tan-example (used to crash)

Percentage Accurate: 78.7% → 99.7%

Time: 2.4min

Alternatives: 12

Speedup: 1.0×

Specification

\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{\frac{\sin z}{\cos z} + \tan y}{1 - \frac{\sin z}{\frac{\cos z}{\tan y}}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (/ (+ (/ (sin z) (cos z)) (tan y)) (- 1.0 (/ (sin z) (/ (cos z) (tan y)))))
   (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + ((((sin(z) / cos(z)) + tan(y)) / (1.0 - (sin(z) / (cos(z) / tan(y))))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((((sin(z) / cos(z)) + tan(y)) / (1.0d0 - (sin(z) / (cos(z) / tan(y))))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + ((((Math.sin(z) / Math.cos(z)) + Math.tan(y)) / (1.0 - (Math.sin(z) / (Math.cos(z) / Math.tan(y))))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + ((((math.sin(z) / math.cos(z)) + math.tan(y)) / (1.0 - (math.sin(z) / (math.cos(z) / math.tan(y))))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(Float64(sin(z) / cos(z)) + tan(y)) / Float64(1.0 - Float64(sin(z) / Float64(cos(z) / tan(y))))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + ((((sin(z) / cos(z)) + tan(y)) / (1.0 - (sin(z) / (cos(z) / tan(y))))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[(N[Sin[z], $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Sin[z], $MachinePrecision] / N[(N[Cos[z], $MachinePrecision] / N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{\tan y + \tan z}{1 - \frac{\sin z}{\frac{\cos z}{\tan y}}} - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+
  x
  (- (/ (+ (tan y) (tan z)) (- 1.0 (/ (sin z) (/ (cos z) (tan y))))) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - (sin(z) / (cos(z) / tan(y))))) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) + tan(z)) / (1.0d0 - (sin(z) / (cos(z) / tan(y))))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.sin(z) / (Math.cos(z) / Math.tan(y))))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.sin(z) / (math.cos(z) / math.tan(y))))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(sin(z) / Float64(cos(z) / tan(y))))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - (sin(z) / (cos(z) / tan(y))))) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Sin[z], $MachinePrecision] / N[(N[Cos[z], $MachinePrecision] / N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x - \left(\tan a - \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (- x (- (tan a) (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x - (tan(a) - ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x - (tan(a) - ((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x - (Math.tan(a) - ((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x - (math.tan(a) - ((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x - Float64(tan(a) - Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z))))))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x - (tan(a) - ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x - N[(N[Tan[a], $MachinePrecision] - N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 89.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-8} \lor \neg \left(a \leq 3.9 \cdot 10^{-7}\right):\\ \;\;\;\;x + \frac{1}{\frac{1}{\tan \left(z + y\right) - \tan a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.4e-8) (not (<= a 3.9e-7)))
   (+ x (/ 1.0 (/ 1.0 (- (tan (+ z y)) (tan a)))))
   (+ (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (- x a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.4e-8) || !(a <= 3.9e-7)) {
		tmp = x + (1.0 / (1.0 / (tan((z + y)) - tan(a))));
	} else {
		tmp = ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) + (x - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.4d-8)) .or. (.not. (a <= 3.9d-7))) then
        tmp = x + (1.0d0 / (1.0d0 / (tan((z + y)) - tan(a))))
    else
        tmp = ((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) + (x - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.4e-8) || !(a <= 3.9e-7)) {
		tmp = x + (1.0 / (1.0 / (Math.tan((z + y)) - Math.tan(a))));
	} else {
		tmp = ((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) + (x - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -2.4e-8) or not (a <= 3.9e-7):
		tmp = x + (1.0 / (1.0 / (math.tan((z + y)) - math.tan(a))))
	else:
		tmp = ((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) + (x - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.4e-8) || !(a <= 3.9e-7))
		tmp = Float64(x + Float64(1.0 / Float64(1.0 / Float64(tan(Float64(z + y)) - tan(a)))));
	else
		tmp = Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) + Float64(x - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -2.4e-8) || ~((a <= 3.9e-7)))
		tmp = x + (1.0 / (1.0 / (tan((z + y)) - tan(a))));
	else
		tmp = ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) + (x - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.4e-8], N[Not[LessEqual[a, 3.9e-7]], $MachinePrecision]], N[(x + N[(1.0 / N[(1.0 / N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 52.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{1}{\frac{1}{x}}\\ \mathbf{elif}\;\tan a \leq 10^{-7}:\\ \;\;\;\;a + \left(x + \tan \left(z + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -2e-6)
   (/ 1.0 (/ 1.0 x))
   (if (<= (tan a) 1e-7) (+ a (+ x (tan (+ z y)))) (+ x (- y (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -2e-6) {
		tmp = 1.0 / (1.0 / x);
	} else if (tan(a) <= 1e-7) {
		tmp = a + (x + tan((z + y)));
	} else {
		tmp = x + (y - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-2d-6)) then
        tmp = 1.0d0 / (1.0d0 / x)
    else if (tan(a) <= 1d-7) then
        tmp = a + (x + tan((z + y)))
    else
        tmp = x + (y - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -2e-6) {
		tmp = 1.0 / (1.0 / x);
	} else if (Math.tan(a) <= 1e-7) {
		tmp = a + (x + Math.tan((z + y)));
	} else {
		tmp = x + (y - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -2e-6:
		tmp = 1.0 / (1.0 / x)
	elif math.tan(a) <= 1e-7:
		tmp = a + (x + math.tan((z + y)))
	else:
		tmp = x + (y - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -2e-6)
		tmp = Float64(1.0 / Float64(1.0 / x));
	elseif (tan(a) <= 1e-7)
		tmp = Float64(a + Float64(x + tan(Float64(z + y))));
	else
		tmp = Float64(x + Float64(y - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -2e-6)
		tmp = 1.0 / (1.0 / x);
	elseif (tan(a) <= 1e-7)
		tmp = a + (x + tan((z + y)));
	else
		tmp = x + (y - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -2e-6], N[(1.0 / N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 1e-7], N[(a + N[(x + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005:\\ \;\;\;\;x\\ \mathbf{elif}\;\tan a \leq 0.035:\\ \;\;\;\;\tan \left(z + y\right) + \left(x - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -0.005)
   x
   (if (<= (tan a) 0.035) (+ (tan (+ z y)) (- x a)) (+ x (- y (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.005) {
		tmp = x;
	} else if (tan(a) <= 0.035) {
		tmp = tan((z + y)) + (x - a);
	} else {
		tmp = x + (y - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-0.005d0)) then
        tmp = x
    else if (tan(a) <= 0.035d0) then
        tmp = tan((z + y)) + (x - a)
    else
        tmp = x + (y - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -0.005) {
		tmp = x;
	} else if (Math.tan(a) <= 0.035) {
		tmp = Math.tan((z + y)) + (x - a);
	} else {
		tmp = x + (y - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -0.005:
		tmp = x
	elif math.tan(a) <= 0.035:
		tmp = math.tan((z + y)) + (x - a)
	else:
		tmp = x + (y - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -0.005)
		tmp = x;
	elseif (tan(a) <= 0.035)
		tmp = Float64(tan(Float64(z + y)) + Float64(x - a));
	else
		tmp = Float64(x + Float64(y - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -0.005)
		tmp = x;
	elseif (tan(a) <= 0.035)
		tmp = tan((z + y)) + (x - a);
	else
		tmp = x + (y - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -0.005], x, If[LessEqual[N[Tan[a], $MachinePrecision], 0.035], N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.005:\\ \;\;\;\;e^{\log x}\\ \mathbf{elif}\;\tan a \leq 0.035:\\ \;\;\;\;\tan \left(z + y\right) + \left(x - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (tan a) -0.005)
   (exp (log x))
   (if (<= (tan a) 0.035) (+ (tan (+ z y)) (- x a)) (+ x (- y (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.005) {
		tmp = exp(log(x));
	} else if (tan(a) <= 0.035) {
		tmp = tan((z + y)) + (x - a);
	} else {
		tmp = x + (y - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (tan(a) <= (-0.005d0)) then
        tmp = exp(log(x))
    else if (tan(a) <= 0.035d0) then
        tmp = tan((z + y)) + (x - a)
    else
        tmp = x + (y - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (Math.tan(a) <= -0.005) {
		tmp = Math.exp(Math.log(x));
	} else if (Math.tan(a) <= 0.035) {
		tmp = Math.tan((z + y)) + (x - a);
	} else {
		tmp = x + (y - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if math.tan(a) <= -0.005:
		tmp = math.exp(math.log(x))
	elif math.tan(a) <= 0.035:
		tmp = math.tan((z + y)) + (x - a)
	else:
		tmp = x + (y - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (tan(a) <= -0.005)
		tmp = exp(log(x));
	elseif (tan(a) <= 0.035)
		tmp = Float64(tan(Float64(z + y)) + Float64(x - a));
	else
		tmp = Float64(x + Float64(y - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (tan(a) <= -0.005)
		tmp = exp(log(x));
	elseif (tan(a) <= 0.035)
		tmp = tan((z + y)) + (x - a);
	else
		tmp = x + (y - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[Tan[a], $MachinePrecision], -0.005], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 0.035], N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-8} \lor \neg \left(a \leq 14.4\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\tan \left(z + y\right) + \left(x - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.4e-8) (not (<= a 14.4)))
   (+ x (- (tan y) (tan a)))
   (+ (tan (+ z y)) (- x a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.4e-8) || !(a <= 14.4)) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = tan((z + y)) + (x - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.4d-8)) .or. (.not. (a <= 14.4d0))) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = tan((z + y)) + (x - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.4e-8) || !(a <= 14.4)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = Math.tan((z + y)) + (x - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -2.4e-8) or not (a <= 14.4):
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = math.tan((z + y)) + (x - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.4e-8) || !(a <= 14.4))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(tan(Float64(z + y)) + Float64(x - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -2.4e-8) || ~((a <= 14.4)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = tan((z + y)) + (x - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.4e-8], N[Not[LessEqual[a, 14.4]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] + N[(x - a), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \frac{1}{\frac{1}{\tan \left(z + y\right) - \tan a}} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (+ x (/ 1.0 (/ 1.0 (- (tan (+ z y)) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (1.0 / (1.0 / (tan((z + y)) - tan(a))));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (1.0d0 / (1.0d0 / (tan((z + y)) - tan(a))))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + (1.0 / (1.0 / (Math.tan((z + y)) - Math.tan(a))));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (1.0 / (1.0 / (math.tan((z + y)) - math.tan(a))))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(1.0 / Float64(1.0 / Float64(tan(Float64(z + y)) - tan(a)))))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (1.0 / (1.0 / (tan((z + y)) - tan(a))));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(1.0 / N[(1.0 / N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 78.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\tan \left(z + y\right) - \tan a\right) \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ z y)) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (tan((z + y)) - tan(a));
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((z + y)) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((z + y)) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x + (math.tan((z + y)) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(z + y)) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x + (tan((z + y)) - tan(a));
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 40.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 (if (<= y -1.8) x (+ x (- y (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -1.8) {
		tmp = x;
	} else {
		tmp = x + (y - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.8d0)) then
        tmp = x
    else
        tmp = x + (y - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -1.8) {
		tmp = x;
	} else {
		tmp = x + (y - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if y <= -1.8:
		tmp = x
	else:
		tmp = x + (y - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -1.8)
		tmp = x;
	else
		tmp = Float64(x + Float64(y - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -1.8)
		tmp = x;
	else
		tmp = x + (y - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -1.8], x, N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 31.2% accurate, 207.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a) :precision binary64 x)

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	return x;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return x
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := x

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2024006 
(FPCore (x y z a)
  :name "tan-example (used to crash)"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))