tan-example (used to crash)

Percentage Accurate: 79.5% → 99.7%

Time: 49.0s

Alternatives: 8

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: 79.5% 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

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ x + \left(\frac{1}{\frac{1}{t\_0} - \tan y \cdot \frac{\tan z}{t\_0}} - \tan a\right) \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (+ x (- (/ 1.0 (- (/ 1.0 t_0) (* (tan y) (/ (tan z) t_0)))) (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	return x + ((1.0 / ((1.0 / t_0) - (tan(y) * (tan(z) / t_0)))) - 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
    real(8) :: t_0
    t_0 = tan(y) + tan(z)
    code = x + ((1.0d0 / ((1.0d0 / t_0) - (tan(y) * (tan(z) / t_0)))) - tan(a))
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double t_0 = Math.tan(y) + Math.tan(z);
	return x + ((1.0 / ((1.0 / t_0) - (Math.tan(y) * (Math.tan(z) / t_0)))) - Math.tan(a));
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	return x + ((1.0 / ((1.0 / t_0) - (math.tan(y) * (math.tan(z) / t_0)))) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	return Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 / t_0) - Float64(tan(y) * Float64(tan(z) / t_0)))) - tan(a)))
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	t_0 = tan(y) + tan(z);
	tmp = x + ((1.0 / ((1.0 / t_0) - (tan(y) * (tan(z) / t_0)))) - 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_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, N[(x + N[(N[(1.0 / N[(N[(1.0 / t$95$0), $MachinePrecision] - N[(N[Tan[y], $MachinePrecision] * N[(N[Tan[z], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 81.8%

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

   1. tan-sum 99.7%

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

   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. div-sub 99.7%

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

6. Applied egg-rr 99.7%

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

   1. associate-/l* 99.7%

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

8. Simplified 99.7%

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

9. Final simplification 99.7%

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

Alternative 2: 99.7% accurate, 0.4× speedup

Math

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

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 (* (tan y) (tan z)))) (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 - (tan(y) * tan(z)))) - 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 - (tan(y) * tan(z)))) - 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.tan(y) * Math.tan(z)))) - 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.tan(y) * math.tan(z)))) - 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(tan(y) * tan(z)))) - 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 - (tan(y) * tan(z)))) - 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[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

7. Final simplification 99.7%

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

Alternative 3: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;z \leq 0.0146:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan y \cdot z}{t\_0}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{t\_0} - y} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (<= z 0.0146)
     (+ x (- (/ 1.0 (/ (- 1.0 (* (tan y) z)) t_0)) (tan a)))
     (+ x (- (/ 1.0 (- (/ 1.0 t_0) y)) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if (z <= 0.0146) {
		tmp = x + ((1.0 / ((1.0 - (tan(y) * z)) / t_0)) - tan(a));
	} else {
		tmp = x + ((1.0 / ((1.0 / t_0) - 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) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if (z <= 0.0146d0) then
        tmp = x + ((1.0d0 / ((1.0d0 - (tan(y) * z)) / t_0)) - tan(a))
    else
        tmp = x + ((1.0d0 / ((1.0d0 / t_0) - 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 t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if (z <= 0.0146) {
		tmp = x + ((1.0 / ((1.0 - (Math.tan(y) * z)) / t_0)) - Math.tan(a));
	} else {
		tmp = x + ((1.0 / ((1.0 / t_0) - y)) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if z <= 0.0146:
		tmp = x + ((1.0 / ((1.0 - (math.tan(y) * z)) / t_0)) - math.tan(a))
	else:
		tmp = x + ((1.0 / ((1.0 / t_0) - y)) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if (z <= 0.0146)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(tan(y) * z)) / t_0)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 / t_0) - 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)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if (z <= 0.0146)
		tmp = x + ((1.0 / ((1.0 - (tan(y) * z)) / t_0)) - tan(a));
	else
		tmp = x + ((1.0 / ((1.0 / t_0) - 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_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 0.0146], N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[Tan[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(N[(1.0 / t$95$0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 0.0146000000000000001

   1. Initial program 87.3%

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

      1. tan-sum 99.7%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*r/ 99.7%

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

      2. *-rgt-identity 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 80.0%

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

      1. clear-num 79.9%

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

      2. inv-pow 79.9%

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

      3. associate-/l* 79.9%

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

      4. tan-quot 79.9%

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

   9. Applied egg-rr 79.9%

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

       1. unpow-1 79.9%

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

   11. Simplified 79.9%

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

   if 0.0146000000000000001 < z

   1. Initial program 62.8%

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

      1. tan-sum 99.5%

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

      2. clear-num 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. div-sub 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. associate-/l* 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in y around 0 64.5%

      \[\leadsto x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - \color{blue}{y}} - \tan a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.0146:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan y \cdot z}{\tan y + \tan z}} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - y} - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;z \leq 0.0146:\\ \;\;\;\;\left(x + \frac{t\_0}{1 - \tan y \cdot z}\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{t\_0} - y} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (<= z 0.0146)
     (- (+ x (/ t_0 (- 1.0 (* (tan y) z)))) (tan a))
     (+ x (- (/ 1.0 (- (/ 1.0 t_0) y)) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if (z <= 0.0146) {
		tmp = (x + (t_0 / (1.0 - (tan(y) * z)))) - tan(a);
	} else {
		tmp = x + ((1.0 / ((1.0 / t_0) - 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) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if (z <= 0.0146d0) then
        tmp = (x + (t_0 / (1.0d0 - (tan(y) * z)))) - tan(a)
    else
        tmp = x + ((1.0d0 / ((1.0d0 / t_0) - 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 t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if (z <= 0.0146) {
		tmp = (x + (t_0 / (1.0 - (Math.tan(y) * z)))) - Math.tan(a);
	} else {
		tmp = x + ((1.0 / ((1.0 / t_0) - y)) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if z <= 0.0146:
		tmp = (x + (t_0 / (1.0 - (math.tan(y) * z)))) - math.tan(a)
	else:
		tmp = x + ((1.0 / ((1.0 / t_0) - y)) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if (z <= 0.0146)
		tmp = Float64(Float64(x + Float64(t_0 / Float64(1.0 - Float64(tan(y) * z)))) - tan(a));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 / t_0) - 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)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if (z <= 0.0146)
		tmp = (x + (t_0 / (1.0 - (tan(y) * z)))) - tan(a);
	else
		tmp = x + ((1.0 / ((1.0 / t_0) - 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_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 0.0146], N[(N[(x + N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(N[(1.0 / t$95$0), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < 0.0146000000000000001

   1. Initial program 87.3%

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

      1. tan-sum 99.7%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*r/ 99.7%

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

      2. *-rgt-identity 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in z around 0 80.0%

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

      1. associate-+r- 79.9%

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

      2. associate-/l* 79.9%

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

      3. tan-quot 79.9%

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

   9. Applied egg-rr 79.9%

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

   if 0.0146000000000000001 < z

   1. Initial program 62.8%

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

      1. tan-sum 99.5%

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

      2. clear-num 99.5%

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

   4. Applied egg-rr 99.5%

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

      1. div-sub 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. associate-/l* 99.5%

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

   8. Simplified 99.5%

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

   9. Taylor expanded in y around 0 64.5%

      \[\leadsto x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - \color{blue}{y}} - \tan a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.0146:\\ \;\;\;\;\left(x + \frac{\tan y + \tan z}{1 - \tan y \cdot z}\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - y} - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \frac{1}{\tan y + \tan z}\\ \mathbf{if}\;y \leq -300000000:\\ \;\;\;\;x + \left(\frac{1}{t\_0 - z} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{t\_0 - y} - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ (tan y) (tan z)))))
   (if (<= y -300000000.0)
     (+ x (- (/ 1.0 (- t_0 z)) (tan a)))
     (+ x (- (/ 1.0 (- t_0 y)) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = 1.0 / (tan(y) + tan(z));
	double tmp;
	if (y <= -300000000.0) {
		tmp = x + ((1.0 / (t_0 - z)) - tan(a));
	} else {
		tmp = x + ((1.0 / (t_0 - 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 / (tan(y) + tan(z))
    if (y <= (-300000000.0d0)) then
        tmp = x + ((1.0d0 / (t_0 - z)) - tan(a))
    else
        tmp = x + ((1.0d0 / (t_0 - 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 t_0 = 1.0 / (Math.tan(y) + Math.tan(z));
	double tmp;
	if (y <= -300000000.0) {
		tmp = x + ((1.0 / (t_0 - z)) - Math.tan(a));
	} else {
		tmp = x + ((1.0 / (t_0 - y)) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = 1.0 / (math.tan(y) + math.tan(z))
	tmp = 0
	if y <= -300000000.0:
		tmp = x + ((1.0 / (t_0 - z)) - math.tan(a))
	else:
		tmp = x + ((1.0 / (t_0 - y)) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(1.0 / Float64(tan(y) + tan(z)))
	tmp = 0.0
	if (y <= -300000000.0)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(t_0 - z)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(t_0 - 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)
	t_0 = 1.0 / (tan(y) + tan(z));
	tmp = 0.0;
	if (y <= -300000000.0)
		tmp = x + ((1.0 / (t_0 - z)) - tan(a));
	else
		tmp = x + ((1.0 / (t_0 - 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_] := Block[{t$95$0 = N[(1.0 / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -300000000.0], N[(x + N[(N[(1.0 / N[(t$95$0 - z), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(t$95$0 - y), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3e8

   1. Initial program 63.3%

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

      1. tan-sum 99.7%

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

      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. div-sub 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. associate-/l* 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in z around 0 66.1%

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

   if -3e8 < y

   1. Initial program 87.2%

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

      1. tan-sum 99.7%

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

      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. div-sub 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. associate-/l* 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around 0 76.1%

      \[\leadsto x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - \color{blue}{y}} - \tan a\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300000000:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - z} - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1}{\tan y + \tan z} - y} - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.5% accurate, 1.0× speedup

Math

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

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 (+ y z)) (tan a))))

C

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

Python

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

Derivation

1. Initial program 81.8%

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

3. Final simplification 81.8%

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

Alternative 7: 41.4% accurate, 1.0× speedup

Math

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

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 (/ (sin a) (cos a))))

C

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

Python

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

Julia

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

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x - (sin(a) / cos(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[Sin[a], $MachinePrecision] / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 81.8%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

7. Taylor expanded in z around 0 73.7%

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

8. Taylor expanded in z around inf 41.2%

   \[\leadsto \color{blue}{x - \frac{\sin a}{\cos a}} \]

9. Final simplification 41.2%

   \[\leadsto x - \frac{\sin a}{\cos a} \]
10. Add Preprocessing

Alternative 8: 31.4% 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

1. Initial program 81.8%

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

3. Taylor expanded in x around inf 31.6%

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

4. Final simplification 31.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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))))