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

Percentage Accurate: 58.4% → 97.3%

Time: 17.4s

Alternatives: 14

Speedup: 2.5×

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: 58.4% 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: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;x + t\_2 \cdot \left(y \cdot \frac{1}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + t \cdot \frac{y}{z \cdot z}\right)\right) - \frac{y \cdot -556.47806218377}{z \cdot z}\right) - \left(\frac{y \cdot 47.69379582500642}{z} + \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        (t_2
         (+
          b
          (*
           z
           (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ x (* t_2 (* y (/ 1.0 t_1))))
     (-
      (-
       (+
        (+ x (* y 3.13060547623))
        (+ (/ (* y 11.1667541262) z) (* t (/ y (* z z)))))
       (/ (* y -556.47806218377) (* z z)))
      (+ (/ (* y 47.69379582500642) z) (/ (* y 98.5170599679272) (* z z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = x + (t_2 * (y * (1.0 / t_1)));
	} else {
		tmp = (((x + (y * 3.13060547623)) + (((y * 11.1667541262) / z) + (t * (y / (z * z))))) - ((y * -556.47806218377) / (z * z))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (t_2 * (y * (1.0 / t_1)));
	} else {
		tmp = (((x + (y * 3.13060547623)) + (((y * 11.1667541262) / z) + (t * (y / (z * z))))) - ((y * -556.47806218377) / (z * z))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))
	tmp = 0
	if ((y * t_2) / t_1) <= math.inf:
		tmp = x + (t_2 * (y * (1.0 / t_1)))
	else:
		tmp = (((x + (y * 3.13060547623)) + (((y * 11.1667541262) / z) + (t * (y / (z * z))))) - ((y * -556.47806218377) / (z * z))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	t_2 = Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))
	tmp = 0.0
	if (Float64(Float64(y * t_2) / t_1) <= Inf)
		tmp = Float64(x + Float64(t_2 * Float64(y * Float64(1.0 / t_1))));
	else
		tmp = Float64(Float64(Float64(Float64(x + Float64(y * 3.13060547623)) + Float64(Float64(Float64(y * 11.1667541262) / z) + Float64(t * Float64(y / Float64(z * z))))) - Float64(Float64(y * -556.47806218377) / Float64(z * z))) - Float64(Float64(Float64(y * 47.69379582500642) / z) + Float64(Float64(y * 98.5170599679272) / Float64(z * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	tmp = 0.0;
	if (((y * t_2) / t_1) <= Inf)
		tmp = x + (t_2 * (y * (1.0 / t_1)));
	else
		tmp = (((x + (y * 3.13060547623)) + (((y * 11.1667541262) / z) + (t * (y / (z * z))))) - ((y * -556.47806218377) / (z * z))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(t$95$2 * N[(y * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y * 11.1667541262), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * 47.69379582500642), $MachinePrecision] / z), $MachinePrecision] + N[(N[(y * 98.5170599679272), $MachinePrecision] / N[(z * z), $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 #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 93.2%

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

      1. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\right) \cdot \color{blue}{\frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y\right) \cdot \frac{\color{blue}{1}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right), \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

   4. Applied egg-rr 97.8%

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

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{t \cdot y}{{z}^{2}}\right)\right)\right) - \left(\frac{15234687407}{1000000000} \cdot \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{{z}^{2}} + \left(\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z} + \frac{98517059967927196814627}{1000000000000000000000} \cdot \frac{y}{{z}^{2}}\right)\right)} \]

   5. Simplified 97.8%

      \[\leadsto \color{blue}{\left(\left(\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + t \cdot \frac{y}{z \cdot z}\right)\right) - \frac{y \cdot -556.47806218377}{z \cdot z}\right) - \left(\frac{y \cdot 47.69379582500642}{z} + \frac{y \cdot 98.5170599679272}{z \cdot z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq \infty:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \left(y \cdot \frac{1}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x + y \cdot 3.13060547623\right) + \left(\frac{y \cdot 11.1667541262}{z} + t \cdot \frac{y}{z \cdot z}\right)\right) - \frac{y \cdot -556.47806218377}{z \cdot z}\right) - \left(\frac{y \cdot 47.69379582500642}{z} + \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;x + t\_2 \cdot \left(y \cdot \frac{1}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        (t_2
         (+
          b
          (*
           z
           (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ x (* t_2 (* y (/ 1.0 t_1))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = x + (t_2 * (y * (1.0 / t_1)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (t_2 * (y * (1.0 / t_1)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))
	tmp = 0
	if ((y * t_2) / t_1) <= math.inf:
		tmp = x + (t_2 * (y * (1.0 / t_1)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	t_2 = Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))
	tmp = 0.0
	if (Float64(Float64(y * t_2) / t_1) <= Inf)
		tmp = Float64(x + Float64(t_2 * Float64(y * Float64(1.0 / t_1))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	tmp = 0.0;
	if (((y * t_2) / t_1) <= Inf)
		tmp = x + (t_2 * (y * (1.0 / t_1)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(t$95$2 * N[(y * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 93.2%

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

      1. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\right) \cdot \color{blue}{\frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y\right) \cdot \frac{\color{blue}{1}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right), \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

   4. Applied egg-rr 97.8%

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

   if +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.9%

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

4. Final simplification 97.1%

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

Alternative 3: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.6e+50)
     t_1
     (if (<= z 8.7e+46)
       (+
        (/
         (*
          y
          (+
           b
           (*
            z
            (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.6e+50) {
		tmp = t_1;
	} else if (z <= 8.7e+46) {
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x;
	} 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 * 3.13060547623d0)
    if (z <= (-2.6d+50)) then
        tmp = t_1
    else if (z <= 8.7d+46) then
        tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0)))))))) + x
    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 * 3.13060547623);
	double tmp;
	if (z <= -2.6e+50) {
		tmp = t_1;
	} else if (z <= 8.7e+46) {
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.6e+50:
		tmp = t_1
	elif z <= 8.7e+46:
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.6e+50)
		tmp = t_1;
	elseif (z <= 8.7e+46)
		tmp = Float64(Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))) + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.6e+50)
		tmp = t_1;
	elseif (z <= 8.7e+46)
		tmp = ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) + x;
	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 * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+50], t$95$1, If[LessEqual[z, 8.7e+46], N[(N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e50 or 8.69999999999999961e46 < z

   1. Initial program 4.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.5%

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

   if -2.6000000000000002e50 < z < 8.69999999999999961e46

   1. Initial program 97.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 8.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.3e+47)
     t_1
     (if (<= z 1.04e+46)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z t)))))
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.3e+47) {
		tmp = t_1;
	} else if (z <= 1.04e+46) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} 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 * 3.13060547623d0)
    if (z <= (-2.3d+47)) then
        tmp = t_1
    else if (z <= 1.04d+46) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 * 3.13060547623);
	double tmp;
	if (z <= -2.3e+47) {
		tmp = t_1;
	} else if (z <= 1.04e+46) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.3e+47:
		tmp = t_1
	elif z <= 1.04e+46:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.3e+47)
		tmp = t_1;
	elseif (z <= 1.04e+46)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.3e+47)
		tmp = t_1;
	elseif (z <= 1.04e+46)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	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 * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+47], t$95$1, If[LessEqual[z, 1.04e+46], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e47 or 1.04000000000000003e46 < z

   1. Initial program 4.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.5%

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

   if -2.2999999999999999e47 < z < 1.04000000000000003e46

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(a \cdot z + \left(t \cdot z\right) \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(a \cdot z + t \cdot \left(z \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(b + \left(a \cdot z + t \cdot {z}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z + t \cdot {z}^{2}\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z + t \cdot \left(z \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z + \left(t \cdot z\right) \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      7. distribute-rgt-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(z \cdot t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      11. *-lowering-*.f64 97.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 97.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+47}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1e+19)
     t_1
     (if (<= z 6.4e+42)
       (+
        x
        (*
         (+
          b
          (* z (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))
         (* 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 * 3.13060547623);
	double tmp;
	if (z <= -1e+19) {
		tmp = t_1;
	} else if (z <= 6.4e+42) {
		tmp = x + ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (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 * 3.13060547623d0)
    if (z <= (-1d+19)) then
        tmp = t_1
    else if (z <= 6.4d+42) then
        tmp = x + ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0))))))) * (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 * 3.13060547623);
	double tmp;
	if (z <= -1e+19) {
		tmp = t_1;
	} else if (z <= 6.4e+42) {
		tmp = x + ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1e+19:
		tmp = t_1
	elif z <= 6.4e+42:
		tmp = x + ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1e+19)
		tmp = t_1;
	elseif (z <= 6.4e+42)
		tmp = Float64(x + Float64(Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262))))))) * 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 * 3.13060547623);
	tmp = 0.0;
	if (z <= -1e+19)
		tmp = t_1;
	elseif (z <= 6.4e+42)
		tmp = x + ((b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))) * (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 * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+19], t$95$1, If[LessEqual[z, 6.4e+42], N[(x + N[(N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1e19 or 6.40000000000000004e42 < z

   1. Initial program 6.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.6%

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

   if -1e19 < z < 6.40000000000000004e42

   1. Initial program 97.8%

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

      1. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)\right) \cdot \color{blue}{\frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot y\right) \cdot \frac{\color{blue}{1}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right) \cdot \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right), \color{blue}{\left(y \cdot \frac{1}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)}\right)\right) \]

   4. Applied egg-rr 99.0%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right)\right), t\right)\right), a\right)\right), b\right), \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot y\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right)\right), t\right)\right), a\right)\right), b\right), \left(y \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

      2. *-lowering-*.f64 93.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right)\right), t\right)\right), a\right)\right), b\right), \mathsf{*.f64}\left(y, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   7. Simplified 93.5%

      \[\leadsto x + \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \color{blue}{\left(y \cdot 1.6453555072203998\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;x + \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right) \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -290.0)
   (+ (* y 3.13060547623) (- x (/ (* y 36.52704169880642) z)))
   (if (<= z 6.4e+42)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z t)))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -290.0) {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	} else if (z <= 6.4e+42) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-290.0d0)) then
        tmp = (y * 3.13060547623d0) + (x - ((y * 36.52704169880642d0) / z))
    else if (z <= 6.4d+42) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -290.0) {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	} else if (z <= 6.4e+42) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -290.0:
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z))
	elif z <= 6.4e+42:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -290.0)
		tmp = Float64(Float64(y * 3.13060547623) + Float64(x - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 6.4e+42)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -290.0)
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	elseif (z <= 6.4e+42)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -290.0], N[(N[(y * 3.13060547623), $MachinePrecision] + N[(x - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e+42], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -290

   1. Initial program 15.5%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

      2. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x + \left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x - \color{blue}{\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      12. metadata-eval 89.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{3652704169880641883561}{100000000000000000000}\right), z\right)\right)\right) \]

   5. Simplified 89.6%

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

   if -290 < z < 6.40000000000000004e42

   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. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 95.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 95.7%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + z \cdot \left(a + t \cdot z\right)\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \left(a + t \cdot z\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(t \cdot z\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \left(z \cdot t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      5. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(z, t\right)\right)\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 95.2%

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

   if 6.40000000000000004e42 < z

   1. Initial program 6.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 96.2%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -290:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{-50}:\\ \;\;\;\;1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-24}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* y 3.13060547623) (- x (/ (* y 36.52704169880642) z)))))
   (if (<= z -3e-26)
     t_1
     (if (<= z -8.1e-50)
       (* 1.6453555072203998 (* a (* y z)))
       (if (<= z 4.6e-24) (+ 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 = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	double tmp;
	if (z <= -3e-26) {
		tmp = t_1;
	} else if (z <= -8.1e-50) {
		tmp = 1.6453555072203998 * (a * (y * z));
	} else if (z <= 4.6e-24) {
		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 = (y * 3.13060547623d0) + (x - ((y * 36.52704169880642d0) / z))
    if (z <= (-3d-26)) then
        tmp = t_1
    else if (z <= (-8.1d-50)) then
        tmp = 1.6453555072203998d0 * (a * (y * z))
    else if (z <= 4.6d-24) 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 = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	double tmp;
	if (z <= -3e-26) {
		tmp = t_1;
	} else if (z <= -8.1e-50) {
		tmp = 1.6453555072203998 * (a * (y * z));
	} else if (z <= 4.6e-24) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z))
	tmp = 0
	if z <= -3e-26:
		tmp = t_1
	elif z <= -8.1e-50:
		tmp = 1.6453555072203998 * (a * (y * z))
	elif z <= 4.6e-24:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * 3.13060547623) + Float64(x - Float64(Float64(y * 36.52704169880642) / z)))
	tmp = 0.0
	if (z <= -3e-26)
		tmp = t_1;
	elseif (z <= -8.1e-50)
		tmp = Float64(1.6453555072203998 * Float64(a * Float64(y * z)));
	elseif (z <= 4.6e-24)
		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 = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	tmp = 0.0;
	if (z <= -3e-26)
		tmp = t_1;
	elseif (z <= -8.1e-50)
		tmp = 1.6453555072203998 * (a * (y * z));
	elseif (z <= 4.6e-24)
		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[(N[(y * 3.13060547623), $MachinePrecision] + N[(x - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-26], t$95$1, If[LessEqual[z, -8.1e-50], N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-24], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000012e-26 or 4.6000000000000002e-24 < z

   1. Initial program 23.4%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

      2. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x + \left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x - \color{blue}{\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      12. metadata-eval 84.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{3652704169880641883561}{100000000000000000000}\right), z\right)\right)\right) \]

   5. Simplified 84.7%

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

   if -3.00000000000000012e-26 < z < -8.0999999999999999e-50

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 99.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{a \cdot \left(y \cdot z\right)}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot z\right)\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y \cdot z\right)\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + \frac{119400905721}{10000000000} \cdot z\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \left(\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \left(z \cdot \color{blue}{\frac{119400905721}{10000000000}}\right)\right)\right) \]

      6. *-lowering-*.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right)\right)\right) \]

   8. Simplified 68.0%

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

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(a \cdot \left(y \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \color{blue}{\left(a \cdot \left(y \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 68.2%

          \[\leadsto \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 68.2%

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

   if -8.0999999999999999e-50 < z < 4.6000000000000002e-24

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      5. *-lowering-*.f64 87.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 87.9%

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

Alternative 8: 90.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.5e+46)
   (+ x (* y 3.13060547623))
   (if (<= z 5.2e-5)
     (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))
     (+ (* y 3.13060547623) (- x (/ (* y 36.52704169880642) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.5e+46) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 5.2e-5) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	}
	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 <= (-7.5d+46)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 5.2d-5) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = (y * 3.13060547623d0) + (x - ((y * 36.52704169880642d0) / z))
    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 <= -7.5e+46) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 5.2e-5) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.5e+46:
		tmp = x + (y * 3.13060547623)
	elif z <= 5.2e-5:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.5e+46)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(Float64(y * 3.13060547623) + Float64(x - Float64(Float64(y * 36.52704169880642) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.5e+46)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 5.2e-5)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.5e+46], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], 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[(N[(y * 3.13060547623), $MachinePrecision] + N[(x - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5000000000000003e46

   1. Initial program 2.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 94.9%

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

   if -7.5000000000000003e46 < z < 5.19999999999999968e-5

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 94.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 93.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 93.5%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 19.6%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

      2. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x + \left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x - \color{blue}{\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      12. metadata-eval 86.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{3652704169880641883561}{100000000000000000000}\right), z\right)\right)\right) \]

   5. Simplified 86.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+46}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3100000000000:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{1}{\frac{0.607771387771}{y \cdot \left(b + z \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3100000000000.0)
   (+ x (* y 3.13060547623))
   (if (<= z 5.2e-5)
     (+ x (/ 1.0 (/ 0.607771387771 (* y (+ b (* z a))))))
     (+ (* y 3.13060547623) (- x (/ (* y 36.52704169880642) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3100000000000.0) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 5.2e-5) {
		tmp = x + (1.0 / (0.607771387771 / (y * (b + (z * a)))));
	} else {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	}
	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 <= (-3100000000000.0d0)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 5.2d-5) then
        tmp = x + (1.0d0 / (0.607771387771d0 / (y * (b + (z * a)))))
    else
        tmp = (y * 3.13060547623d0) + (x - ((y * 36.52704169880642d0) / z))
    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 <= -3100000000000.0) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 5.2e-5) {
		tmp = x + (1.0 / (0.607771387771 / (y * (b + (z * a)))));
	} else {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3100000000000.0:
		tmp = x + (y * 3.13060547623)
	elif z <= 5.2e-5:
		tmp = x + (1.0 / (0.607771387771 / (y * (b + (z * a)))))
	else:
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3100000000000.0)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 5.2e-5)
		tmp = Float64(x + Float64(1.0 / Float64(0.607771387771 / Float64(y * Float64(b + Float64(z * a))))));
	else
		tmp = Float64(Float64(y * 3.13060547623) + Float64(x - Float64(Float64(y * 36.52704169880642) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3100000000000.0)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 5.2e-5)
		tmp = x + (1.0 / (0.607771387771 / (y * (b + (z * a)))));
	else
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3100000000000.0], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-5], N[(x + N[(1.0 / N[(0.607771387771 / N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 3.13060547623), $MachinePrecision] + N[(x - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.1e12

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 93.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 93.6%

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

   if -3.1e12 < z < 5.19999999999999968e-5

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 95.5%

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

      1. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{y \cdot \left(b + z \cdot a\right)}}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}{y \cdot \left(b + z \cdot a\right)}\right)}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{z \cdot \left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) + \frac{607771387771}{1000000000000}}{y \cdot \left(b + z \cdot a\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{z \cdot \left(z \cdot \left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) + \frac{119400905721}{10000000000}\right) + \frac{607771387771}{1000000000000}}{y \cdot \left(b + z \cdot a\right)}\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \left(\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + \frac{15234687407}{1000000000}\right) + \frac{314690115749}{10000000000}\right) + \frac{119400905721}{10000000000}\right) + \frac{607771387771}{1000000000000}}{y \cdot \left(b + z \cdot a\right)}\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(z \cdot \left(z \cdot \left(z \cdot \left(z + \frac{15234687407}{1000000000}\right) + \frac{314690115749}{10000000000}\right) + \frac{119400905721}{10000000000}\right) + \frac{607771387771}{1000000000000}\right), \color{blue}{\left(y \cdot \left(b + z \cdot a\right)\right)}\right)\right)\right) \]

   7. Applied egg-rr 95.5%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\color{blue}{\frac{607771387771}{1000000000000}}, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right)\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 93.3%

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

   if 5.19999999999999968e-5 < z

   1. Initial program 19.6%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

      2. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x + \left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x - \color{blue}{\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      12. metadata-eval 86.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{3652704169880641883561}{100000000000000000000}\right), z\right)\right)\right) \]

   5. Simplified 86.1%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 83.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -5 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.1 \cdot 10^{-50}:\\ \;\;\;\;1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-5}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -5e-26)
     t_1
     (if (<= z -8.1e-50)
       (* 1.6453555072203998 (* a (* y z)))
       (if (<= z 3.8e-5) (+ 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 * 3.13060547623);
	double tmp;
	if (z <= -5e-26) {
		tmp = t_1;
	} else if (z <= -8.1e-50) {
		tmp = 1.6453555072203998 * (a * (y * z));
	} else if (z <= 3.8e-5) {
		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 * 3.13060547623d0)
    if (z <= (-5d-26)) then
        tmp = t_1
    else if (z <= (-8.1d-50)) then
        tmp = 1.6453555072203998d0 * (a * (y * z))
    else if (z <= 3.8d-5) 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 * 3.13060547623);
	double tmp;
	if (z <= -5e-26) {
		tmp = t_1;
	} else if (z <= -8.1e-50) {
		tmp = 1.6453555072203998 * (a * (y * z));
	} else if (z <= 3.8e-5) {
		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 * 3.13060547623)
	tmp = 0
	if z <= -5e-26:
		tmp = t_1
	elif z <= -8.1e-50:
		tmp = 1.6453555072203998 * (a * (y * z))
	elif z <= 3.8e-5:
		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 * 3.13060547623))
	tmp = 0.0
	if (z <= -5e-26)
		tmp = t_1;
	elseif (z <= -8.1e-50)
		tmp = Float64(1.6453555072203998 * Float64(a * Float64(y * z)));
	elseif (z <= 3.8e-5)
		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 * 3.13060547623);
	tmp = 0.0;
	if (z <= -5e-26)
		tmp = t_1;
	elseif (z <= -8.1e-50)
		tmp = 1.6453555072203998 * (a * (y * z));
	elseif (z <= 3.8e-5)
		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 * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e-26], t$95$1, If[LessEqual[z, -8.1e-50], N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-5], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000019e-26 or 3.8000000000000002e-5 < z

   1. Initial program 21.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 85.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 85.7%

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

   if -5.00000000000000019e-26 < z < -8.0999999999999999e-50

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 99.3%

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

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{a \cdot \left(y \cdot z\right)}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \left(y \cdot z\right)\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \left(y \cdot z\right)\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + \frac{119400905721}{10000000000} \cdot z\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \left(\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \left(z \cdot \color{blue}{\frac{119400905721}{10000000000}}\right)\right)\right) \]

      6. *-lowering-*.f64 68.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, z\right)\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\frac{119400905721}{10000000000}}\right)\right)\right) \]

   8. Simplified 68.0%

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

   9. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(a \cdot \left(y \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \color{blue}{\left(a \cdot \left(y \cdot z\right)\right)}\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \mathsf{*.f64}\left(a, \color{blue}{\left(y \cdot z\right)}\right)\right) \]

       3. *-lowering-*.f64 68.2%

          \[\leadsto \mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   11. Simplified 68.2%

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

   if -8.0999999999999999e-50 < z < 3.8000000000000002e-5

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      5. *-lowering-*.f64 86.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 86.5%

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

Alternative 11: 64.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-153}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.5e-63)
     t_1
     (if (<= z 6.2e-153) (* 1.6453555072203998 (* y b)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.5e-63) {
		tmp = t_1;
	} else if (z <= 6.2e-153) {
		tmp = 1.6453555072203998 * (y * 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 + (y * 3.13060547623d0)
    if (z <= (-2.5d-63)) then
        tmp = t_1
    else if (z <= 6.2d-153) then
        tmp = 1.6453555072203998d0 * (y * 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 + (y * 3.13060547623);
	double tmp;
	if (z <= -2.5e-63) {
		tmp = t_1;
	} else if (z <= 6.2e-153) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.5e-63:
		tmp = t_1
	elif z <= 6.2e-153:
		tmp = 1.6453555072203998 * (y * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.5e-63)
		tmp = t_1;
	elseif (z <= 6.2e-153)
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.5e-63)
		tmp = t_1;
	elseif (z <= 6.2e-153)
		tmp = 1.6453555072203998 * (y * 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[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-63], t$95$1, If[LessEqual[z, 6.2e-153], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e-63 or 6.1999999999999999e-153 < z

   1. Initial program 41.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 73.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 73.8%

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

   if -2.5000000000000001e-63 < z < 6.1999999999999999e-153

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 58.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 58.1%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\frac{1000000000000}{607771387771}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right) \]

      4. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right) \]

   8. Simplified 58.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-153}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -210:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-215}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -210.0) x (if (<= x 1.2e-215) (* 1.6453555072203998 (* y b)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -210.0) {
		tmp = x;
	} else if (x <= 1.2e-215) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-210.0d0)) then
        tmp = x
    else if (x <= 1.2d-215) then
        tmp = 1.6453555072203998d0 * (y * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -210.0) {
		tmp = x;
	} else if (x <= 1.2e-215) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -210.0:
		tmp = x
	elif x <= 1.2e-215:
		tmp = 1.6453555072203998 * (y * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -210.0)
		tmp = x;
	elseif (x <= 1.2e-215)
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -210.0)
		tmp = x;
	elseif (x <= 1.2e-215)
		tmp = 1.6453555072203998 * (y * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -210.0], x, If[LessEqual[x, 1.2e-215], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -210 or 1.20000000000000005e-215 < x

   1. Initial program 57.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 60.2%

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

   if -210 < x < 1.20000000000000005e-215

   1. Initial program 58.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 37.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 37.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\frac{1000000000000}{607771387771}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right) \]

      4. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right) \]

   8. Simplified 36.3%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -210:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-215}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -500:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -500.0) x (if (<= x 1.25e-215) (* b (* y 1.6453555072203998)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -500.0) {
		tmp = x;
	} else if (x <= 1.25e-215) {
		tmp = b * (y * 1.6453555072203998);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-500.0d0)) then
        tmp = x
    else if (x <= 1.25d-215) then
        tmp = b * (y * 1.6453555072203998d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -500.0) {
		tmp = x;
	} else if (x <= 1.25e-215) {
		tmp = b * (y * 1.6453555072203998);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -500.0:
		tmp = x
	elif x <= 1.25e-215:
		tmp = b * (y * 1.6453555072203998)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -500.0)
		tmp = x;
	elseif (x <= 1.25e-215)
		tmp = Float64(b * Float64(y * 1.6453555072203998));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -500.0)
		tmp = x;
	elseif (x <= 1.25e-215)
		tmp = b * (y * 1.6453555072203998);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -500.0], x, If[LessEqual[x, 1.25e-215], N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -500 or 1.24999999999999989e-215 < x

   1. Initial program 57.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 60.2%

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

   if -500 < x < 1.24999999999999989e-215

   1. Initial program 58.8%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 37.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 37.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\frac{1000000000000}{607771387771}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right) \]

      4. *-lowering-*.f64 36.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right) \]

   8. Simplified 36.3%

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

      1. *-commutative N/A

         \[\leadsto \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(y \cdot b\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\frac{1000000000000}{607771387771} \cdot y\right) \cdot \color{blue}{b} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot y\right), \color{blue}{b}\right) \]

      4. *-lowering-*.f64 36.2%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, y\right), b\right) \]

   10. Applied egg-rr 36.2%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -500:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-215}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.5% 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 58.3%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 41.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -649934499625263200000000000000000000000000000000000000) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))) (if (< z 706696543691428700000000000000000000000000000000000000000000) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)))) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))))))

  (+ 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))))