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

Percentage Accurate: 58.0% → 97.7%

Time: 14.8s

Alternatives: 12

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: 58.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (+
          b
          (*
           z
           (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ x (* y (/ t_2 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	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 + (y * (t_2 / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	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 + (y * (t_2 / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	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 + (y * (t_2 / 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(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	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(y * Float64(t_2 / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	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 + (y * (t_2 / 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[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, Block[{t$95$2 = N[(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[(y * N[(t$95$2 / t$95$1), $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 91.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

   4. Applied egg-rr 95.0%

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

   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 99.8%

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

4. Final simplification 97.1%

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

Alternative 2: 97.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(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(y * Float64(t_2 / 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 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	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 + (y * (t_2 / 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[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, Block[{t$95$2 = N[(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[(y * N[(t$95$2 / t$95$1), $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 91.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

   4. Applied egg-rr 95.0%

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

   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 96.6%

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

   5. Simplified 96.6%

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

4. Final simplification 95.7%

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

Alternative 3: 94.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -8.6e+33)
     t_1
     (if (<= z 1.45e+56)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       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 <= -8.6e+33) {
		tmp = t_1;
	} else if (z <= 1.45e+56) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} 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 <= (-8.6d+33)) then
        tmp = t_1
    else if (z <= 1.45d+56) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    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 <= -8.6e+33) {
		tmp = t_1;
	} else if (z <= 1.45e+56) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} 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 <= -8.6e+33:
		tmp = t_1
	elif z <= 1.45e+56:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	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 <= -8.6e+33)
		tmp = t_1;
	elseif (z <= 1.45e+56)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	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 <= -8.6e+33)
		tmp = t_1;
	elseif (z <= 1.45e+56)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	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, -8.6e+33], t$95$1, If[LessEqual[z, 1.45e+56], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.60000000000000057e33 or 1.45000000000000004e56 < z

   1. Initial program 3.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 93.9%

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

   5. Simplified 93.9%

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

   if -8.60000000000000057e33 < z < 1.45000000000000004e56

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{55833770631}{5000000000} \cdot z\right)}, t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-188}:\\ \;\;\;\;\left(x + b \cdot \left(y \cdot 1.6453555072203998\right)\right) + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(z \cdot z + z \cdot 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.7e+16)
     t_1
     (if (<= z -1.1e-188)
       (+
        (+ x (* b (* y 1.6453555072203998)))
        (* z (* y (- (* a 1.6453555072203998) (* b 32.324150453290734)))))
       (if (<= z 550.0)
         (+
          x
          (/
           (* y b)
           (+
            0.607771387771
            (*
             z
             (+
              11.9400905721
              (* z (+ 31.4690115749 (+ (* z z) (* z 15.234687407)))))))))
         (+ t_1 (/ (* y -36.52704169880642) z)))))))

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 <= -2.7e+16) {
		tmp = t_1;
	} else if (z <= -1.1e-188) {
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))));
	} else if (z <= 550.0) {
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + ((z * z) + (z * 15.234687407))))))));
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.7d+16)) then
        tmp = t_1
    else if (z <= (-1.1d-188)) then
        tmp = (x + (b * (y * 1.6453555072203998d0))) + (z * (y * ((a * 1.6453555072203998d0) - (b * 32.324150453290734d0))))
    else if (z <= 550.0d0) then
        tmp = x + ((y * b) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + ((z * z) + (z * 15.234687407d0))))))))
    else
        tmp = t_1 + ((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 t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.7e+16) {
		tmp = t_1;
	} else if (z <= -1.1e-188) {
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))));
	} else if (z <= 550.0) {
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + ((z * z) + (z * 15.234687407))))))));
	} else {
		tmp = t_1 + ((y * -36.52704169880642) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.7e+16:
		tmp = t_1
	elif z <= -1.1e-188:
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))))
	elif z <= 550.0:
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + ((z * z) + (z * 15.234687407))))))))
	else:
		tmp = t_1 + ((y * -36.52704169880642) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.7e+16)
		tmp = t_1;
	elseif (z <= -1.1e-188)
		tmp = Float64(Float64(x + Float64(b * Float64(y * 1.6453555072203998))) + Float64(z * Float64(y * Float64(Float64(a * 1.6453555072203998) - Float64(b * 32.324150453290734)))));
	elseif (z <= 550.0)
		tmp = Float64(x + Float64(Float64(y * b) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(Float64(z * z) + Float64(z * 15.234687407)))))))));
	else
		tmp = Float64(t_1 + Float64(Float64(y * -36.52704169880642) / z));
	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 <= -2.7e+16)
		tmp = t_1;
	elseif (z <= -1.1e-188)
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))));
	elseif (z <= 550.0)
		tmp = x + ((y * b) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + ((z * z) + (z * 15.234687407))))))));
	else
		tmp = t_1 + ((y * -36.52704169880642) / z);
	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, -2.7e+16], t$95$1, If[LessEqual[z, -1.1e-188], N[(N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y * N[(N[(a * 1.6453555072203998), $MachinePrecision] - N[(b * 32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 550.0], N[(x + N[(N[(y * b), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(N[(z * z), $MachinePrecision] + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e16

   1. Initial program 10.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 92.2%

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

   5. Simplified 92.2%

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

   if -2.7e16 < z < -1.1e-188

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right) + \color{blue}{z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right), \color{blue}{\left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)\right), \left(\color{blue}{z} \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \frac{1000000000000}{607771387771}\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(y \cdot \frac{1000000000000}{607771387771}\right)\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y \cdot \frac{1000000000000}{607771387771}\right)\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) \cdot \color{blue}{y}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot a\right), \color{blue}{\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(a \cdot \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot b\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot b\right)\right)\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(b \cdot \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}}\right)\right)\right)\right)\right) \]

      17. *-lowering-*.f64 86.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(b, \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}}\right)\right)\right)\right)\right) \]

   5. Simplified 86.2%

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

   if -1.1e-188 < z < 550

   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. Step-by-step derivation

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

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

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

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

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

      5. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 86.0%

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

   7. Simplified 86.0%

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

   if 550 < z

   1. Initial program 11.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. div-sub N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. *-commutative N/A

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

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

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

      14. /-lowering-/.f64 N/A

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

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

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

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

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

      17. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-188}:\\ \;\;\;\;\left(x + b \cdot \left(y \cdot 1.6453555072203998\right)\right) + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(z \cdot z + z \cdot 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15000000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + y \cdot -98.5170599679272}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -15000000000000.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (/
      (-
       (/ (+ (- (* y t) (* y -556.47806218377)) (* y -98.5170599679272)) z)
       (* y 36.52704169880642))
      z)))
   (if (<= z 550.0)
     (+
      x
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))
       0.607771387771))
     (+ (+ x (* y 3.13060547623)) (/ (* y -36.52704169880642) z)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -15000000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((((((y * t) - (y * -556.47806218377)) + (y * -98.5170599679272)) / z) - (y * 36.52704169880642)) / z));
	} else if (z <= 550.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771);
	} else {
		tmp = (x + (y * 3.13060547623)) + ((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 <= (-15000000000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((((((y * t) - (y * (-556.47806218377d0))) + (y * (-98.5170599679272d0))) / z) - (y * 36.52704169880642d0)) / z))
    else if (z <= 550.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))) / 0.607771387771d0)
    else
        tmp = (x + (y * 3.13060547623d0)) + ((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 <= -15000000000000.0) {
		tmp = x + ((y * 3.13060547623) + ((((((y * t) - (y * -556.47806218377)) + (y * -98.5170599679272)) / z) - (y * 36.52704169880642)) / z));
	} else if (z <= 550.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771);
	} else {
		tmp = (x + (y * 3.13060547623)) + ((y * -36.52704169880642) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -15000000000000.0:
		tmp = x + ((y * 3.13060547623) + ((((((y * t) - (y * -556.47806218377)) + (y * -98.5170599679272)) / z) - (y * 36.52704169880642)) / z))
	elif z <= 550.0:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771)
	else:
		tmp = (x + (y * 3.13060547623)) + ((y * -36.52704169880642) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -15000000000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(Float64(Float64(Float64(y * t) - Float64(y * -556.47806218377)) + Float64(y * -98.5170599679272)) / z) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 550.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771));
	else
		tmp = Float64(Float64(x + Float64(y * 3.13060547623)) + 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 <= -15000000000000.0)
		tmp = x + ((y * 3.13060547623) + ((((((y * t) - (y * -556.47806218377)) + (y * -98.5170599679272)) / z) - (y * 36.52704169880642)) / z));
	elseif (z <= 550.0)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771);
	else
		tmp = (x + (y * 3.13060547623)) + ((y * -36.52704169880642) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -15000000000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(N[(N[(N[(y * t), $MachinePrecision] - N[(y * -556.47806218377), $MachinePrecision]), $MachinePrecision] + N[(y * -98.5170599679272), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 550.0], N[(x + 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] / 0.607771387771), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5e13

   1. Initial program 11.4%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 92.6%

      \[\leadsto \color{blue}{x + \left(y \cdot 3.13060547623 - \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + -98.5170599679272 \cdot y}{0 - z} + y \cdot 36.52704169880642}{z}\right)} \]

   if -1.5e13 < z < 550

   1. Initial program 99.6%

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

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

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

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

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

      5. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 98.6%

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

   if 550 < z

   1. Initial program 11.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. div-sub N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. *-commutative N/A

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

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

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

      14. /-lowering-/.f64 N/A

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

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

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

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

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

      17. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15000000000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{\frac{\left(y \cdot t - y \cdot -556.47806218377\right) + y \cdot -98.5170599679272}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.15e+15)
     t_1
     (if (<= z 550.0)
       (+
        x
        (/
         (*
          y
          (+
           b
           (*
            z
            (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))
         0.607771387771))
       (+ t_1 (/ (* y -36.52704169880642) z))))))

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 <= -1.15e+15) {
		tmp = t_1;
	} else if (z <= 550.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771);
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-1.15d+15)) then
        tmp = t_1
    else if (z <= 550.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))) / 0.607771387771d0)
    else
        tmp = t_1 + ((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 t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.15e+15) {
		tmp = t_1;
	} else if (z <= 550.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771);
	} else {
		tmp = t_1 + ((y * -36.52704169880642) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.15e+15:
		tmp = t_1
	elif z <= 550.0:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771)
	else:
		tmp = t_1 + ((y * -36.52704169880642) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.15e+15)
		tmp = t_1;
	elseif (z <= 550.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771));
	else
		tmp = Float64(t_1 + Float64(Float64(y * -36.52704169880642) / z));
	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 <= -1.15e+15)
		tmp = t_1;
	elseif (z <= 550.0)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / 0.607771387771);
	else
		tmp = t_1 + ((y * -36.52704169880642) / z);
	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, -1.15e+15], t$95$1, If[LessEqual[z, 550.0], N[(x + 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] / 0.607771387771), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15e15

   1. Initial program 11.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 92.3%

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

   5. Simplified 92.3%

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

   if -1.15e15 < z < 550

   1. Initial program 99.6%

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

      1. *-commutative N/A

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

      2. distribute-lft-in N/A

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

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

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

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

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

      5. *-lowering-*.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 98.6%

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

   if 550 < z

   1. Initial program 11.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. div-sub N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. *-commutative N/A

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

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

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

      14. /-lowering-/.f64 N/A

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

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

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

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

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

      17. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-189}:\\ \;\;\;\;\left(x + b \cdot \left(y \cdot 1.6453555072203998\right)\right) + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 510:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -5.2e+15)
     t_1
     (if (<= z -8e-189)
       (+
        (+ x (* b (* y 1.6453555072203998)))
        (* z (* y (- (* a 1.6453555072203998) (* b 32.324150453290734)))))
       (if (<= z 510.0)
         (+ x (* 1.6453555072203998 (* y b)))
         (+ t_1 (/ (* y -36.52704169880642) z)))))))

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 <= -5.2e+15) {
		tmp = t_1;
	} else if (z <= -8e-189) {
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))));
	} else if (z <= 510.0) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-5.2d+15)) then
        tmp = t_1
    else if (z <= (-8d-189)) then
        tmp = (x + (b * (y * 1.6453555072203998d0))) + (z * (y * ((a * 1.6453555072203998d0) - (b * 32.324150453290734d0))))
    else if (z <= 510.0d0) then
        tmp = x + (1.6453555072203998d0 * (y * b))
    else
        tmp = t_1 + ((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 t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -5.2e+15) {
		tmp = t_1;
	} else if (z <= -8e-189) {
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))));
	} else if (z <= 510.0) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = t_1 + ((y * -36.52704169880642) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -5.2e+15:
		tmp = t_1
	elif z <= -8e-189:
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))))
	elif z <= 510.0:
		tmp = x + (1.6453555072203998 * (y * b))
	else:
		tmp = t_1 + ((y * -36.52704169880642) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -5.2e+15)
		tmp = t_1;
	elseif (z <= -8e-189)
		tmp = Float64(Float64(x + Float64(b * Float64(y * 1.6453555072203998))) + Float64(z * Float64(y * Float64(Float64(a * 1.6453555072203998) - Float64(b * 32.324150453290734)))));
	elseif (z <= 510.0)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	else
		tmp = Float64(t_1 + Float64(Float64(y * -36.52704169880642) / z));
	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 <= -5.2e+15)
		tmp = t_1;
	elseif (z <= -8e-189)
		tmp = (x + (b * (y * 1.6453555072203998))) + (z * (y * ((a * 1.6453555072203998) - (b * 32.324150453290734))));
	elseif (z <= 510.0)
		tmp = x + (1.6453555072203998 * (y * b));
	else
		tmp = t_1 + ((y * -36.52704169880642) / z);
	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, -5.2e+15], t$95$1, If[LessEqual[z, -8e-189], N[(N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(y * N[(N[(a * 1.6453555072203998), $MachinePrecision] - N[(b * 32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 510.0], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e15

   1. Initial program 10.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 92.2%

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

   5. Simplified 92.2%

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

   if -5.2e15 < z < -8.00000000000000055e-189

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right) + \color{blue}{z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right), \color{blue}{\left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)\right), \left(\color{blue}{z} \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \frac{1000000000000}{607771387771}\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      5. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(b \cdot \left(y \cdot \frac{1000000000000}{607771387771}\right)\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \left(y \cdot \frac{1000000000000}{607771387771}\right)\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \left(z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)}\right)\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot \left(b \cdot y\right)\right)\right)\right) \]

      10. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) \cdot \color{blue}{y}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot a\right), \color{blue}{\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\left(a \cdot \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot b\right)\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(\color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}} \cdot b\right)\right)\right)\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \left(b \cdot \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}}\right)\right)\right)\right)\right) \]

      17. *-lowering-*.f64 86.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \frac{1000000000000}{607771387771}\right)\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(a, \frac{1000000000000}{607771387771}\right), \mathsf{*.f64}\left(b, \color{blue}{\frac{11940090572100000000000000}{369386059793087248348441}}\right)\right)\right)\right)\right) \]

   5. Simplified 86.2%

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

   if -8.00000000000000055e-189 < z < 510

   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

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. 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. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 85.9%

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

   8. Simplified 85.9%

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

   if 510 < z

   1. Initial program 11.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. div-sub N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. *-commutative N/A

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

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

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

      14. /-lowering-/.f64 N/A

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

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

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

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

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

      17. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

Alternative 8: 83.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -9 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 52:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y \cdot -36.52704169880642}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -9e+16)
     t_1
     (if (<= z 52.0)
       (+ x (* 1.6453555072203998 (* y b)))
       (+ t_1 (/ (* y -36.52704169880642) z))))))

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 <= -9e+16) {
		tmp = t_1;
	} else if (z <= 52.0) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = t_1 + ((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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-9d+16)) then
        tmp = t_1
    else if (z <= 52.0d0) then
        tmp = x + (1.6453555072203998d0 * (y * b))
    else
        tmp = t_1 + ((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 t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -9e+16) {
		tmp = t_1;
	} else if (z <= 52.0) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = t_1 + ((y * -36.52704169880642) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -9e+16:
		tmp = t_1
	elif z <= 52.0:
		tmp = x + (1.6453555072203998 * (y * b))
	else:
		tmp = t_1 + ((y * -36.52704169880642) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -9e+16)
		tmp = t_1;
	elseif (z <= 52.0)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	else
		tmp = Float64(t_1 + Float64(Float64(y * -36.52704169880642) / z));
	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 <= -9e+16)
		tmp = t_1;
	elseif (z <= 52.0)
		tmp = x + (1.6453555072203998 * (y * b));
	else
		tmp = t_1 + ((y * -36.52704169880642) / z);
	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, -9e+16], t$95$1, If[LessEqual[z, 52.0], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9e16

   1. Initial program 10.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 92.2%

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

   5. Simplified 92.2%

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

   if -9e16 < z < 52

   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

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. 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. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 80.6%

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

   8. Simplified 80.6%

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

   if 52 < z

   1. Initial program 11.1%

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

   3. Taylor expanded in z around inf

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

      1. associate-+r+ N/A

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

      2. associate--l+ N/A

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

      3. associate-*r/ N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. distribute-lft-neg-in N/A

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

      7. div-sub N/A

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

      8. distribute-lft-neg-in N/A

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

      9. metadata-eval N/A

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

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

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

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

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

      12. *-commutative N/A

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

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

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

      14. /-lowering-/.f64 N/A

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

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

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

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

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

      17. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

Alternative 9: 83.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-13}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -7.5e+16)
     t_1
     (if (<= z 8.4e-13) (+ x (* 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 <= -7.5e+16) {
		tmp = t_1;
	} else if (z <= 8.4e-13) {
		tmp = x + (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 <= (-7.5d+16)) then
        tmp = t_1
    else if (z <= 8.4d-13) then
        tmp = x + (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 <= -7.5e+16) {
		tmp = t_1;
	} else if (z <= 8.4e-13) {
		tmp = x + (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 <= -7.5e+16:
		tmp = t_1
	elif z <= 8.4e-13:
		tmp = x + (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 <= -7.5e+16)
		tmp = t_1;
	elseif (z <= 8.4e-13)
		tmp = Float64(x + 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 <= -7.5e+16)
		tmp = t_1;
	elseif (z <= 8.4e-13)
		tmp = x + (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, -7.5e+16], t$95$1, If[LessEqual[z, 8.4e-13], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e16 or 8.39999999999999955e-13 < z

   1. Initial program 11.2%

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

   3. Taylor expanded in z around 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 90.0%

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

   5. Simplified 90.0%

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

   if -7.5e16 < z < 8.39999999999999955e-13

   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

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. 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. *-lowering-*.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 81.3%

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

   8. Simplified 81.3%

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

Alternative 10: 62.6% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-265}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.05e-204)
     t_1
     (if (<= z 2.4e-265) (* 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 <= -2.05e-204) {
		tmp = t_1;
	} else if (z <= 2.4e-265) {
		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 <= (-2.05d-204)) then
        tmp = t_1
    else if (z <= 2.4d-265) 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 <= -2.05e-204) {
		tmp = t_1;
	} else if (z <= 2.4e-265) {
		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 <= -2.05e-204:
		tmp = t_1
	elif z <= 2.4e-265:
		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 <= -2.05e-204)
		tmp = t_1;
	elseif (z <= 2.4e-265)
		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 <= -2.05e-204)
		tmp = t_1;
	elseif (z <= 2.4e-265)
		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, -2.05e-204], t$95$1, If[LessEqual[z, 2.4e-265], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e-204 or 2.4e-265 < z

   1. Initial program 44.5%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 74.5%

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

   5. Simplified 74.5%

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

   if -2.05e-204 < z < 2.4e-265

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. 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 61.7%

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

   5. Simplified 61.7%

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

   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. associate-*l* N/A

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

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

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

      4. *-lowering-*.f64 61.8%

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

   8. Simplified 61.8%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

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

      4. *-lowering-*.f64 61.8%

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

   10. Applied egg-rr 61.8%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-204}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-265}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.1e-165) x (if (<= x 8.5e-63) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.1e-165) {
		tmp = x;
	} else if (x <= 8.5e-63) {
		tmp = y * 3.13060547623;
	} 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 <= (-4.1d-165)) then
        tmp = x
    else if (x <= 8.5d-63) then
        tmp = y * 3.13060547623d0
    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 <= -4.1e-165) {
		tmp = x;
	} else if (x <= 8.5e-63) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.1e-165:
		tmp = x
	elif x <= 8.5e-63:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.1e-165)
		tmp = x;
	elseif (x <= 8.5e-63)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -4.1e-165)
		tmp = x;
	elseif (x <= 8.5e-63)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.1e-165], x, If[LessEqual[x, 8.5e-63], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1000000000000002e-165 or 8.49999999999999969e-63 < x

   1. Initial program 52.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 66.3%

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

   if -4.1000000000000002e-165 < x < 8.49999999999999969e-63

   1. Initial program 49.8%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 41.6%

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

   8. Simplified 41.6%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-165}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-63}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.3% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 51.6%

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

3. Taylor expanded in x around inf

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

5. Simplified 52.8%

   \[\leadsto \color{blue}{x} \]
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 2024139 
(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))))