tan-example (used to crash)

Percentage Accurate: 80.0% → 99.7%

Time: 38.4s

Alternatives: 10

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: 80.0% 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, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.8%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.8%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

5. Final simplification 99.8%

   \[\leadsto x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}} - \tan a\right) \]
6. Add Preprocessing

Alternative 2: 89.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan \left(y + z\right)\\ \mathbf{if}\;\tan a \leq -0.02:\\ \;\;\;\;x + \left(t\_0 - \log \left(e^{\tan a}\right)\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-46}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{t\_0}} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (tan (+ y z))))
   (if (<= (tan a) -0.02)
     (+ x (- t_0 (log (exp (tan a)))))
     (if (<= (tan a) 5e-46)
       (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) a))
       (+ x (- (/ 1.0 (/ 1.0 t_0)) (tan a)))))))

C

double code(double x, double y, double z, double a) {
	double t_0 = tan((y + z));
	double tmp;
	if (tan(a) <= -0.02) {
		tmp = x + (t_0 - log(exp(tan(a))));
	} else if (tan(a) <= 5e-46) {
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	} else {
		tmp = x + ((1.0 / (1.0 / t_0)) - 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) :: t_0
    real(8) :: tmp
    t_0 = tan((y + z))
    if (tan(a) <= (-0.02d0)) then
        tmp = x + (t_0 - log(exp(tan(a))))
    else if (tan(a) <= 5d-46) then
        tmp = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - a)
    else
        tmp = x + ((1.0d0 / (1.0d0 / t_0)) - tan(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) <= -0.02) {
		tmp = x + (t_0 - Math.log(Math.exp(Math.tan(a))));
	} else if (Math.tan(a) <= 5e-46) {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	} else {
		tmp = x + ((1.0 / (1.0 / t_0)) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	t_0 = math.tan((y + z))
	tmp = 0
	if math.tan(a) <= -0.02:
		tmp = x + (t_0 - math.log(math.exp(math.tan(a))))
	elif math.tan(a) <= 5e-46:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	else:
		tmp = x + ((1.0 / (1.0 / t_0)) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	t_0 = tan(Float64(y + z))
	tmp = 0.0
	if (tan(a) <= -0.02)
		tmp = Float64(x + Float64(t_0 - log(exp(tan(a)))));
	elseif (tan(a) <= 5e-46)
		tmp = Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(1.0 / t_0)) - tan(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) <= -0.02)
		tmp = x + (t_0 - log(exp(tan(a))));
	elseif (tan(a) <= 5e-46)
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	else
		tmp = x + ((1.0 / (1.0 / t_0)) - tan(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], -0.02], N[(x + N[(t$95$0 - N[Log[N[Exp[N[Tan[a], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 5e-46], 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[(N[(1.0 / N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.0200000000000000004

   1. Initial program 84.3%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-log-exp 84.3%

         \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\log \left(e^{\tan a}\right)}\right) \]

   4. Applied egg-rr 84.3%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\log \left(e^{\tan a}\right)}\right) \]

   if -0.0200000000000000004 < (tan.f64 a) < 4.99999999999999992e-46

   1. Initial program 79.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-sum 99.9%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. div-inv 99.9%

         \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   4. Applied egg-rr 99.9%

      \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
   5. Step-by-step derivation

      1. associate-*r/ 99.9%

         \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. *-rgt-identity 99.9%

         \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

   6. Simplified 99.9%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   7. Taylor expanded in a around 0 99.9%

      \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \color{blue}{a}\right) \]

   if 4.99999999999999992e-46 < (tan.f64 a)

   1. Initial program 81.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-sum 99.6%

         \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

      2. clear-num 99.7%

         \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
   5. Step-by-step derivation

      1. *-un-lft-identity 99.7%

         \[\leadsto x + \left(\frac{1}{\color{blue}{1 \cdot \frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

      2. clear-num 99.6%

         \[\leadsto x + \left(\frac{1}{1 \cdot \color{blue}{\frac{1}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}}}} - \tan a\right) \]

      3. tan-sum 81.2%

         \[\leadsto x + \left(\frac{1}{1 \cdot \frac{1}{\color{blue}{\tan \left(y + z\right)}}} - \tan a\right) \]

   6. Applied egg-rr 81.2%

      \[\leadsto x + \left(\frac{1}{\color{blue}{1 \cdot \frac{1}{\tan \left(y + z\right)}}} - \tan a\right) \]
   7. Step-by-step derivation

      1. *-lft-identity 81.2%

         \[\leadsto x + \left(\frac{1}{\color{blue}{\frac{1}{\tan \left(y + z\right)}}} - \tan a\right) \]

      2. +-commutative 81.2%

         \[\leadsto x + \left(\frac{1}{\frac{1}{\tan \color{blue}{\left(z + y\right)}}} - \tan a\right) \]

   8. Simplified 81.2%

      \[\leadsto x + \left(\frac{1}{\color{blue}{\frac{1}{\tan \left(z + y\right)}}} - \tan a\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.02:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \log \left(e^{\tan a}\right)\right)\\ \mathbf{elif}\;\tan a \leq 5 \cdot 10^{-46}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan \left(y + z\right)}} - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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

1. Initial program 80.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.8%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. div-inv 99.8%

      \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
5. Step-by-step derivation

   1. associate-*r/ 99.8%

      \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. *-rgt-identity 99.8%

      \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

6. Simplified 99.8%

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

7. Final simplification 99.8%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \]
8. Add Preprocessing

Alternative 4: 69.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-31} \lor \neg \left(\tan a \leq 4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -5e-31) (not (<= (tan a) 4e-27)))
   (+ x (- (tan z) (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -5e-31) || !(tan(a) <= 4e-27)) {
		tmp = x + (tan(z) - 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) <= (-5d-31)) .or. (.not. (tan(a) <= 4d-27))) then
        tmp = x + (tan(z) - 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) <= -5e-31) || !(Math.tan(a) <= 4e-27)) {
		tmp = x + (Math.tan(z) - 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) <= -5e-31) or not (math.tan(a) <= 4e-27):
		tmp = x + (math.tan(z) - 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) <= -5e-31) || !(tan(a) <= 4e-27))
		tmp = Float64(x + Float64(tan(z) - 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) <= -5e-31) || ~((tan(a) <= 4e-27)))
		tmp = x + (tan(z) - 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], -5e-31], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 4e-27]], $MachinePrecision]], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -5e-31 or 4.0000000000000002e-27 < (tan.f64 a)

   1. Initial program 81.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.6%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]
   4. Step-by-step derivation

      1. tan-quot 63.6%

         \[\leadsto x + \left(\color{blue}{\tan z} - \tan a\right) \]

      2. *-un-lft-identity 63.6%

         \[\leadsto x + \left(\color{blue}{1 \cdot \tan z} - \tan a\right) \]

   5. Applied egg-rr 63.6%

      \[\leadsto x + \left(\color{blue}{1 \cdot \tan z} - \tan a\right) \]
   6. Step-by-step derivation

      1. *-lft-identity 63.6%

         \[\leadsto x + \left(\color{blue}{\tan z} - \tan a\right) \]

   7. Simplified 63.6%

      \[\leadsto x + \left(\color{blue}{\tan z} - \tan a\right) \]

   if -5e-31 < (tan.f64 a) < 4.0000000000000002e-27

   1. Initial program 80.0%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 80.0%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -5 \cdot 10^{-31} \lor \neg \left(\tan a \leq 4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -50:\\ \;\;\;\;x + \left(\tan a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -50.0)
   (+ x (+ (tan a) (tan (+ y z))))
   (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -50.0) {
		tmp = x + (tan(a) + tan((y + z)));
	} else {
		tmp = x + (tan(z) - 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 + z) <= (-50.0d0)) then
        tmp = x + (tan(a) + tan((y + z)))
    else
        tmp = x + (tan(z) - 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 + z) <= -50.0) {
		tmp = x + (Math.tan(a) + Math.tan((y + z)));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -50.0:
		tmp = x + (math.tan(a) + math.tan((y + z)))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -50.0)
		tmp = Float64(x + Float64(tan(a) + tan(Float64(y + z))));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -50.0)
		tmp = x + (tan(a) + tan((y + z)));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -50.0], N[(x + N[(N[Tan[a], $MachinePrecision] + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -50

   1. Initial program 75.4%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. sub-neg 75.4%

         \[\leadsto x + \color{blue}{\left(\tan \left(y + z\right) + \left(-\tan a\right)\right)} \]

   4. Applied egg-rr 75.4%

      \[\leadsto x + \color{blue}{\left(\tan \left(y + z\right) + \left(-\tan a\right)\right)} \]
   5. Step-by-step derivation

      1. rem-square-sqrt 26.6%

         \[\leadsto x + \left(\tan \left(y + z\right) + \color{blue}{\sqrt{-\tan a} \cdot \sqrt{-\tan a}}\right) \]

      2. fabs-sqr 26.6%

         \[\leadsto x + \left(\tan \left(y + z\right) + \color{blue}{\left|\sqrt{-\tan a} \cdot \sqrt{-\tan a}\right|}\right) \]

      3. rem-square-sqrt 57.7%

         \[\leadsto x + \left(\tan \left(y + z\right) + \left|\color{blue}{-\tan a}\right|\right) \]

      4. fabs-neg 57.7%

         \[\leadsto x + \left(\tan \left(y + z\right) + \color{blue}{\left|\tan a\right|}\right) \]

      5. rem-square-sqrt 31.1%

         \[\leadsto x + \left(\tan \left(y + z\right) + \left|\color{blue}{\sqrt{\tan a} \cdot \sqrt{\tan a}}\right|\right) \]

      6. fabs-sqr 31.1%

         \[\leadsto x + \left(\tan \left(y + z\right) + \color{blue}{\sqrt{\tan a} \cdot \sqrt{\tan a}}\right) \]

      7. rem-square-sqrt 46.8%

         \[\leadsto x + \left(\tan \left(y + z\right) + \color{blue}{\tan a}\right) \]

      8. +-commutative 46.8%

         \[\leadsto x + \left(\tan \color{blue}{\left(z + y\right)} + \tan a\right) \]

   6. Simplified 46.8%

      \[\leadsto x + \color{blue}{\left(\tan \left(z + y\right) + \tan a\right)} \]

   if -50 < (+.f64 y z)

   1. Initial program 84.3%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.8%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]
   4. Step-by-step derivation

      1. tan-quot 67.8%

         \[\leadsto x + \left(\color{blue}{\tan z} - \tan a\right) \]

      2. *-un-lft-identity 67.8%

         \[\leadsto x + \left(\color{blue}{1 \cdot \tan z} - \tan a\right) \]

   5. Applied egg-rr 67.8%

      \[\leadsto x + \left(\color{blue}{1 \cdot \tan z} - \tan a\right) \]
   6. Step-by-step derivation

      1. *-lft-identity 67.8%

         \[\leadsto x + \left(\color{blue}{\tan z} - \tan a\right) \]

   7. Simplified 67.8%

      \[\leadsto x + \left(\color{blue}{\tan z} - \tan a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -50:\\ \;\;\;\;x + \left(\tan a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.0% 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

1. Initial program 80.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Final simplification 80.9%

   \[\leadsto x + \left(\tan \left(y + z\right) - \tan a\right) \]
4. Add Preprocessing

Alternative 7: 55.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+19} \lor \neg \left(a \leq 0.56\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.9e+19) (not (<= a 0.56)))
   (+ x (- z (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.9e+19) || !(a <= 0.56)) {
		tmp = x + (z - 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 ((a <= (-2.9d+19)) .or. (.not. (a <= 0.56d0))) then
        tmp = x + (z - 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 ((a <= -2.9e+19) || !(a <= 0.56)) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -2.9e+19) or not (a <= 0.56):
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.9e+19) || !(a <= 0.56))
		tmp = Float64(x + Float64(z - 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 ((a <= -2.9e+19) || ~((a <= 0.56)))
		tmp = x + (z - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.9e+19], N[Not[LessEqual[a, 0.56]], $MachinePrecision]], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9e19 or 0.56000000000000005 < a

   1. Initial program 82.6%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.8%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 36.5%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if -2.9e19 < a < 0.56000000000000005

   1. Initial program 79.2%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around 0 79.0%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+19} \lor \neg \left(a \leq 0.56\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+19} \lor \neg \left(a \leq 3.2 \cdot 10^{-44}\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan z\right) - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -2.9e+19) (not (<= a 3.2e-44)))
   (+ x (- z (tan a)))
   (- (+ x (tan z)) a)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -2.9e+19) || !(a <= 3.2e-44)) {
		tmp = x + (z - tan(a));
	} else {
		tmp = (x + tan(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 <= (-2.9d+19)) .or. (.not. (a <= 3.2d-44))) then
        tmp = x + (z - tan(a))
    else
        tmp = (x + tan(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 <= -2.9e+19) || !(a <= 3.2e-44)) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = (x + Math.tan(z)) - a;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -2.9e+19) or not (a <= 3.2e-44):
		tmp = x + (z - math.tan(a))
	else:
		tmp = (x + math.tan(z)) - a
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -2.9e+19) || !(a <= 3.2e-44))
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(Float64(x + tan(z)) - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -2.9e+19) || ~((a <= 3.2e-44)))
		tmp = x + (z - tan(a));
	else
		tmp = (x + tan(z)) - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -2.9e+19], N[Not[LessEqual[a, 3.2e-44]], $MachinePrecision]], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9e19 or 3.19999999999999995e-44 < a

   1. Initial program 82.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 65.6%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 36.5%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if -2.9e19 < a < 3.19999999999999995e-44

   1. Initial program 78.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 55.2%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in a around 0 55.0%

      \[\leadsto \color{blue}{x + \left(-1 \cdot a + \frac{\sin z}{\cos z}\right)} \]
   5. Step-by-step derivation

      1. associate-+r+ 55.0%

         \[\leadsto \color{blue}{\left(x + -1 \cdot a\right) + \frac{\sin z}{\cos z}} \]

      2. mul-1-neg 55.0%

         \[\leadsto \left(x + \color{blue}{\left(-a\right)}\right) + \frac{\sin z}{\cos z} \]

      3. unsub-neg 55.0%

         \[\leadsto \color{blue}{\left(x - a\right)} + \frac{\sin z}{\cos z} \]

   6. Simplified 55.0%

      \[\leadsto \color{blue}{\left(x - a\right) + \frac{\sin z}{\cos z}} \]
   7. Step-by-step derivation

      1. +-commutative 55.0%

         \[\leadsto \color{blue}{\frac{\sin z}{\cos z} + \left(x - a\right)} \]

      2. associate-+r- 55.0%

         \[\leadsto \color{blue}{\left(\frac{\sin z}{\cos z} + x\right) - a} \]

      3. quot-tan 55.0%

         \[\leadsto \left(\color{blue}{\tan z} + x\right) - a \]

   8. Applied egg-rr 55.0%

      \[\leadsto \color{blue}{\left(\tan z + x\right) - a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{+19} \lor \neg \left(a \leq 3.2 \cdot 10^{-44}\right):\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan z\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.2:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (if (<= z 2.2) (+ x (- z (tan a))) x))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.2) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x;
	}
	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 (z <= 2.2d0) then
        tmp = x + (z - tan(a))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 2.2) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if z <= 2.2:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (z <= 2.2)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (z <= 2.2)
		tmp = x + (z - tan(a));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[z, 2.2], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < 2.2000000000000002

   1. Initial program 88.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 62.4%

      \[\leadsto x + \left(\color{blue}{\frac{\sin z}{\cos z}} - \tan a\right) \]

   4. Taylor expanded in z around 0 42.7%

      \[\leadsto x + \left(\color{blue}{z} - \tan a\right) \]

   if 2.2000000000000002 < z

   1. Initial program 54.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 24.0%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.2:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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

1. Initial program 80.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 31.8%

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

4. Final simplification 31.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(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))))