tan-example (used to crash)

Percentage Accurate: 79.7% → 99.6%

Time: 28.6s

Alternatives: 17

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: 79.7% 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: 99.6% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (fma
  (+ (tan y) (tan z))
  (/ 1.0 (+ 1.0 (+ 1.0 (- -1.0 (* (tan y) (tan z))))))
  (- x (tan a))))

C

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

Julia

function code(x, y, z, a)
	return fma(Float64(tan(y) + tan(z)), Float64(1.0 / Float64(1.0 + Float64(1.0 + Float64(-1.0 - Float64(tan(y) * tan(z)))))), Float64(x - tan(a)))
end

Wolfram

code[x_, y_, z_, a_] := N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 + N[(1.0 + N[(-1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 2: 99.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+
  x
  (fma
   (+ (tan y) (tan z))
   (/ 1.0 (+ 1.0 (+ 1.0 (- -1.0 (* (tan y) (tan z))))))
   (- (tan a)))))

C

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

Julia

function code(x, y, z, a)
	return Float64(x + fma(Float64(tan(y) + tan(z)), Float64(1.0 / Float64(1.0 + Float64(1.0 + Float64(-1.0 - Float64(tan(y) * tan(z)))))), Float64(-tan(a))))
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 + N[(1.0 + N[(-1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-N[Tan[a], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 3: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan \left(y + z\right)\\ \mathbf{if}\;\tan a \leq -0.002:\\ \;\;\;\;\left(x - \tan a\right) + t_0\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-10}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_0 + \frac{-1}{\frac{\cos a}{\sin a}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (tan (+ y z))))
   (if (<= (tan a) -0.002)
     (+ (- x (tan a)) t_0)
     (if (<= (tan a) 2e-10)
       (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) a))
       (+ x (+ t_0 (/ -1.0 (/ (cos a) (sin a)))))))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan((y + z));
	double tmp;
	if (tan(a) <= -0.002) {
		tmp = (x - tan(a)) + t_0;
	} else if (tan(a) <= 2e-10) {
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	} else {
		tmp = x + (t_0 + (-1.0 / (cos(a) / sin(a))));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = tan((y + z))
    if (tan(a) <= (-0.002d0)) then
        tmp = (x - tan(a)) + t_0
    else if (tan(a) <= 2d-10) then
        tmp = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - a)
    else
        tmp = x + (t_0 + ((-1.0d0) / (cos(a) / sin(a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan((y + z));
	double tmp;
	if (Math.tan(a) <= -0.002) {
		tmp = (x - Math.tan(a)) + t_0;
	} else if (Math.tan(a) <= 2e-10) {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	} else {
		tmp = x + (t_0 + (-1.0 / (Math.cos(a) / Math.sin(a))));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.tan((y + z))
	tmp = 0
	if math.tan(a) <= -0.002:
		tmp = (x - math.tan(a)) + t_0
	elif math.tan(a) <= 2e-10:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	else:
		tmp = x + (t_0 + (-1.0 / (math.cos(a) / math.sin(a))))
	return tmp

Julia

function code(x, y, z, a)
	t_0 = tan(Float64(y + z))
	tmp = 0.0
	if (tan(a) <= -0.002)
		tmp = Float64(Float64(x - tan(a)) + t_0);
	elseif (tan(a) <= 2e-10)
		tmp = Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	else
		tmp = Float64(x + Float64(t_0 + Float64(-1.0 / Float64(cos(a) / sin(a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	t_0 = tan((y + z));
	tmp = 0.0;
	if (tan(a) <= -0.002)
		tmp = (x - tan(a)) + t_0;
	elseif (tan(a) <= 2e-10)
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	else
		tmp = x + (t_0 + (-1.0 / (cos(a) / sin(a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[Tan[a], $MachinePrecision], -0.002], N[(N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 2e-10], N[(x + 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] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 + N[(-1.0 / N[(N[Cos[a], $MachinePrecision] / N[Sin[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 4: 99.7% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+
  x
  (fma (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z)))) (- (tan a)))))

C

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

Julia

function code(x, y, z, a)
	return Float64(x + fma(Float64(tan(y) + tan(z)), Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z)))), Float64(-tan(a))))
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + (-N[Tan[a], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 5: 99.6% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (fma (+ (tan y) (tan z)) (/ 1.0 (- 1.0 (* (tan y) (tan z)))) (- x (tan a))))

C

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

Julia

function code(x, y, z, a)
	return fma(Float64(tan(y) + tan(z)), Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(z)))), Float64(x - tan(a)))
end

Wolfram

code[x_, y_, z_, a_] := N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 6: 99.7% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(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) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
end

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 7: 99.6% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ (- x (tan a)) (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z))))))

C

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

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

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

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

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

MATLAB

function tmp = code(x, y, z, a)
	tmp = (x - tan(a)) + ((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z))));
end

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 8: 55.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.002 \lor \neg \left(\tan a \leq 2 \cdot 10^{-10}\right):\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.002) (not (<= (tan a) 2e-10)))
   (+ x (- y (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.002) || !(tan(a) <= 2e-10)) {
		tmp = x + (y - tan(a));
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((tan(a) <= (-0.002d0)) .or. (.not. (tan(a) <= 2d-10))) then
        tmp = x + (y - tan(a))
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.002) || !(Math.tan(a) <= 2e-10)) {
		tmp = x + (y - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.002) or not (math.tan(a) <= 2e-10):
		tmp = x + (y - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.002) || !(tan(a) <= 2e-10))
		tmp = Float64(x + Float64(y - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.002) || ~((tan(a) <= 2e-10)))
		tmp = x + (y - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.002], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 2e-10]], $MachinePrecision]], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 9: 79.7% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (+ (tan (+ y z)) (/ -1.0 (/ (cos a) (sin a))))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) + (-1.0 / (cos(a) / sin(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)) + ((-1.0d0) / (cos(a) / sin(a))))
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) + (-1.0 / (cos(a) / sin(a))));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] + N[(-1.0 / N[(N[Cos[a], $MachinePrecision] / N[Sin[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 10: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -500000000000:\\ \;\;\;\;x + \frac{\sin y}{\cos y}\\ \mathbf{elif}\;y + z \leq 0.001:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sin z}{\cos z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -500000000000.0)
   (+ x (/ (sin y) (cos y)))
   (if (<= (+ y z) 0.001) (+ x (- y (tan a))) (+ x (/ (sin z) (cos z))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -500000000000.0) {
		tmp = x + (sin(y) / cos(y));
	} else if ((y + z) <= 0.001) {
		tmp = x + (y - tan(a));
	} else {
		tmp = x + (sin(z) / cos(z));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y + z) <= (-500000000000.0d0)) then
        tmp = x + (sin(y) / cos(y))
    else if ((y + z) <= 0.001d0) then
        tmp = x + (y - tan(a))
    else
        tmp = x + (sin(z) / cos(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -500000000000.0) {
		tmp = x + (Math.sin(y) / Math.cos(y));
	} else if ((y + z) <= 0.001) {
		tmp = x + (y - Math.tan(a));
	} else {
		tmp = x + (Math.sin(z) / Math.cos(z));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -500000000000.0:
		tmp = x + (math.sin(y) / math.cos(y))
	elif (y + z) <= 0.001:
		tmp = x + (y - math.tan(a))
	else:
		tmp = x + (math.sin(z) / math.cos(z))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -500000000000.0)
		tmp = Float64(x + Float64(sin(y) / cos(y)));
	elseif (Float64(y + z) <= 0.001)
		tmp = Float64(x + Float64(y - tan(a)));
	else
		tmp = Float64(x + Float64(sin(z) / cos(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -500000000000.0)
		tmp = x + (sin(y) / cos(y));
	elseif ((y + z) <= 0.001)
		tmp = x + (y - tan(a));
	else
		tmp = x + (sin(z) / cos(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -500000000000.0], N[(x + N[(N[Sin[y], $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y + z), $MachinePrecision], 0.001], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Sin[z], $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.15 \cdot 10^{-6} \lor \neg \left(a \leq 1.7 \cdot 10^{-21}\right):\\ \;\;\;\;\left(x - \tan a\right) + \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.15e-6) (not (<= a 1.7e-21)))
   (+ (- x (tan a)) (sin y))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.15e-6) || !(a <= 1.7e-21)) {
		tmp = (x - tan(a)) + sin(y);
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-2.15d-6)) .or. (.not. (a <= 1.7d-21))) then
        tmp = (x - tan(a)) + sin(y)
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.15e-6) || !(a <= 1.7e-21)) {
		tmp = (x - Math.tan(a)) + Math.sin(y);
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -2.15e-6) or not (a <= 1.7e-21):
		tmp = (x - math.tan(a)) + math.sin(y)
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.15e-6) || !(a <= 1.7e-21))
		tmp = Float64(Float64(x - tan(a)) + sin(y));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -2.15e-6) || ~((a <= 1.7e-21)))
		tmp = (x - tan(a)) + sin(y);
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.15e-6], N[Not[LessEqual[a, 1.7e-21]], $MachinePrecision]], N[(N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision] + N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq 0.001:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sin z}{\cos z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) 0.001) (+ x (- (tan y) (tan a))) (+ x (/ (sin z) (cos z)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 0.001) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (sin(z) / cos(z));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y + z) <= 0.001d0) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (sin(z) / cos(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 0.001) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.sin(z) / Math.cos(z));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= 0.001:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.sin(z) / math.cos(z))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= 0.001)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(sin(z) / cos(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= 0.001)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (sin(z) / cos(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], 0.001], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Sin[z], $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 13: 55.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq 0.001:\\ \;\;\;\;\left(\tan y + x\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\sin z}{\cos z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) 0.001) (- (+ (tan y) x) (tan a)) (+ x (/ (sin z) (cos z)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 0.001) {
		tmp = (tan(y) + x) - tan(a);
	} else {
		tmp = x + (sin(z) / cos(z));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y + z) <= 0.001d0) then
        tmp = (tan(y) + x) - tan(a)
    else
        tmp = x + (sin(z) / cos(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 0.001) {
		tmp = (Math.tan(y) + x) - Math.tan(a);
	} else {
		tmp = x + (Math.sin(z) / Math.cos(z));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= 0.001:
		tmp = (math.tan(y) + x) - math.tan(a)
	else:
		tmp = x + (math.sin(z) / math.cos(z))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= 0.001)
		tmp = Float64(Float64(tan(y) + x) - tan(a));
	else
		tmp = Float64(x + Float64(sin(z) / cos(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= 0.001)
		tmp = (tan(y) + x) - tan(a);
	else
		tmp = x + (sin(z) / cos(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], 0.001], N[(N[(N[Tan[y], $MachinePrecision] + x), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Sin[z], $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 79.7% 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]

Derivation

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

Alternative 15: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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(a)) + tan((y + z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 16: 37.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (if (<= y -1.35) x (+ x (- y (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -1.35) {
		tmp = x;
	} else {
		tmp = x + (y - tan(a));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-1.35d0)) then
        tmp = x
    else
        tmp = x + (y - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -1.35) {
		tmp = x;
	} else {
		tmp = x + (y - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if y <= -1.35:
		tmp = x
	else:
		tmp = x + (y - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (y <= -1.35)
		tmp = x;
	else
		tmp = Float64(x + Float64(y - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -1.35)
		tmp = x;
	else
		tmp = x + (y - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[y, -1.35], x, N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 17: 31.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2024008 
(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))))