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

Percentage Accurate: 93.6% → 93.6%

Time: 5.5s

Alternatives: 12

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

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: 93.6% 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: 93.6% 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 96.1%

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

Alternative 2: 48.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\\ \mathbf{if}\;\frac{x}{x + y \cdot t\_1} \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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-106) (/ 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-106) {
		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-106) 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-106) {
		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-106:
		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-106)
		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-106)
		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-106], 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))))))))))) < 4.99999999999999983e-106

   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 54.8%

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

   6. Taylor expanded in x around -inf

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

   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 4.99999999999999983e-106 < (/.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 93.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 8.5%

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

Alternative 3: 33.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t}\\ t_2 := t\_1 - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\\ \mathbf{if}\;t\_2 \leq 0.05:\\ \;\;\;\;e^{2 \cdot t\_2}\\ \mathbf{elif}\;t\_2 \leq 10^{+193}:\\ \;\;\;\;\frac{x}{\frac{x}{t\_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_2}\\ \end{array} \end{array} \]

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 0.05)
     (exp (* 2.0 t_2))
     (if (<= t_2 1e+193) (/ 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 <= 0.05) {
		tmp = exp((2.0 * t_2));
	} else if (t_2 <= 1e+193) {
		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 <= 0.05d0) then
        tmp = exp((2.0d0 * t_2))
    else if (t_2 <= 1d+193) 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 <= 0.05) {
		tmp = Math.exp((2.0 * t_2));
	} else if (t_2 <= 1e+193) {
		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 <= 0.05:
		tmp = math.exp((2.0 * t_2))
	elif t_2 <= 1e+193:
		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 <= 0.05)
		tmp = exp(Float64(2.0 * t_2));
	elseif (t_2 <= 1e+193)
		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 <= 0.05)
		tmp = exp((2.0 * t_2));
	elseif (t_2 <= 1e+193)
		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, 0.05], N[Exp[N[(2.0 * t$95$2), $MachinePrecision]], $MachinePrecision], If[LessEqual[t$95$2, 1e+193], 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)))))) < 0.050000000000000003

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 8.6%

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

   if 0.050000000000000003 < (-.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)))))) < 1.00000000000000007e193

   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 13.7%

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

   6. Taylor expanded in x around 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 33.4%

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

   if 1.00000000000000007e193 < (-.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 91.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 70.5%

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

Alternative 4: 31.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{t + a}\\ t_2 := \frac{z \cdot t\_1}{t}\\ t_3 := t\_2 - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\\ \mathbf{if}\;t\_3 \leq 5 \cdot 10^{-136}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 10^{+193}:\\ \;\;\;\;\frac{x}{\frac{x}{t\_2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_3}\\ \end{array} \end{array} \]

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 5e-136) t_1 (if (<= t_3 1e+193) (/ 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 <= 5e-136) {
		tmp = t_1;
	} else if (t_3 <= 1e+193) {
		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 <= 5d-136) then
        tmp = t_1
    else if (t_3 <= 1d+193) 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 <= 5e-136) {
		tmp = t_1;
	} else if (t_3 <= 1e+193) {
		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 <= 5e-136:
		tmp = t_1
	elif t_3 <= 1e+193:
		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 <= 5e-136)
		tmp = t_1;
	elseif (t_3 <= 1e+193)
		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 <= 5e-136)
		tmp = t_1;
	elseif (t_3 <= 1e+193)
		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, 5e-136], t$95$1, If[LessEqual[t$95$3, 1e+193], 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)))))) < 5.0000000000000002e-136

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 4.7%

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

   6. Taylor expanded in x around 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 6.6%

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

   if 5.0000000000000002e-136 < (-.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)))))) < 1.00000000000000007e193

   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 12.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 30.1%

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

   if 1.00000000000000007e193 < (-.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 91.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 70.5%

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

Alternative 5: 21.3% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := \frac{x}{\frac{t\_1}{t}}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{t\_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))) (t_2 (/ x (/ t_1 t))))
   (if (<= z -1.6e-75) t_2 (if (<= z 1.3e-105) (/ x t_2) (/ x t_1)))))

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 = x / (t_1 / t);
	double tmp;
	if (z <= -1.6e-75) {
		tmp = t_2;
	} else if (z <= 1.3e-105) {
		tmp = x / t_2;
	} else {
		tmp = x / 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 = z * sqrt((t + a))
    t_2 = x / (t_1 / t)
    if (z <= (-1.6d-75)) then
        tmp = t_2
    else if (z <= 1.3d-105) then
        tmp = x / t_2
    else
        tmp = x / 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 = z * Math.sqrt((t + a));
	double t_2 = x / (t_1 / t);
	double tmp;
	if (z <= -1.6e-75) {
		tmp = t_2;
	} else if (z <= 1.3e-105) {
		tmp = x / t_2;
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	t_2 = x / (t_1 / t)
	tmp = 0
	if z <= -1.6e-75:
		tmp = t_2
	elif z <= 1.3e-105:
		tmp = x / t_2
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	t_2 = Float64(x / Float64(t_1 / t))
	tmp = 0.0
	if (z <= -1.6e-75)
		tmp = t_2;
	elseif (z <= 1.3e-105)
		tmp = Float64(x / t_2);
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	t_2 = x / (t_1 / t);
	tmp = 0.0;
	if (z <= -1.6e-75)
		tmp = t_2;
	elseif (z <= 1.3e-105)
		tmp = x / t_2;
	else
		tmp = x / t_1;
	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[(x / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-75], t$95$2, If[LessEqual[z, 1.3e-105], N[(x / t$95$2), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999988e-75

   1. Initial program 93.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 19.1%

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

   if -1.59999999999999988e-75 < z < 1.2999999999999999e-105

   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 22.8%

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

   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 26.3%

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

   if 1.2999999999999999e-105 < z

   1. Initial program 94.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 37.6%

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

   6. Taylor expanded in x around -inf

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

   8. Applied rewrites 60.5%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 23.8%

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

Alternative 6: 19.7% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ \mathbf{if}\;t \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{\frac{t\_1}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))))
   (if (<= t 9.5e-19) (/ x (/ t_1 t)) (/ x t_1))))

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 tmp;
	if (t <= 9.5e-19) {
		tmp = x / (t_1 / t);
	} else {
		tmp = x / 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 = z * sqrt((t + a))
    if (t <= 9.5d-19) then
        tmp = x / (t_1 / t)
    else
        tmp = x / 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 = z * Math.sqrt((t + a));
	double tmp;
	if (t <= 9.5e-19) {
		tmp = x / (t_1 / t);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	tmp = 0
	if t <= 9.5e-19:
		tmp = x / (t_1 / t)
	else:
		tmp = x / t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	tmp = 0.0
	if (t <= 9.5e-19)
		tmp = Float64(x / Float64(t_1 / t));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	tmp = 0.0;
	if (t <= 9.5e-19)
		tmp = x / (t_1 / t);
	else
		tmp = x / t_1;
	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]}, If[LessEqual[t, 9.5e-19], N[(x / N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 9.4999999999999995e-19

   1. Initial program 95.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 16.9%

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

   if 9.4999999999999995e-19 < t

   1. Initial program 96.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 24.4%

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

   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 48.4%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 21.7%

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

Alternative 7: 15.9% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.22 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{\frac{2}{t \cdot 3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \sqrt{t + a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 2.22e-116) (/ x (/ 2.0 (* t 3.0))) (/ x (* z (sqrt (+ t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 2.22e-116) {
		tmp = x / (2.0 / (t * 3.0));
	} else {
		tmp = x / (z * sqrt((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 <= 2.22d-116) then
        tmp = x / (2.0d0 / (t * 3.0d0))
    else
        tmp = x / (z * sqrt((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 <= 2.22e-116) {
		tmp = x / (2.0 / (t * 3.0));
	} else {
		tmp = x / (z * Math.sqrt((t + a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 2.22e-116:
		tmp = x / (2.0 / (t * 3.0))
	else:
		tmp = x / (z * math.sqrt((t + a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 2.22e-116)
		tmp = Float64(x / Float64(2.0 / Float64(t * 3.0)));
	else
		tmp = Float64(x / Float64(z * sqrt(Float64(t + a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 2.22e-116)
		tmp = x / (2.0 / (t * 3.0));
	else
		tmp = x / (z * sqrt((t + a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 2.22e-116], N[(x / N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.2200000000000001e-116

   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 41.3%

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

   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 16.9%

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

   if 2.2200000000000001e-116 < t

   1. Initial program 96.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 22.7%

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

   6. Taylor expanded in x around -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 46.6%

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

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 18.5%

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

Alternative 8: 15.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{2}{t \cdot 3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t + a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 6.4e-16) (/ 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 <= 6.4e-16) {
		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 <= 6.4d-16) 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 <= 6.4e-16) {
		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 <= 6.4e-16:
		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 <= 6.4e-16)
		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 <= 6.4e-16)
		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, 6.4e-16], 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 < 6.40000000000000046e-16

   1. Initial program 95.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 35.0%

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

   6. Taylor expanded in x around 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 13.7%

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

   if 6.40000000000000046e-16 < t

   1. Initial program 96.7%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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 24.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 15.1%

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

Alternative 9: 13.7% 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 96.1%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
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 30.2%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 12.2%

   \[\leadsto \frac{x}{\color{blue}{t + a}} \]
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 96.1%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
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 30.2%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 4.7%

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

Alternative 11: 4.2% accurate, 33.0× speedup

Math

\[\begin{array}{l} \\ t \cdot 3 \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (* t 3.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return 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 = 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 t * 3.0;
}

Python

def code(x, y, z, t, a, b, c):
	return t * 3.0

Julia

function code(x, y, z, t, a, b, c)
	return Float64(t * 3.0)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = t * 3.0;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(t * 3.0), $MachinePrecision]

Derivation

1. Initial program 96.1%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
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 30.2%

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

6. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]

8. Applied rewrites 4.1%

   \[\leadsto \color{blue}{t \cdot 3} \]
9. Add Preprocessing

Alternative 12: 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 96.1%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
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 30.2%

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

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 49.1%

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

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 3.8%

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

Developer Target 1: 95.4% 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 2024321 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64
  :pre (TRUE)

  :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)))))))))))