tan-example (used to crash)

Percentage Accurate: 79.3% → 99.7%

Time: 34.2s

Alternatives: 12

Speedup: 1.0×

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.3% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.2%

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

   1. +-commutative 80.2%

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

   2. sub-neg 80.2%

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

   3. associate-+l+ 80.1%

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

   4. tan-sum 99.6%

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

   5. div-inv 99.6%

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

   6. fma-define 99.6%

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

   7. neg-mul-1 99.6%

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

   8. fma-define 99.6%

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

4. Applied egg-rr 99.6%

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

   1. fma-undefine 99.6%

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

   2. fma-undefine 99.6%

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

   3. neg-mul-1 99.6%

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

   4. associate-+r+ 99.7%

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

   5. unsub-neg 99.7%

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

   6. associate-*r/ 99.7%

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

   7. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

   1. tan-quot 99.7%

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

   2. frac-2neg 99.7%

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

8. Applied egg-rr 99.7%

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

   1. sub-neg 99.7%

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

10. Applied egg-rr 99.7%

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

    1. sub-neg 99.7%

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

    2. +-commutative 99.7%

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

    3. distribute-frac-neg 99.7%

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

    4. distribute-frac-neg2 99.7%

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

    5. remove-double-neg 99.7%

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

12. Simplified 99.7%

    \[\leadsto \color{blue}{\left(\frac{\frac{\sin z}{\cos z} + \tan y}{1 - \tan y \cdot \tan z} - \tan a\right)} + x \]
13. 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 80.2%

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

   1. +-commutative 80.2%

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

   2. sub-neg 80.2%

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

   3. associate-+l+ 80.1%

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

   4. tan-sum 99.6%

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

   5. div-inv 99.6%

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

   6. fma-define 99.6%

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

   7. neg-mul-1 99.6%

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

   8. fma-define 99.6%

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

4. Applied egg-rr 99.6%

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

   1. fma-undefine 99.6%

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

   2. fma-undefine 99.6%

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

   3. neg-mul-1 99.6%

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

   4. associate-+r+ 99.7%

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

   5. unsub-neg 99.7%

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

   6. associate-*r/ 99.7%

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

   7. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

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: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -0.0004:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(z + y\right)}{\sin \left(z + y\right)}} - \tan a\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-48}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - \frac{\sin a}{\cos a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -0.0004)
   (+ x (- (/ 1.0 (/ (cos (+ z y)) (sin (+ z y)))) (tan a)))
   (if (<= a 1.6e-48)
     (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) a))
     (+ x (- (tan (+ z y)) (/ (sin a) (cos a)))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.0004) {
		tmp = x + ((1.0 / (cos((z + y)) / sin((z + y)))) - tan(a));
	} else if (a <= 1.6e-48) {
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	} else {
		tmp = x + (tan((z + y)) - (sin(a) / cos(a)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-0.0004d0)) then
        tmp = x + ((1.0d0 / (cos((z + y)) / sin((z + y)))) - tan(a))
    else if (a <= 1.6d-48) then
        tmp = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - a)
    else
        tmp = x + (tan((z + y)) - (sin(a) / cos(a)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.0004) {
		tmp = x + ((1.0 / (Math.cos((z + y)) / Math.sin((z + y)))) - Math.tan(a));
	} else if (a <= 1.6e-48) {
		tmp = x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	} else {
		tmp = x + (Math.tan((z + y)) - (Math.sin(a) / Math.cos(a)));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -0.0004:
		tmp = x + ((1.0 / (math.cos((z + y)) / math.sin((z + y)))) - math.tan(a))
	elif a <= 1.6e-48:
		tmp = x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	else:
		tmp = x + (math.tan((z + y)) - (math.sin(a) / math.cos(a)))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -0.0004)
		tmp = Float64(x + Float64(Float64(1.0 / Float64(cos(Float64(z + y)) / sin(Float64(z + y)))) - tan(a)));
	elseif (a <= 1.6e-48)
		tmp = Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	else
		tmp = Float64(x + Float64(tan(Float64(z + y)) - Float64(sin(a) / cos(a))));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -0.0004)
		tmp = x + ((1.0 / (cos((z + y)) / sin((z + y)))) - tan(a));
	elseif (a <= 1.6e-48)
		tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - a);
	else
		tmp = x + (tan((z + y)) - (sin(a) / cos(a)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -0.0004], N[(x + N[(N[(1.0 / N[(N[Cos[N[(z + y), $MachinePrecision]], $MachinePrecision] / N[Sin[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.6e-48], 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[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sin[a], $MachinePrecision] / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.00000000000000019e-4

   1. Initial program 80.5%

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

      1. tan-quot 80.6%

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

      2. clear-num 80.5%

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

   4. Applied egg-rr 80.5%

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

   if -4.00000000000000019e-4 < a < 1.5999999999999999e-48

   1. Initial program 74.5%

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

   3. Taylor expanded in a around 0 74.5%

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

      1. tan-sum 99.7%

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

      2. div-inv 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. associate-*r/ 99.7%

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

      2. *-rgt-identity 99.7%

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

   7. Simplified 99.7%

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

   if 1.5999999999999999e-48 < a

   1. Initial program 87.2%

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

   3. Taylor expanded in a around inf 87.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.0004:\\ \;\;\;\;x + \left(\frac{1}{\frac{\cos \left(z + y\right)}{\sin \left(z + y\right)}} - \tan a\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-48}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - \frac{\sin a}{\cos a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x + (tan((z + y)) - (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 + (tan((z + y)) - (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.tan((z + y)) - (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.tan((z + y)) - (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(tan(Float64(z + y)) - 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 + (tan((z + y)) - (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[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sin[a], $MachinePrecision] / N[Cos[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.2%

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

3. Taylor expanded in a around inf 80.2%

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

4. Final simplification 80.2%

   \[\leadsto x + \left(\tan \left(z + y\right) - \frac{\sin a}{\cos a}\right) \]
5. Add Preprocessing

Alternative 5: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-25} \lor \neg \left(a \leq 0.00056\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -7.8e-25) (not (<= a 0.00056)))
   (+ x (- (tan y) (tan a)))
   (+ x (- (tan (+ z y)) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -7.8e-25) || !(a <= 0.00056)) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan((z + y)) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.8d-25)) .or. (.not. (a <= 0.00056d0))) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan((z + y)) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -7.8e-25) || !(a <= 0.00056)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan((z + y)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -7.8e-25) or not (a <= 0.00056):
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan((z + y)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -7.8e-25) || !(a <= 0.00056))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(z + y)) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -7.8e-25) || ~((a <= 0.00056)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan((z + y)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -7.8e-25], N[Not[LessEqual[a, 0.00056]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.8e-25 or 5.5999999999999995e-4 < a

   1. Initial program 82.7%

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

   3. Taylor expanded in y around inf 60.3%

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

   if -7.8e-25 < a < 5.5999999999999995e-4

   1. Initial program 77.2%

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

   3. Taylor expanded in a around 0 77.2%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{-25} \lor \neg \left(a \leq 0.00056\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \lor \neg \left(a \leq 1.55\right):\\ \;\;\;\;e^{\log x}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -1.65) (not (<= a 1.55)))
   (exp (log x))
   (+ x (- (tan (+ z y)) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.65) || !(a <= 1.55)) {
		tmp = exp(log(x));
	} else {
		tmp = x + (tan((z + y)) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.65d0)) .or. (.not. (a <= 1.55d0))) then
        tmp = exp(log(x))
    else
        tmp = x + (tan((z + y)) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -1.65) || !(a <= 1.55)) {
		tmp = Math.exp(Math.log(x));
	} else {
		tmp = x + (Math.tan((z + y)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -1.65) or not (a <= 1.55):
		tmp = math.exp(math.log(x))
	else:
		tmp = x + (math.tan((z + y)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -1.65) || !(a <= 1.55))
		tmp = exp(log(x));
	else
		tmp = Float64(x + Float64(tan(Float64(z + y)) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -1.65) || ~((a <= 1.55)))
		tmp = exp(log(x));
	else
		tmp = x + (tan((z + y)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -1.65], N[Not[LessEqual[a, 1.55]], $MachinePrecision]], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6499999999999999 or 1.55000000000000004 < a

   1. Initial program 82.8%

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

   3. Taylor expanded in a around 0 3.0%

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

      1. add-exp-log 2.4%

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

   5. Applied egg-rr 2.4%

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

   6. Taylor expanded in x around inf 23.7%

      \[\leadsto e^{\color{blue}{-1 \cdot \log \left(\frac{1}{x}\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 23.7%

         \[\leadsto e^{\color{blue}{-\log \left(\frac{1}{x}\right)}} \]

      2. log-rec 23.7%

         \[\leadsto e^{-\color{blue}{\left(-\log x\right)}} \]

      3. remove-double-neg 23.7%

         \[\leadsto e^{\color{blue}{\log x}} \]

   8. Simplified 23.7%

      \[\leadsto e^{\color{blue}{\log x}} \]

   if -1.6499999999999999 < a < 1.55000000000000004

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0 77.4%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \lor \neg \left(a \leq 1.55\right):\\ \;\;\;\;e^{\log x}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2:\\ \;\;\;\;e^{-\log \left(\frac{1}{x}\right)}\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\log x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -2.0)
   (exp (- (log (/ 1.0 x))))
   (if (<= a 1.55) (+ x (- (tan (+ z y)) a)) (exp (log x)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.0) {
		tmp = exp(-log((1.0 / x)));
	} else if (a <= 1.55) {
		tmp = x + (tan((z + y)) - a);
	} else {
		tmp = exp(log(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.0d0)) then
        tmp = exp(-log((1.0d0 / x)))
    else if (a <= 1.55d0) then
        tmp = x + (tan((z + y)) - a)
    else
        tmp = exp(log(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.0) {
		tmp = Math.exp(-Math.log((1.0 / x)));
	} else if (a <= 1.55) {
		tmp = x + (Math.tan((z + y)) - a);
	} else {
		tmp = Math.exp(Math.log(x));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -2.0:
		tmp = math.exp(-math.log((1.0 / x)))
	elif a <= 1.55:
		tmp = x + (math.tan((z + y)) - a)
	else:
		tmp = math.exp(math.log(x))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -2.0)
		tmp = exp(Float64(-log(Float64(1.0 / x))));
	elseif (a <= 1.55)
		tmp = Float64(x + Float64(tan(Float64(z + y)) - a));
	else
		tmp = exp(log(x));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -2.0)
		tmp = exp(-log((1.0 / x)));
	elseif (a <= 1.55)
		tmp = x + (tan((z + y)) - a);
	else
		tmp = exp(log(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -2.0], N[Exp[(-N[Log[N[(1.0 / x), $MachinePrecision]], $MachinePrecision])], $MachinePrecision], If[LessEqual[a, 1.55], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[Exp[N[Log[x], $MachinePrecision]], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2

   1. Initial program 80.5%

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

   3. Taylor expanded in a around 0 5.1%

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

      1. add-exp-log 5.1%

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

   5. Applied egg-rr 5.1%

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

   6. Taylor expanded in x around inf 23.7%

      \[\leadsto e^{\color{blue}{-1 \cdot \log \left(\frac{1}{x}\right)}} \]

   if -2 < a < 1.55000000000000004

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0 77.4%

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

   if 1.55000000000000004 < a

   1. Initial program 84.8%

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

   3. Taylor expanded in a around 0 1.2%

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

      1. add-exp-log 0.0%

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

   5. Applied egg-rr 0.0%

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

   6. Taylor expanded in x around inf 23.7%

      \[\leadsto e^{\color{blue}{-1 \cdot \log \left(\frac{1}{x}\right)}} \]
   7. Step-by-step derivation

      1. mul-1-neg 23.7%

         \[\leadsto e^{\color{blue}{-\log \left(\frac{1}{x}\right)}} \]

      2. log-rec 23.7%

         \[\leadsto e^{-\color{blue}{\left(-\log x\right)}} \]

      3. remove-double-neg 23.7%

         \[\leadsto e^{\color{blue}{\log x}} \]

   8. Simplified 23.7%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2:\\ \;\;\;\;e^{-\log \left(\frac{1}{x}\right)}\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;e^{\log x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= y -6.5e-8) (+ x (- (tan y) (tan a))) (+ x (- (tan z) (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -6.5e-8) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.5d-8)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -6.5e-8) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if y <= -6.5e-8:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -6.5e-8)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -6.5e-8)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -6.5e-8], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $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 y < -6.49999999999999997e-8

   1. Initial program 63.7%

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

   3. Taylor expanded in y around inf 62.4%

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

   if -6.49999999999999997e-8 < y

   1. Initial program 87.0%

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

   3. Taylor expanded in y around 0 77.4%

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

Alternative 9: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.2%

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

3. Final simplification 80.2%

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

Alternative 10: 50.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.8) x (if (<= a 1.55) (+ x (- (tan (+ z y)) a)) x)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.8) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (tan((z + y)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.8d0)) then
        tmp = x
    else if (a <= 1.55d0) then
        tmp = x + (tan((z + y)) - a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.8) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (Math.tan((z + y)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.8:
		tmp = x
	elif a <= 1.55:
		tmp = x + (math.tan((z + y)) - a)
	else:
		tmp = x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.8)
		tmp = x;
	elseif (a <= 1.55)
		tmp = Float64(x + Float64(tan(Float64(z + y)) - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.8)
		tmp = x;
	elseif (a <= 1.55)
		tmp = x + (tan((z + y)) - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -1.8], x, If[LessEqual[a, 1.55], N[(x + N[(N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.80000000000000004 or 1.55000000000000004 < a

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 23.7%

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

   if -1.80000000000000004 < a < 1.55000000000000004

   1. Initial program 77.4%

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

   3. Taylor expanded in a around 0 77.4%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan \left(z + y\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.65) x (if (<= a 4.4e-5) (+ x (- (tan y) a)) x)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.65) {
		tmp = x;
	} else if (a <= 4.4e-5) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.65d0)) then
        tmp = x
    else if (a <= 4.4d-5) then
        tmp = x + (tan(y) - a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.65) {
		tmp = x;
	} else if (a <= 4.4e-5) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.65:
		tmp = x
	elif a <= 4.4e-5:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.65)
		tmp = x;
	elseif (a <= 4.4e-5)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.65)
		tmp = x;
	elseif (a <= 4.4e-5)
		tmp = x + (tan(y) - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -1.65], x, If[LessEqual[a, 4.4e-5], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6499999999999999 or 4.3999999999999999e-5 < a

   1. Initial program 82.9%

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

   3. Taylor expanded in x around inf 23.7%

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

   if -1.6499999999999999 < a < 4.3999999999999999e-5

   1. Initial program 77.2%

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

   3. Taylor expanded in a around 0 77.2%

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

   4. Taylor expanded in y around inf 62.9%

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

Alternative 12: 31.9% 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 80.2%

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

3. Taylor expanded in x around inf 33.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024145 
(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))))