tan-example (used to crash)

Percentage Accurate: 79.1% → 99.7%

Time: 24.9s

Alternatives: 15

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: 79.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{\tan y + \tan z}{\mathsf{fma}\left(\frac{1}{\frac{\cos y}{\sin y}}, 0 - \tan z, 1\right)} - \tan a\right) \end{array} \]

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) (tan z))
    (fma (/ 1.0 (/ (cos y) (sin y))) (- 0.0 (tan z)) 1.0))
   (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)) / fma((1.0 / (cos(y) / sin(y))), (0.0 - tan(z)), 1.0)) - 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)) / fma(Float64(1.0 / Float64(cos(y) / sin(y))), Float64(0.0 - tan(z)), 1.0)) - 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_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(N[(1.0 / N[(N[Cos[y], $MachinePrecision] / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.0 - N[Tan[z], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. tan-sum N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   9. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

4. Applied egg-rr 99.7%

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

   1. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 + \left(\mathsf{neg}\left(\tan y \cdot \tan z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\left(\mathsf{neg}\left(\tan y \cdot \tan z\right)\right) + 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   3. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\tan y \cdot \left(\mathsf{neg}\left(\tan z\right)\right) + 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. fma-define N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\mathsf{fma}\left(\tan y, \mathsf{neg}\left(\tan z\right), 1\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\tan y, \left(\mathsf{neg}\left(\tan z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{tan.f64}\left(y\right), \left(\mathsf{neg}\left(\tan z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. neg-lowering-neg.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{neg.f64}\left(\tan z\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

6. Applied egg-rr 99.7%

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

   1. tan-quot N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\left(\frac{\sin y}{\cos y}\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\left(\frac{1}{\frac{\cos y}{\sin y}}\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\cos y}{\sin y}\right)\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\cos y, \sin y\right)\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. cos-lowering-cos.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{cos.f64}\left(y\right), \sin y\right)\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. sin-lowering-sin.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{sin.f64}\left(y\right)\right)\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

8. Applied egg-rr 99.7%

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

9. Final simplification 99.7%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{\mathsf{fma}\left(\frac{1}{\frac{\cos y}{\sin y}}, 0 - \tan z, 1\right)} - \tan a\right) \]
10. Add Preprocessing

Alternative 2: 89.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -0.01:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-6}:\\ \;\;\;\;x + \left(\frac{t\_0}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_0 - \tan a\right)\\ \end{array} \end{array} \]

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))))
   (if (<= (tan a) -0.01)
     (+ x (- (* (/ 1.0 (cos (+ y z))) (sin (+ y z))) (tan a)))
     (if (<= (tan a) 2e-6)
       (+ x (- (/ t_0 (- 1.0 (* (tan y) (tan z)))) a))
       (+ x (- 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);
	double tmp;
	if (tan(a) <= -0.01) {
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	} else if (tan(a) <= 2e-6) {
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
	} else {
		tmp = x + (t_0 - 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 (tan(a) <= (-0.01d0)) then
        tmp = x + (((1.0d0 / cos((y + z))) * sin((y + z))) - tan(a))
    else if (tan(a) <= 2d-6) then
        tmp = x + ((t_0 / (1.0d0 - (tan(y) * tan(z)))) - a)
    else
        tmp = x + (t_0 - 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 (Math.tan(a) <= -0.01) {
		tmp = x + (((1.0 / Math.cos((y + z))) * Math.sin((y + z))) - Math.tan(a));
	} else if (Math.tan(a) <= 2e-6) {
		tmp = x + ((t_0 / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	} else {
		tmp = x + (t_0 - 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 math.tan(a) <= -0.01:
		tmp = x + (((1.0 / math.cos((y + z))) * math.sin((y + z))) - math.tan(a))
	elif math.tan(a) <= 2e-6:
		tmp = x + ((t_0 / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	else:
		tmp = x + (t_0 - 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 (tan(a) <= -0.01)
		tmp = Float64(x + Float64(Float64(Float64(1.0 / cos(Float64(y + z))) * sin(Float64(y + z))) - tan(a)));
	elseif (tan(a) <= 2e-6)
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))) - a));
	else
		tmp = Float64(x + Float64(t_0 - 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 (tan(a) <= -0.01)
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	elseif (tan(a) <= 2e-6)
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(z)))) - a);
	else
		tmp = x + (t_0 - 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[N[Tan[a], $MachinePrecision], -0.01], N[(x + N[(N[(N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 2e-6], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.0100000000000000002

   1. Initial program 91.2%

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

      1. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\cos \left(y + z\right)}\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \cos \left(y + z\right)\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(y + z\right)\right)\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \mathsf{sin.f64}\left(\left(y + z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      9. +-lowering-+.f64 91.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \mathsf{sin.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 91.3%

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

   if -0.0100000000000000002 < (tan.f64 a) < 1.99999999999999991e-6

   1. Initial program 81.2%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 81.2%

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

      1. tan-sum N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), a\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), a\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), a\right)\right) \]

      4. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), a\right)\right) \]

      5. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), a\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), a\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), a\right)\right) \]

      8. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), a\right)\right) \]

      9. tan-lowering-tan.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), a\right)\right) \]

   7. Applied egg-rr 99.7%

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

   if 1.99999999999999991e-6 < (tan.f64 a)

   1. Initial program 83.0%

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

      1. tan-sum N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      4. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      9. tan-lowering-tan.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \color{blue}{1}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 83.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.01:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-6}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;\tan a \leq -0.01:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{t\_0}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_0 - \tan a\right)\\ \end{array} \end{array} \]

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))))
   (if (<= (tan a) -0.01)
     (+ x (- (* (/ 1.0 (cos (+ y z))) (sin (+ y z))) (tan a)))
     (if (<= (tan a) 2e-6)
       (+ x (/ t_0 (- 1.0 (* (tan y) (tan z)))))
       (+ x (- 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);
	double tmp;
	if (tan(a) <= -0.01) {
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	} else if (tan(a) <= 2e-6) {
		tmp = x + (t_0 / (1.0 - (tan(y) * tan(z))));
	} else {
		tmp = x + (t_0 - 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 (tan(a) <= (-0.01d0)) then
        tmp = x + (((1.0d0 / cos((y + z))) * sin((y + z))) - tan(a))
    else if (tan(a) <= 2d-6) then
        tmp = x + (t_0 / (1.0d0 - (tan(y) * tan(z))))
    else
        tmp = x + (t_0 - 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 (Math.tan(a) <= -0.01) {
		tmp = x + (((1.0 / Math.cos((y + z))) * Math.sin((y + z))) - Math.tan(a));
	} else if (Math.tan(a) <= 2e-6) {
		tmp = x + (t_0 / (1.0 - (Math.tan(y) * Math.tan(z))));
	} else {
		tmp = x + (t_0 - 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 math.tan(a) <= -0.01:
		tmp = x + (((1.0 / math.cos((y + z))) * math.sin((y + z))) - math.tan(a))
	elif math.tan(a) <= 2e-6:
		tmp = x + (t_0 / (1.0 - (math.tan(y) * math.tan(z))))
	else:
		tmp = x + (t_0 - 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 (tan(a) <= -0.01)
		tmp = Float64(x + Float64(Float64(Float64(1.0 / cos(Float64(y + z))) * sin(Float64(y + z))) - tan(a)));
	elseif (tan(a) <= 2e-6)
		tmp = Float64(x + Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(z)))));
	else
		tmp = Float64(x + Float64(t_0 - 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 (tan(a) <= -0.01)
		tmp = x + (((1.0 / cos((y + z))) * sin((y + z))) - tan(a));
	elseif (tan(a) <= 2e-6)
		tmp = x + (t_0 / (1.0 - (tan(y) * tan(z))));
	else
		tmp = x + (t_0 - 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[N[Tan[a], $MachinePrecision], -0.01], N[(x + N[(N[(N[(1.0 / N[Cos[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 2e-6], N[(x + N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.0100000000000000002

   1. Initial program 91.2%

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

      1. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{\cos \left(y + z\right)}\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \cos \left(y + z\right)\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\left(y + z\right)\right)\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \sin \left(y + z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \mathsf{sin.f64}\left(\left(y + z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      9. +-lowering-+.f64 91.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(1, \mathsf{cos.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \mathsf{sin.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 91.3%

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

   if -0.0100000000000000002 < (tan.f64 a) < 1.99999999999999991e-6

   1. Initial program 81.2%

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

      1. +-commutative N/A

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

      2. associate-+l- N/A

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

      3. tan-sum N/A

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

      4. div-inv N/A

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

      5. fmm-def N/A

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

      6. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\left(\tan y + \tan z\right), \color{blue}{\left(\frac{1}{1 - \tan y \cdot \tan z}\right)}, \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(\frac{\color{blue}{1}}{1 - \tan y \cdot \tan z}\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      8. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(\frac{1}{1 - \tan y \cdot \tan z}\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      9. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\frac{1}{1 - \tan y \cdot \tan z}\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \color{blue}{\left(1 - \tan y \cdot \tan z\right)}\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      11. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \color{blue}{\left(\tan y \cdot \tan z\right)}\right)\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \color{blue}{\tan z}\right)\right)\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      13. tan-lowering-tan.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan \color{blue}{z}\right)\right)\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      14. tan-lowering-tan.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(\tan a - x\right)\right)\right)\right) \]

      15. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{neg.f64}\left(\left(\tan a - x\right)\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\tan a, x\right)\right)\right) \]

      17. tan-lowering-tan.f64 99.7%

          \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{neg.f64}\left(\mathsf{\_.f64}\left(\mathsf{tan.f64}\left(a\right), x\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around 0

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \color{blue}{x}\right) \]
   6. Step-by-step derivation

   7. Simplified 98.4%

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

      1. sub-neg N/A

         \[\leadsto \left(\tan y + \tan z\right) \cdot \frac{1}{1 + \left(\mathsf{neg}\left(\tan y \cdot \tan z\right)\right)} + x \]

      2. distribute-rgt-neg-out N/A

         \[\leadsto \left(\tan y + \tan z\right) \cdot \frac{1}{1 + \tan y \cdot \left(\mathsf{neg}\left(\tan z\right)\right)} + x \]

      3. +-commutative N/A

         \[\leadsto \left(\tan y + \tan z\right) \cdot \frac{1}{\tan y \cdot \left(\mathsf{neg}\left(\tan z\right)\right) + 1} + x \]

      4. div-inv N/A

         \[\leadsto \frac{\tan y + \tan z}{\tan y \cdot \left(\mathsf{neg}\left(\tan z\right)\right) + 1} + x \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{\tan y + \tan z}{\tan y \cdot \left(\mathsf{neg}\left(\tan z\right)\right) + 1}\right), \color{blue}{x}\right) \]

   9. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} + x} \]

   if 1.99999999999999991e-6 < (tan.f64 a)

   1. Initial program 83.0%

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

      1. tan-sum N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      4. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      9. tan-lowering-tan.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \color{blue}{1}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 83.3%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.01:\\ \;\;\;\;x + \left(\frac{1}{\cos \left(y + z\right)} \cdot \sin \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) - \tan a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.3× speedup

Math

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

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) (sin z)) (cos 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) * sin(z)) / cos(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) * sin(z)) / cos(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.sin(z)) / Math.cos(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.sin(z)) / math.cos(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(Float64(tan(y) * sin(z)) / cos(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) * sin(z)) / cos(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[(N[Tan[y], $MachinePrecision] * N[Sin[z], $MachinePrecision]), $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. tan-sum N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   9. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

4. Applied egg-rr 99.7%

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

   1. tan-quot N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \frac{\sin z}{\cos z}\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   2. associate-*r/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\frac{\tan y \cdot \sin z}{\cos z}\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\left(\tan y \cdot \sin z\right), \cos z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\tan y, \sin z\right), \cos z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \sin z\right), \cos z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. sin-lowering-sin.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{sin.f64}\left(z\right)\right), \cos z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. cos-lowering-cos.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{sin.f64}\left(z\right)\right), \mathsf{cos.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

6. Applied egg-rr 99.7%

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

Alternative 5: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ x + \left(\frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, 0 - \tan z, 1\right)} - \tan a\right) \end{array} \]

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) (tan z)) (fma (tan y) (- 0.0 (tan z)) 1.0)) (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)) / fma(tan(y), (0.0 - tan(z)), 1.0)) - 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)) / fma(tan(y), Float64(0.0 - tan(z)), 1.0)) - 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_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] * N[(0.0 - N[Tan[z], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. tan-sum N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   9. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

4. Applied egg-rr 99.7%

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

   1. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 + \left(\mathsf{neg}\left(\tan y \cdot \tan z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   2. +-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\left(\mathsf{neg}\left(\tan y \cdot \tan z\right)\right) + 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   3. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\tan y \cdot \left(\mathsf{neg}\left(\tan z\right)\right) + 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. fma-define N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(\mathsf{fma}\left(\tan y, \mathsf{neg}\left(\tan z\right), 1\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\tan y, \left(\mathsf{neg}\left(\tan z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{tan.f64}\left(y\right), \left(\mathsf{neg}\left(\tan z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. neg-lowering-neg.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{neg.f64}\left(\tan z\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{fma.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{neg.f64}\left(\mathsf{tan.f64}\left(z\right)\right), 1\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

   \[\leadsto x + \left(\frac{\tan y + \tan z}{\mathsf{fma}\left(\tan y, 0 - \tan z, 1\right)} - \tan a\right) \]
8. Add Preprocessing

Alternative 6: 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 83.7%

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

   1. tan-sum N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   9. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

4. Applied egg-rr 99.7%

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

Alternative 7: 79.5% accurate, 0.7× speedup

Math

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

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) (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)) - 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)) - 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)) - 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)) - math.tan(a))

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return Float64(x + Float64(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)) - 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[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. tan-sum N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\tan y + \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\tan y, \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   5. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \left(1 - \tan y \cdot \tan z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \left(\tan y \cdot \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\tan y, \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   8. tan-lowering-tan.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \tan z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   9. tan-lowering-tan.f64 99.7%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \mathsf{\_.f64}\left(1, \mathsf{*.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

4. Applied egg-rr 99.7%

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

5. Taylor expanded in y around 0

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{tan.f64}\left(y\right), \mathsf{tan.f64}\left(z\right)\right), \color{blue}{1}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
6. Step-by-step derivation

7. Simplified 83.9%

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

8. Final simplification 83.9%

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

Alternative 8: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := x + \left(\tan y - \tan a\right)\\ \mathbf{if}\;a \leq -0.00082:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;a \leq 0.00044:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (+ x (- (tan y) (tan a)))))
   (if (<= a -0.00082) t_0 (if (<= a 0.00044) (+ x (- (tan (+ y z)) a)) t_0))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = x + (tan(y) - tan(a));
	double tmp;
	if (a <= -0.00082) {
		tmp = t_0;
	} else if (a <= 0.00044) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = t_0;
	}
	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 = x + (tan(y) - tan(a))
    if (a <= (-0.00082d0)) then
        tmp = t_0
    else if (a <= 0.00044d0) then
        tmp = x + (tan((y + z)) - a)
    else
        tmp = t_0
    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 = x + (Math.tan(y) - Math.tan(a));
	double tmp;
	if (a <= -0.00082) {
		tmp = t_0;
	} else if (a <= 0.00044) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = x + (math.tan(y) - math.tan(a))
	tmp = 0
	if a <= -0.00082:
		tmp = t_0
	elif a <= 0.00044:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = t_0
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(x + Float64(tan(y) - tan(a)))
	tmp = 0.0
	if (a <= -0.00082)
		tmp = t_0;
	elseif (a <= 0.00044)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = t_0;
	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 = x + (tan(y) - tan(a));
	tmp = 0.0;
	if (a <= -0.00082)
		tmp = t_0;
	elseif (a <= 0.00044)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = t_0;
	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[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.00082], t$95$0, If[LessEqual[a, 0.00044], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.1999999999999998e-4 or 4.40000000000000016e-4 < a

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\color{blue}{y}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 58.7%

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

   if -8.1999999999999998e-4 < a < 4.40000000000000016e-4

   1. Initial program 81.2%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 81.2%

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

Alternative 9: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -5 \cdot 10^{-13}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

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 z) -5e-13) (+ 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 + z) <= -5e-13) {
		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 + z) <= (-5d-13)) 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 + z) <= -5e-13) {
		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 + z) <= -5e-13:
		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 (Float64(y + z) <= -5e-13)
		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 + z) <= -5e-13)
		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[N[(y + z), $MachinePrecision], -5e-13], 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 (+.f64 y z) < -4.9999999999999999e-13

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\color{blue}{y}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 49.1%

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

   if -4.9999999999999999e-13 < (+.f64 y z)

   1. Initial program 88.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\color{blue}{z}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 74.0%

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

Alternative 10: 79.1% 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 83.7%

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

Alternative 11: 59.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := x + \left(\frac{1}{\frac{1 + -0.3333333333333333 \cdot \left(z \cdot z\right)}{z}} - \tan a\right)\\ \mathbf{if}\;a \leq -0.19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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
         (+
          x
          (- (/ 1.0 (/ (+ 1.0 (* -0.3333333333333333 (* z z))) z)) (tan a)))))
   (if (<= a -0.19) t_0 (if (<= a 7.2e-7) (+ x (- (tan (+ y z)) a)) t_0))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = x + ((1.0 / ((1.0 + (-0.3333333333333333 * (z * z))) / z)) - tan(a));
	double tmp;
	if (a <= -0.19) {
		tmp = t_0;
	} else if (a <= 7.2e-7) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = t_0;
	}
	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 = x + ((1.0d0 / ((1.0d0 + ((-0.3333333333333333d0) * (z * z))) / z)) - tan(a))
    if (a <= (-0.19d0)) then
        tmp = t_0
    else if (a <= 7.2d-7) then
        tmp = x + (tan((y + z)) - a)
    else
        tmp = t_0
    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 = x + ((1.0 / ((1.0 + (-0.3333333333333333 * (z * z))) / z)) - Math.tan(a));
	double tmp;
	if (a <= -0.19) {
		tmp = t_0;
	} else if (a <= 7.2e-7) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = x + ((1.0 / ((1.0 + (-0.3333333333333333 * (z * z))) / z)) - math.tan(a))
	tmp = 0
	if a <= -0.19:
		tmp = t_0
	elif a <= 7.2e-7:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = t_0
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 + Float64(-0.3333333333333333 * Float64(z * z))) / z)) - tan(a)))
	tmp = 0.0
	if (a <= -0.19)
		tmp = t_0;
	elseif (a <= 7.2e-7)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = t_0;
	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 = x + ((1.0 / ((1.0 + (-0.3333333333333333 * (z * z))) / z)) - tan(a));
	tmp = 0.0;
	if (a <= -0.19)
		tmp = t_0;
	elseif (a <= 7.2e-7)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = t_0;
	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[(x + N[(N[(1.0 / N[(N[(1.0 + N[(-0.3333333333333333 * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.19], t$95$0, If[LessEqual[a, 7.2e-7], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if a < -0.19 or 7.19999999999999989e-7 < a

   1. Initial program 85.7%

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

      1. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\tan \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \tan \left(y + z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\left(y + z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. +-lowering-+.f64 85.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 85.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\color{blue}{z}\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 66.3%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \color{blue}{\left(\frac{1 + \frac{-1}{3} \cdot {z}^{2}}{z}\right)}\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\left(1 + \frac{-1}{3} \cdot {z}^{2}\right), z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{-1}{3} \cdot {z}^{2}\right)\right), z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{3}, \left({z}^{2}\right)\right)\right), z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{3}, \left(z \cdot z\right)\right)\right), z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. *-lowering-*.f64 39.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-1}{3}, \mathsf{*.f64}\left(z, z\right)\right)\right), z\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   10. Simplified 39.7%

       \[\leadsto x + \left(\frac{1}{\color{blue}{\frac{1 + -0.3333333333333333 \cdot \left(z \cdot z\right)}{z}}} - \tan a\right) \]

   if -0.19 < a < 7.19999999999999989e-7

   1. Initial program 82.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 82.0%

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

Alternative 12: 54.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := x + \left(z - \tan a\right)\\ \mathbf{if}\;a \leq -400000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+16}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (+ x (- z (tan a)))))
   (if (<= a -400000000.0)
     t_0
     (if (<= a 1.2e+16) (+ x (- (tan (+ y z)) a)) t_0))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = x + (z - tan(a));
	double tmp;
	if (a <= -400000000.0) {
		tmp = t_0;
	} else if (a <= 1.2e+16) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = t_0;
	}
	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 = x + (z - tan(a))
    if (a <= (-400000000.0d0)) then
        tmp = t_0
    else if (a <= 1.2d+16) then
        tmp = x + (tan((y + z)) - a)
    else
        tmp = t_0
    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 = x + (z - Math.tan(a));
	double tmp;
	if (a <= -400000000.0) {
		tmp = t_0;
	} else if (a <= 1.2e+16) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = x + (z - math.tan(a))
	tmp = 0
	if a <= -400000000.0:
		tmp = t_0
	elif a <= 1.2e+16:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = t_0
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(x + Float64(z - tan(a)))
	tmp = 0.0
	if (a <= -400000000.0)
		tmp = t_0;
	elseif (a <= 1.2e+16)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = t_0;
	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 = x + (z - tan(a));
	tmp = 0.0;
	if (a <= -400000000.0)
		tmp = t_0;
	elseif (a <= 1.2e+16)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = t_0;
	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[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -400000000.0], t$95$0, If[LessEqual[a, 1.2e+16], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if a < -4e8 or 1.2e16 < a

   1. Initial program 86.8%

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

      1. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\tan \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \tan \left(y + z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\left(y + z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. +-lowering-+.f64 86.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 86.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\color{blue}{z}\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 67.8%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\color{blue}{z}, \mathsf{tan.f64}\left(a\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 30.5%

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

   if -4e8 < a < 1.2e16

   1. Initial program 81.3%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.7%

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

Alternative 13: 45.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := x + \left(z - \tan a\right)\\ \mathbf{if}\;a \leq -400000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+16}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (+ x (- z (tan a)))))
   (if (<= a -400000000.0) t_0 (if (<= a 1.2e+16) (+ x (- (tan y) a)) t_0))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = x + (z - tan(a));
	double tmp;
	if (a <= -400000000.0) {
		tmp = t_0;
	} else if (a <= 1.2e+16) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = t_0;
	}
	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 = x + (z - tan(a))
    if (a <= (-400000000.0d0)) then
        tmp = t_0
    else if (a <= 1.2d+16) then
        tmp = x + (tan(y) - a)
    else
        tmp = t_0
    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 = x + (z - Math.tan(a));
	double tmp;
	if (a <= -400000000.0) {
		tmp = t_0;
	} else if (a <= 1.2e+16) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = x + (z - math.tan(a))
	tmp = 0
	if a <= -400000000.0:
		tmp = t_0
	elif a <= 1.2e+16:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = t_0
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(x + Float64(z - tan(a)))
	tmp = 0.0
	if (a <= -400000000.0)
		tmp = t_0;
	elseif (a <= 1.2e+16)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = t_0;
	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 = x + (z - tan(a));
	tmp = 0.0;
	if (a <= -400000000.0)
		tmp = t_0;
	elseif (a <= 1.2e+16)
		tmp = x + (tan(y) - a);
	else
		tmp = t_0;
	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[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -400000000.0], t$95$0, If[LessEqual[a, 1.2e+16], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if a < -4e8 or 1.2e16 < a

   1. Initial program 86.8%

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

      1. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\tan \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \tan \left(y + z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\left(y + z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. +-lowering-+.f64 86.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 86.8%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\color{blue}{z}\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 67.8%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\color{blue}{z}, \mathsf{tan.f64}\left(a\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 30.5%

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

   if -4e8 < a < 1.2e16

   1. Initial program 81.3%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right), \color{blue}{a}\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 78.7%

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

   6. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{tan.f64}\left(\color{blue}{y}\right), a\right)\right) \]
   7. Step-by-step derivation

   8. Simplified 59.2%

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

Alternative 14: 40.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 0.043:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 (<= z 0.043) (+ x (- z (tan a))) x))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 0.043) {
		tmp = x + (z - tan(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 (z <= 0.043d0) then
        tmp = x + (z - tan(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 (z <= 0.043) {
		tmp = x + (z - Math.tan(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 z <= 0.043:
		tmp = x + (z - math.tan(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 (z <= 0.043)
		tmp = Float64(x + Float64(z - tan(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 (z <= 0.043)
		tmp = x + (z - tan(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[z, 0.043], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < 0.042999999999999997

   1. Initial program 88.4%

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

      1. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\left(\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(\color{blue}{a}\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      5. tan-quot N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \left(\frac{1}{\tan \left(y + z\right)}\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \tan \left(y + z\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      7. tan-lowering-tan.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\left(y + z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

      8. +-lowering-+.f64 88.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\mathsf{+.f64}\left(y, z\right)\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]

   4. Applied egg-rr 88.4%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(1, \mathsf{/.f64}\left(1, \mathsf{tan.f64}\left(\color{blue}{z}\right)\right)\right), \mathsf{tan.f64}\left(a\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 63.6%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{\_.f64}\left(\color{blue}{z}, \mathsf{tan.f64}\left(a\right)\right)\right) \]
   9. Step-by-step derivation

   10. Simplified 40.2%

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

   if 0.042999999999999997 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 23.3%

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

Alternative 15: 31.5% 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 83.7%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 33.2%

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

Reproduce

herbie shell --seed 2024161 
(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))))