)
		tmp = t_1;
	elseif (z <= 8.8e-178)
		tmp = Float64(x + Float64(Float64(y * b) * 1.6453555072203998));
	elseif (z <= 4.7e-91)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(a * Float64(y * z))));
	elseif (z <= 2e+35)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y / 0.31942702700572795);
	tmp = 0.0;
	if (z <= -8.6e+48)
		tmp = t_1;
	elseif (z <= 8.8e-178)
		tmp = x + ((y * b) * 1.6453555072203998);
	elseif (z <= 4.7e-91)
		tmp = x + (1.6453555072203998 * (a * (y * z)));
	elseif (z <= 2e+35)
		tmp = x + (b * (y * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+48], t$95$1, If[LessEqual[z, 8.8e-178], N[(x + N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e-91], N[(x + N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+35], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.59999999999999957e48 or 1.9999999999999999e35 < z

   1. Initial program 10.4%

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

      1. associate-/l* 15.5%

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

      2. fma-def 15.5%

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

      3. fma-def 15.5%

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

      4. fma-def 15.5%

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

      5. fma-def 15.5%

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

      6. fma-def 15.5%

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

      7. fma-def 15.5%

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

      8. fma-def 15.5%

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

   3. Simplified 15.5%

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

   4. Taylor expanded in z around inf 91.6%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

   if -8.59999999999999957e48 < z < 8.8000000000000005e-178

   1. Initial program 97.6%

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

      1. associate-*l/ 97.6%

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

      2. *-commutative 97.6%

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

      3. fma-def 97.6%

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

      4. *-commutative 97.6%

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

      5. fma-def 97.6%

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

      6. *-commutative 97.6%

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

      7. fma-def 97.6%

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

      8. *-commutative 97.6%

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

      9. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 80.3%

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

   if 8.8000000000000005e-178 < z < 4.70000000000000006e-91

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 84.0%

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

      1. associate-*r* 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in z around 0 84.1%

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

   if 4.70000000000000006e-91 < z < 1.9999999999999999e35

   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 86.0%

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

      1. fma-def 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around 0 63.5%

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

      1. *-commutative 63.5%

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

      2. *-commutative 63.5%

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

      3. associate-*l* 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-178}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-91}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 12: 82.4% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{0.31942702700572795}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-178}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-91}:\\ \;\;\;\;x + \left(a \cdot 1.6453555072203998\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ y 0.31942702700572795))))
   (if (<= z -8.6e+48)
     t_1
     (if (<= z 1.35e-178)
       (+ x (* (* y b) 1.6453555072203998))
       (if (<= z 6.6e-91)
         (+ x (* (* a 1.6453555072203998) (* y z)))
         (if (<= z 4.5e+35) (+ x (* b (* y 1.6453555072203998))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / 0.31942702700572795);
	double tmp;
	if (z <= -8.6e+48) {
		tmp = t_1;
	} else if (z <= 1.35e-178) {
		tmp = x + ((y * b) * 1.6453555072203998);
	} else if (z <= 6.6e-91) {
		tmp = x + ((a * 1.6453555072203998) * (y * z));
	} else if (z <= 4.5e+35) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / 0.31942702700572795d0)
    if (z <= (-8.6d+48)) then
        tmp = t_1
    else if (z <= 1.35d-178) then
        tmp = x + ((y * b) * 1.6453555072203998d0)
    else if (z <= 6.6d-91) then
        tmp = x + ((a * 1.6453555072203998d0) * (y * z))
    else if (z <= 4.5d+35) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y / 0.31942702700572795);
	double tmp;
	if (z <= -8.6e+48) {
		tmp = t_1;
	} else if (z <= 1.35e-178) {
		tmp = x + ((y * b) * 1.6453555072203998);
	} else if (z <= 6.6e-91) {
		tmp = x + ((a * 1.6453555072203998) * (y * z));
	} else if (z <= 4.5e+35) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y / 0.31942702700572795)
	tmp = 0
	if z <= -8.6e+48:
		tmp = t_1
	elif z <= 1.35e-178:
		tmp = x + ((y * b) * 1.6453555072203998)
	elif z <= 6.6e-91:
		tmp = x + ((a * 1.6453555072203998) * (y * z))
	elif z <= 4.5e+35:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y / 0.31942702700572795))
	tmp = 0.0
	if (z <= -8.6e+48)
		tmp = t_1;
	elseif (z <= 1.35e-178)
		tmp = Float64(x + Float64(Float64(y * b) * 1.6453555072203998));
	elseif (z <= 6.6e-91)
		tmp = Float64(x + Float64(Float64(a * 1.6453555072203998) * Float64(y * z)));
	elseif (z <= 4.5e+35)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y / 0.31942702700572795);
	tmp = 0.0;
	if (z <= -8.6e+48)
		tmp = t_1;
	elseif (z <= 1.35e-178)
		tmp = x + ((y * b) * 1.6453555072203998);
	elseif (z <= 6.6e-91)
		tmp = x + ((a * 1.6453555072203998) * (y * z));
	elseif (z <= 4.5e+35)
		tmp = x + (b * (y * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+48], t$95$1, If[LessEqual[z, 1.35e-178], N[(x + N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e-91], N[(x + N[(N[(a * 1.6453555072203998), $MachinePrecision] * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+35], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.59999999999999957e48 or 4.4999999999999997e35 < z

   1. Initial program 10.4%

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

      1. associate-/l* 15.5%

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

      2. fma-def 15.5%

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

      3. fma-def 15.5%

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

      4. fma-def 15.5%

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

      5. fma-def 15.5%

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

      6. fma-def 15.5%

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

      7. fma-def 15.5%

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

      8. fma-def 15.5%

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

   3. Simplified 15.5%

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

   4. Taylor expanded in z around inf 91.6%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

   if -8.59999999999999957e48 < z < 1.35000000000000004e-178

   1. Initial program 97.6%

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

      1. associate-*l/ 97.6%

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

      2. *-commutative 97.6%

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

      3. fma-def 97.6%

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

      4. *-commutative 97.6%

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

      5. fma-def 97.6%

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

      6. *-commutative 97.6%

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

      7. fma-def 97.6%

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

      8. *-commutative 97.6%

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

      9. fma-def 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 80.3%

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

   if 1.35000000000000004e-178 < z < 6.60000000000000023e-91

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 84.0%

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

      1. associate-*r* 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*r* 84.1%

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

   4. Simplified 84.1%

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

   5. Taylor expanded in z around 0 84.1%

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

      1. associate-*r* 84.2%

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

   7. Simplified 84.2%

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

   if 6.60000000000000023e-91 < z < 4.4999999999999997e35

   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 86.0%

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

      1. fma-def 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in z around 0 63.5%

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

      1. *-commutative 63.5%

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

      2. *-commutative 63.5%

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

      3. associate-*l* 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-178}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-91}:\\ \;\;\;\;x + \left(a \cdot 1.6453555072203998\right) \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+35}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 13: 84.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+48} \lor \neg \left(z \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.6e+48) (not (<= z 2e+35)))
   (+ x (/ y 0.31942702700572795))
   (+ x (* (* y b) 1.6453555072203998))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.6e+48) || !(z <= 2e+35)) {
		tmp = x + (y / 0.31942702700572795);
	} 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 <= (-8.6d+48)) .or. (.not. (z <= 2d+35))) then
        tmp = x + (y / 0.31942702700572795d0)
    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 <= -8.6e+48) || !(z <= 2e+35)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + ((y * b) * 1.6453555072203998);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.6e+48) or not (z <= 2e+35):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + ((y * b) * 1.6453555072203998)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.6e+48) || !(z <= 2e+35))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(Float64(y * b) * 1.6453555072203998));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.6e+48) || ~((z <= 2e+35)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + ((y * b) * 1.6453555072203998);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.6e+48], N[Not[LessEqual[z, 2e+35]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.59999999999999957e48 or 1.9999999999999999e35 < z

   1. Initial program 10.4%

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

      1. associate-/l* 15.5%

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

      2. fma-def 15.5%

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

      3. fma-def 15.5%

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

      4. fma-def 15.5%

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

      5. fma-def 15.5%

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

      6. fma-def 15.5%

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

      7. fma-def 15.5%

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

      8. fma-def 15.5%

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

   3. Simplified 15.5%

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

   4. Taylor expanded in z around inf 91.6%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

   if -8.59999999999999957e48 < z < 1.9999999999999999e35

   1. Initial program 97.7%

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

      1. associate-*l/ 98.3%

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

      2. *-commutative 98.3%

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

      3. fma-def 98.3%

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

      4. *-commutative 98.3%

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

      5. fma-def 98.3%

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

      6. *-commutative 98.3%

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

      7. fma-def 98.3%

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

      8. *-commutative 98.3%

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

      9. fma-def 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in z around 0 73.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+48} \lor \neg \left(z \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \]

Alternative 14: 84.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+48} \lor \neg \left(z \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9e+48) (not (<= z 2e+35)))
   (+ x (/ y 0.31942702700572795))
   (+ x (* b (* y 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+48) || !(z <= 2e+35)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-9d+48)) .or. (.not. (z <= 2d+35))) then
        tmp = x + (y / 0.31942702700572795d0)
    else
        tmp = x + (b * (y * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9e+48) || !(z <= 2e+35)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9e+48) or not (z <= 2e+35):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + (b * (y * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9e+48) || !(z <= 2e+35))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9e+48) || ~((z <= 2e+35)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + (b * (y * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9e+48], N[Not[LessEqual[z, 2e+35]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999991e48 or 1.9999999999999999e35 < z

   1. Initial program 10.4%

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

      1. associate-/l* 15.5%

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

      2. fma-def 15.5%

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

      3. fma-def 15.5%

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

      4. fma-def 15.5%

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

      5. fma-def 15.5%

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

      6. fma-def 15.5%

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

      7. fma-def 15.5%

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

      8. fma-def 15.5%

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

   3. Simplified 15.5%

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

   4. Taylor expanded in z around inf 91.6%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

   if -8.99999999999999991e48 < z < 1.9999999999999999e35

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 91.3%

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

      1. fma-def 91.3%

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

   4. Simplified 91.3%

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

   5. Taylor expanded in z around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*l* 73.9%

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

   7. Simplified 73.9%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+48} \lor \neg \left(z \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 15: 63.3% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{0.31942702700572795} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x (/ y 0.31942702700572795)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (y / 0.31942702700572795);
}

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 / 0.31942702700572795d0)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (y / 0.31942702700572795);
}

Python

def code(x, y, z, t, a, b):
	return x + (y / 0.31942702700572795)

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(y / 0.31942702700572795))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + (y / 0.31942702700572795);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]

Derivation

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. associate-/l* 62.7%

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

   2. fma-def 62.7%

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

   3. fma-def 62.7%

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

   4. fma-def 62.7%

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

   5. fma-def 62.7%

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

   6. fma-def 62.7%

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

   7. fma-def 62.7%

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

   8. fma-def 62.7%

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

3. Simplified 62.7%

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

4. Taylor expanded in z around inf 59.7%

   \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

5. Final simplification 59.7%

   \[\leadsto x + \frac{y}{0.31942702700572795} \]

Alternative 16: 46.2% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. associate-/l* 62.7%

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

   2. fma-def 62.7%

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

   3. fma-def 62.7%

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

   4. fma-def 62.7%

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

   5. fma-def 62.7%

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

   6. fma-def 62.7%

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

   7. fma-def 62.7%

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

   8. fma-def 62.7%

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

3. Simplified 62.7%

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

4. Taylor expanded in z around inf 59.7%

   \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]

5. Taylor expanded in x around inf 45.2%

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

6. Final simplification 45.2%

   \[\leadsto x \]

Developer target: 98.7% 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 2023181 
(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))))