Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I

Percentage Accurate: 93.8% → 93.8%

Time: 5.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\\ t_2 := y \cdot t\_1\\ \mathbf{if}\;\frac{x}{x + t\_2} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (exp
          (*
           2.0
           (-
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))
        (t_2 (* y t_1)))
   (if (<= (/ x (+ x t_2)) 5e-11) (/ x t_2) t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))));
	double t_2 = y * t_1;
	double tmp;
	if ((x / (x + t_2)) <= 5e-11) {
		tmp = x / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))
    t_2 = y * t_1
    if ((x / (x + t_2)) <= 5d-11) then
        tmp = x / t_2
    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 c) {
	double t_1 = Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))));
	double t_2 = y * t_1;
	double tmp;
	if ((x / (x + t_2)) <= 5e-11) {
		tmp = x / t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))
	t_2 = y * t_1
	tmp = 0
	if (x / (x + t_2)) <= 5e-11:
		tmp = x / t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))))
	t_2 = Float64(y * t_1)
	tmp = 0.0
	if (Float64(x / Float64(x + t_2)) <= 5e-11)
		tmp = Float64(x / t_2);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))));
	t_2 = y * t_1;
	tmp = 0.0;
	if ((x / (x + t_2)) <= 5e-11)
		tmp = x / t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(y * t$95$1), $MachinePrecision]}, If[LessEqual[N[(x / N[(x + t$95$2), $MachinePrecision]), $MachinePrecision], 5e-11], N[(x / t$95$2), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 5.00000000000000018e-11

   1. Initial program 99.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 52.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   8. Applied rewrites 16.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{t \cdot 3}}} \]

   9. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   11. Applied rewrites 98.9%

       \[\leadsto \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}} \]

   if 5.00000000000000018e-11 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 89.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(x \cdot \left(-1 \cdot \frac{x}{{y}^{4} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{4}} + \frac{1}{{y}^{3} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{3}}\right) - \frac{1}{{y}^{2} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{2}}\right) + \frac{1}{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}\right)} \]

   5. Applied rewrites 8.8%

      \[\leadsto \color{blue}{e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 48.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\\ \mathbf{if}\;\frac{x}{x + y \cdot t\_1} \leq 5 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (exp
          (*
           2.0
           (-
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))
   (if (<= (/ x (+ x (* y t_1))) 5e-121) (/ x t_1) t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))));
	double tmp;
	if ((x / (x + (y * t_1))) <= 5e-121) {
		tmp = x / t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))
    if ((x / (x + (y * t_1))) <= 5d-121) then
        tmp = x / t_1
    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 c) {
	double t_1 = Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))));
	double tmp;
	if ((x / (x + (y * t_1))) <= 5e-121) {
		tmp = x / t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))
	tmp = 0
	if (x / (x + (y * t_1))) <= 5e-121:
		tmp = x / t_1
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))))
	tmp = 0.0
	if (Float64(x / Float64(x + Float64(y * t_1))) <= 5e-121)
		tmp = Float64(x / t_1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))));
	tmp = 0.0;
	if ((x / (x + (y * t_1))) <= 5e-121)
		tmp = x / t_1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(x / N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e-121], N[(x / t$95$1), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))))))) < 4.99999999999999989e-121

   1. Initial program 99.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 53.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around -inf

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

   8. Applied rewrites 94.2%

      \[\leadsto \frac{x}{\color{blue}{e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}} \]

   if 4.99999999999999989e-121 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))))))))

   1. Initial program 89.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(x \cdot \left(-1 \cdot \frac{x}{{y}^{4} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{4}} + \frac{1}{{y}^{3} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{3}}\right) - \frac{1}{{y}^{2} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{2}}\right) + \frac{1}{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}\right)} \]

   5. Applied rewrites 8.8%

      \[\leadsto \color{blue}{e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 32.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t}\\ t_2 := t\_1 - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\\ \mathbf{if}\;t\_2 \leq 0.0001:\\ \;\;\;\;e^{2 \cdot t\_2}\\ \mathbf{elif}\;t\_2 \leq 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{x}{t\_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z (sqrt (+ t a))) t))
        (t_2 (- t_1 (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
   (if (<= t_2 0.0001)
     (exp (* 2.0 t_2))
     (if (<= t_2 1e+153) (/ x (/ x t_1)) (/ x t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * sqrt((t + a))) / t;
	double t_2 = t_1 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_2 <= 0.0001) {
		tmp = exp((2.0 * t_2));
	} else if (t_2 <= 1e+153) {
		tmp = x / (x / t_1);
	} else {
		tmp = x / t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * sqrt((t + a))) / t
    t_2 = t_1 - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0))))
    if (t_2 <= 0.0001d0) then
        tmp = exp((2.0d0 * t_2))
    else if (t_2 <= 1d+153) then
        tmp = x / (x / t_1)
    else
        tmp = x / t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * Math.sqrt((t + a))) / t;
	double t_2 = t_1 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_2 <= 0.0001) {
		tmp = Math.exp((2.0 * t_2));
	} else if (t_2 <= 1e+153) {
		tmp = x / (x / t_1);
	} else {
		tmp = x / t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * math.sqrt((t + a))) / t
	t_2 = t_1 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))
	tmp = 0
	if t_2 <= 0.0001:
		tmp = math.exp((2.0 * t_2))
	elif t_2 <= 1e+153:
		tmp = x / (x / t_1)
	else:
		tmp = x / t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * sqrt(Float64(t + a))) / t)
	t_2 = Float64(t_1 - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))
	tmp = 0.0
	if (t_2 <= 0.0001)
		tmp = exp(Float64(2.0 * t_2));
	elseif (t_2 <= 1e+153)
		tmp = Float64(x / Float64(x / t_1));
	else
		tmp = Float64(x / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * sqrt((t + a))) / t;
	t_2 = t_1 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))));
	tmp = 0.0;
	if (t_2 <= 0.0001)
		tmp = exp((2.0 * t_2));
	elseif (t_2 <= 1e+153)
		tmp = x / (x / t_1);
	else
		tmp = x / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.0001], N[Exp[N[(2.0 * t$95$2), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$2, 1e+153], N[(x / N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x / t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 1.00000000000000005e-4

   1. Initial program 98.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(x \cdot \left(-1 \cdot \frac{x}{{y}^{4} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{4}} + \frac{1}{{y}^{3} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{3}}\right) - \frac{1}{{y}^{2} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{2}}\right) + \frac{1}{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}\right)} \]

   5. Applied rewrites 9.5%

      \[\leadsto \color{blue}{e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   if 1.00000000000000005e-4 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 1e153

   1. Initial program 99.9%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 11.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{x \cdot \left(1 + \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x}\right)}} \]

   8. Applied rewrites 34.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{x}{\frac{z \cdot \sqrt{t + a}}{t}}}} \]

   if 1e153 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 86.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 58.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 31.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{t + a}\\ t_2 := \frac{z \cdot t\_1}{t}\\ t_3 := t\_2 - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\\ \mathbf{if}\;t\_3 \leq 0.0001:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{+153}:\\ \;\;\;\;\frac{x}{\frac{x}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (sqrt (+ t a)))
        (t_2 (/ (* z t_1) t))
        (t_3 (- t_2 (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))
   (if (<= t_3 0.0001) t_1 (if (<= t_3 1e+153) (/ x (/ x t_2)) (/ x t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = sqrt((t + a));
	double t_2 = (z * t_1) / t;
	double t_3 = t_2 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_3 <= 0.0001) {
		tmp = t_1;
	} else if (t_3 <= 1e+153) {
		tmp = x / (x / t_2);
	} else {
		tmp = x / t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = sqrt((t + a))
    t_2 = (z * t_1) / t
    t_3 = t_2 - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0))))
    if (t_3 <= 0.0001d0) then
        tmp = t_1
    else if (t_3 <= 1d+153) then
        tmp = x / (x / t_2)
    else
        tmp = x / t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = Math.sqrt((t + a));
	double t_2 = (z * t_1) / t;
	double t_3 = t_2 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_3 <= 0.0001) {
		tmp = t_1;
	} else if (t_3 <= 1e+153) {
		tmp = x / (x / t_2);
	} else {
		tmp = x / t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = math.sqrt((t + a))
	t_2 = (z * t_1) / t
	t_3 = t_2 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))))
	tmp = 0
	if t_3 <= 0.0001:
		tmp = t_1
	elif t_3 <= 1e+153:
		tmp = x / (x / t_2)
	else:
		tmp = x / t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = sqrt(Float64(t + a))
	t_2 = Float64(Float64(z * t_1) / t)
	t_3 = Float64(t_2 - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0)))))
	tmp = 0.0
	if (t_3 <= 0.0001)
		tmp = t_1;
	elseif (t_3 <= 1e+153)
		tmp = Float64(x / Float64(x / t_2));
	else
		tmp = Float64(x / t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = sqrt((t + a));
	t_2 = (z * t_1) / t;
	t_3 = t_2 - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0))));
	tmp = 0.0;
	if (t_3 <= 0.0001)
		tmp = t_1;
	elseif (t_3 <= 1e+153)
		tmp = x / (x / t_2);
	else
		tmp = x / t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t$95$1), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, 0.0001], t$95$1, If[LessEqual[t$95$3, 1e+153], N[(x / N[(x / t$95$2), $MachinePrecision]), $MachinePrecision], N[(x / t$95$3), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 1.00000000000000005e-4

   1. Initial program 98.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 4.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{{y}^{3} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{3}}{{x}^{3}}\right) - \left(-1 \cdot \frac{{y}^{2} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{2}}{{x}^{2}} + \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x}\right)} \]

   8. Applied rewrites 6.7%

      \[\leadsto \color{blue}{\sqrt{t + a}} \]

   if 1.00000000000000005e-4 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 1e153

   1. Initial program 99.9%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 11.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{x \cdot \left(1 + \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x}\right)}} \]

   8. Applied rewrites 34.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{x}{\frac{z \cdot \sqrt{t + a}}{t}}}} \]

   if 1e153 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   1. Initial program 86.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 58.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 21.7% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z \cdot \sqrt{t + a}}{t}}\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (/ (* z (sqrt (+ t a))) t))))
   (if (<= z -1.22e-63) t_1 (if (<= z 2.1e+19) (/ x t_1) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / ((z * sqrt((t + a))) / t);
	double tmp;
	if (z <= -1.22e-63) {
		tmp = t_1;
	} else if (z <= 2.1e+19) {
		tmp = x / t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((z * sqrt((t + a))) / t)
    if (z <= (-1.22d-63)) then
        tmp = t_1
    else if (z <= 2.1d+19) then
        tmp = x / t_1
    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 c) {
	double t_1 = x / ((z * Math.sqrt((t + a))) / t);
	double tmp;
	if (z <= -1.22e-63) {
		tmp = t_1;
	} else if (z <= 2.1e+19) {
		tmp = x / t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / ((z * math.sqrt((t + a))) / t)
	tmp = 0
	if z <= -1.22e-63:
		tmp = t_1
	elif z <= 2.1e+19:
		tmp = x / t_1
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(Float64(z * sqrt(Float64(t + a))) / t))
	tmp = 0.0
	if (z <= -1.22e-63)
		tmp = t_1;
	elseif (z <= 2.1e+19)
		tmp = Float64(x / t_1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / ((z * sqrt((t + a))) / t);
	tmp = 0.0;
	if (z <= -1.22e-63)
		tmp = t_1;
	elseif (z <= 2.1e+19)
		tmp = x / t_1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.22e-63], t$95$1, If[LessEqual[z, 2.1e+19], N[(x / t$95$1), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2199999999999999e-63 or 2.1e19 < z

   1. Initial program 87.9%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 22.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t}}} \]

   if -1.2199999999999999e-63 < z < 2.1e19

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 27.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{x \cdot \left(1 + \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x}\right)}} \]

   8. Applied rewrites 15.5%

      \[\leadsto \frac{x}{\color{blue}{\frac{x}{\frac{z \cdot \sqrt{t + a}}{t}}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 20.5% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{z \cdot \sqrt{t + a}}{t}}\\ \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t + a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (/ (* z (sqrt (+ t a))) t))))
   (if (<= z -0.68) t_1 (if (<= z 5.1e+39) (/ x (+ t a)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / ((z * sqrt((t + a))) / t);
	double tmp;
	if (z <= -0.68) {
		tmp = t_1;
	} else if (z <= 5.1e+39) {
		tmp = x / (t + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((z * sqrt((t + a))) / t)
    if (z <= (-0.68d0)) then
        tmp = t_1
    else if (z <= 5.1d+39) then
        tmp = x / (t + a)
    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 c) {
	double t_1 = x / ((z * Math.sqrt((t + a))) / t);
	double tmp;
	if (z <= -0.68) {
		tmp = t_1;
	} else if (z <= 5.1e+39) {
		tmp = x / (t + a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / ((z * math.sqrt((t + a))) / t)
	tmp = 0
	if z <= -0.68:
		tmp = t_1
	elif z <= 5.1e+39:
		tmp = x / (t + a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(Float64(z * sqrt(Float64(t + a))) / t))
	tmp = 0.0
	if (z <= -0.68)
		tmp = t_1;
	elseif (z <= 5.1e+39)
		tmp = Float64(x / Float64(t + a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / ((z * sqrt((t + a))) / t);
	tmp = 0.0;
	if (z <= -0.68)
		tmp = t_1;
	elseif (z <= 5.1e+39)
		tmp = x / (t + a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.68], t$95$1, If[LessEqual[z, 5.1e+39], N[(x / N[(t + a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.680000000000000049 or 5.0999999999999998e39 < z

   1. Initial program 86.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 24.6%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t}}} \]

   if -0.680000000000000049 < z < 5.0999999999999998e39

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 28.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 14.2%

      \[\leadsto \frac{x}{\color{blue}{t + a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 15.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\frac{2}{t \cdot 3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t + a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1.5e-35) (/ x (/ 2.0 (* t 3.0))) (/ x (+ t a))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.5e-35) {
		tmp = x / (2.0 / (t * 3.0));
	} else {
		tmp = x / (t + a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= 1.5d-35) then
        tmp = x / (2.0d0 / (t * 3.0d0))
    else
        tmp = x / (t + a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1.5e-35) {
		tmp = x / (2.0 / (t * 3.0));
	} else {
		tmp = x / (t + a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1.5e-35:
		tmp = x / (2.0 / (t * 3.0))
	else:
		tmp = x / (t + a)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1.5e-35)
		tmp = Float64(x / Float64(2.0 / Float64(t * 3.0)));
	else
		tmp = Float64(x / Float64(t + a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 1.5e-35)
		tmp = x / (2.0 / (t * 3.0));
	else
		tmp = x / (t + a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1.5e-35], N[(x / N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t + a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.49999999999999994e-35

   1. Initial program 91.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 32.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   8. Applied rewrites 16.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{2}{t \cdot 3}}} \]

   if 1.49999999999999994e-35 < t

   1. Initial program 96.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

   5. Applied rewrites 20.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 14.0%

      \[\leadsto \frac{x}{\color{blue}{t + a}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 12.8% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t + a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

5. Applied rewrites 26.4%

   \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

6. Taylor expanded in x around inf

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

8. Applied rewrites 11.8%

   \[\leadsto \frac{x}{\color{blue}{t + a}} \]
9. Add Preprocessing

Alternative 10: 4.9% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{t + a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return Math.sqrt((t + a));
}

Python

def code(x, y, z, t, a, b, c):
	return math.sqrt((t + a))

Julia

function code(x, y, z, t, a, b, c)
	return sqrt(Float64(t + a))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

5. Applied rewrites 26.4%

   \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\left(1 + -1 \cdot \frac{{y}^{3} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{3}}{{x}^{3}}\right) - \left(-1 \cdot \frac{{y}^{2} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{2}}{{x}^{2}} + \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x}\right)} \]

8. Applied rewrites 5.0%

   \[\leadsto \color{blue}{\sqrt{t + a}} \]
9. Add Preprocessing

Alternative 11: 4.0% accurate, 49.5× speedup

Math

\[\begin{array}{l} \\ t + a \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(t + a), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \frac{x}{\color{blue}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}} \]

5. Applied rewrites 26.4%

   \[\leadsto \frac{x}{\color{blue}{\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)}} \]

6. Taylor expanded in x around -inf

   \[\leadsto \frac{x}{\color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x} - 1\right)\right)}} \]

8. Applied rewrites 43.8%

   \[\leadsto \frac{x}{\color{blue}{e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}} \]

9. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\left(1 + \frac{{y}^{2} \cdot {\left(e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}\right)}^{2}}{{x}^{2}}\right) - \frac{y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t} - \left(b - c\right) \cdot \left(\left(\frac{5}{6} + a\right) - \frac{2}{3} \cdot \frac{1}{t}\right)\right)}}{x}} \]

11. Applied rewrites 4.2%

    \[\leadsto \color{blue}{t + a} \]
12. Add Preprocessing

Developer Target 1: 95.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := a - \frac{5}{6}\\ \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{t\_1 \cdot \left(\left(3 \cdot t\right) \cdot t\_2\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(t\_2 \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot t\_2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{t\_1}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))) (t_2 (- a (/ 5.0 6.0))))
   (if (< t -2.118326644891581e-50)
     (/
      x
      (+
       x
       (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b)))))))
     (if (< t 5.196588770651547e-123)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (/
             (-
              (* t_1 (* (* 3.0 t) t_2))
              (*
               (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)
               (* t_2 (* (- b c) t))))
             (* (* (* t t) 3.0) t_2)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (/ t_1 t)
             (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * sqrt((t + a))
    t_2 = a - (5.0d0 / 6.0d0)
    if (t < (-2.118326644891581d-50)) then
        tmp = x / (x + (y * exp((2.0d0 * (((a * c) + (0.8333333333333334d0 * c)) - (a * b))))))
    else if (t < 5.196588770651547d-123) then
        tmp = x / (x + (y * exp((2.0d0 * (((t_1 * ((3.0d0 * t) * t_2)) - (((((5.0d0 / 6.0d0) + a) * (3.0d0 * t)) - 2.0d0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0d0) * t_2))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((t_1 / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * Math.sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * Math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * Math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	t_2 = a - (5.0 / 6.0)
	tmp = 0
	if t < -2.118326644891581e-50:
		tmp = x / (x + (y * math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))))
	elif t < 5.196588770651547e-123:
		tmp = x / (x + (y * math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	t_2 = Float64(a - Float64(5.0 / 6.0))
	tmp = 0.0
	if (t < -2.118326644891581e-50)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(a * c) + Float64(0.8333333333333334 * c)) - Float64(a * b)))))));
	elseif (t < 5.196588770651547e-123)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(t_1 * Float64(Float64(3.0 * t) * t_2)) - Float64(Float64(Float64(Float64(Float64(5.0 / 6.0) + a) * Float64(3.0 * t)) - 2.0) * Float64(t_2 * Float64(Float64(b - c) * t)))) / Float64(Float64(Float64(t * t) * 3.0) * t_2)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(t_1 / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	t_2 = a - (5.0 / 6.0);
	tmp = 0.0;
	if (t < -2.118326644891581e-50)
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	elseif (t < 5.196588770651547e-123)
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -2.118326644891581e-50], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(a * c), $MachinePrecision] + N[(0.8333333333333334 * c), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[t, 5.196588770651547e-123], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(t$95$1 * N[(N[(3.0 * t), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(5.0 / 6.0), $MachinePrecision] + a), $MachinePrecision] * N[(3.0 * t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] * N[(t$95$2 * N[(N[(b - c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * t), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(t$95$1 / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -2118326644891581/100000000000000000000000000000000000000000000000000000000000000000) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 4166666666666667/5000000000000000 c)) (* a b))))))) (if (< t 5196588770651547/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))