tan-example (used to crash)

Percentage Accurate: 79.7% → 99.7%

Time: 44.9s

Alternatives: 10

Speedup: 1.0×

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

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

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

Derivation

1. Initial program 80.7%

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

   1. tan-sum 99.8%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.8%

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

   2. *-rgt-identity 99.8%

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

6. Simplified 99.8%

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

   1. tan-quot 99.8%

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

   2. clear-num 99.8%

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

   3. un-div-inv 99.8%

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

   4. clear-num 99.8%

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

   5. tan-quot 99.8%

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

8. Applied egg-rr 99.8%

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

9. Taylor expanded in z around inf 99.8%

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

10. Final simplification 99.8%

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

Alternative 2: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.7%

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

   1. tan-sum 99.8%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.8%

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

   2. *-rgt-identity 99.8%

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

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

Alternative 3: 79.6% accurate, 0.5× speedup

Math

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

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 (- (log (exp (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 + (log(exp(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 + (log(exp(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.log(Math.exp(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.log(math.exp(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(log(exp(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 + (log(exp(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[Log[N[Exp[N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.7%

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

   1. add-log-exp 80.7%

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

4. Applied egg-rr 80.7%

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

5. Final simplification 80.7%

   \[\leadsto x + \left(\log \left(e^{\tan \left(y + z\right)}\right) - \tan a\right) \]
6. Add Preprocessing

Alternative 4: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

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) -2e-6) (+ x (tan (+ y z))) (+ 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) <= -2e-6) {
		tmp = x + tan((y + z));
	} 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) <= (-2d-6)) then
        tmp = x + tan((y + z))
    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) <= -2e-6) {
		tmp = x + Math.tan((y + z));
	} 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) <= -2e-6:
		tmp = x + math.tan((y + z))
	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) <= -2e-6)
		tmp = Float64(x + tan(Float64(y + z)));
	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) <= -2e-6)
		tmp = x + tan((y + z));
	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], -2e-6], N[(x + N[Tan[N[(y + z), $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) < -1.99999999999999991e-6

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-+l- 79.9%

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

   4. Applied egg-rr 79.9%

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

   5. Taylor expanded in a around 0 54.9%

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

      1. neg-mul-1 54.9%

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

   7. Simplified 54.9%

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

   if -1.99999999999999991e-6 < (+.f64 y z)

   1. Initial program 81.2%

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

   3. Taylor expanded in y around 0 66.4%

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

      1. tan-quot 66.4%

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

      2. *-un-lft-identity 66.4%

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

   5. Applied egg-rr 66.4%

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

      1. *-lft-identity 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 62.2%

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

Alternative 5: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{else}:\\ \;\;\;\;\tan z + \left(x - \tan a\right)\\ \end{array} \end{array} \]

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) -2e-6) (+ x (tan (+ y z))) (+ (tan z) (- x (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) <= -2e-6) {
		tmp = x + tan((y + z));
	} else {
		tmp = tan(z) + (x - 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) <= (-2d-6)) then
        tmp = x + tan((y + z))
    else
        tmp = tan(z) + (x - 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) <= -2e-6) {
		tmp = x + Math.tan((y + z));
	} else {
		tmp = Math.tan(z) + (x - 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) <= -2e-6:
		tmp = x + math.tan((y + z))
	else:
		tmp = math.tan(z) + (x - 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) <= -2e-6)
		tmp = Float64(x + tan(Float64(y + z)));
	else
		tmp = Float64(tan(z) + Float64(x - 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) <= -2e-6)
		tmp = x + tan((y + z));
	else
		tmp = tan(z) + (x - 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], -2e-6], N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Tan[z], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -1.99999999999999991e-6

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-+l- 79.9%

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

   4. Applied egg-rr 79.9%

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

   5. Taylor expanded in a around 0 54.9%

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

      1. neg-mul-1 54.9%

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

   7. Simplified 54.9%

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

   if -1.99999999999999991e-6 < (+.f64 y z)

   1. Initial program 81.2%

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

   3. Taylor expanded in y around 0 66.4%

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

      1. tan-quot 66.4%

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

      2. add-sqr-sqrt 33.9%

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

      3. sqrt-unprod 59.2%

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

      4. pow2 59.2%

         \[\leadsto x + \left(\sqrt{\color{blue}{{\tan z}^{2}}} - \tan a\right) \]

   5. Applied egg-rr 59.2%

      \[\leadsto x + \left(\color{blue}{\sqrt{{\tan z}^{2}}} - \tan a\right) \]
   6. Step-by-step derivation

      1. unpow2 59.2%

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

      2. rem-sqrt-square 59.2%

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

   7. Simplified 59.2%

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

      1. associate-+r- 59.2%

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

      2. add-sqr-sqrt 33.9%

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

      3. fabs-sqr 33.9%

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

      4. add-sqr-sqrt 66.4%

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

   9. Applied egg-rr 66.4%

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

       1. associate-+r- 66.4%

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

       2. +-commutative 66.4%

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

       3. associate-+l- 66.4%

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

   11. Simplified 66.4%

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

4. Final simplification 62.2%

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

Alternative 6: 79.7% 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 80.7%

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

3. Final simplification 80.7%

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

Alternative 7: 60.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{elif}\;y + z \leq 0.2:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \end{array} \]

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) -2e-6)
   (+ x (tan (+ y z)))
   (if (<= (+ y z) 0.2) (+ x (- z (tan a))) (+ x (tan z)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -2e-6) {
		tmp = x + tan((y + z));
	} else if ((y + z) <= 0.2) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + tan(z);
	}
	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) <= (-2d-6)) then
        tmp = x + tan((y + z))
    else if ((y + z) <= 0.2d0) then
        tmp = x + (z - tan(a))
    else
        tmp = x + tan(z)
    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) <= -2e-6) {
		tmp = x + Math.tan((y + z));
	} else if ((y + z) <= 0.2) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + Math.tan(z);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -2e-6:
		tmp = x + math.tan((y + z))
	elif (y + z) <= 0.2:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + math.tan(z)
	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) <= -2e-6)
		tmp = Float64(x + tan(Float64(y + z)));
	elseif (Float64(y + z) <= 0.2)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + tan(z));
	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) <= -2e-6)
		tmp = x + tan((y + z));
	elseif ((y + z) <= 0.2)
		tmp = x + (z - tan(a));
	else
		tmp = x + tan(z);
	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], -2e-6], N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y + z), $MachinePrecision], 0.2], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 y z) < -1.99999999999999991e-6

   1. Initial program 79.9%

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

      1. +-commutative 79.9%

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

      2. associate-+l- 79.9%

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

   4. Applied egg-rr 79.9%

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

   5. Taylor expanded in a around 0 54.9%

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

      1. neg-mul-1 54.9%

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

   7. Simplified 54.9%

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

   if -1.99999999999999991e-6 < (+.f64 y z) < 0.20000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.0%

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

   4. Taylor expanded in z around 0 97.0%

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

   if 0.20000000000000001 < (+.f64 y z)

   1. Initial program 71.6%

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

   3. Taylor expanded in y around 0 49.6%

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

      1. add-cube-cbrt 49.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)} \cdot \sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}\right) \cdot \sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}} \]

      2. pow3 49.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}\right)}^{3}} \]

      3. tan-quot 49.1%

         \[\leadsto {\left(\sqrt[3]{x + \left(\color{blue}{\tan z} - \tan a\right)}\right)}^{3} \]

   5. Applied egg-rr 49.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\tan z - \tan a\right)}\right)}^{3}} \]

   6. Taylor expanded in a around 0 40.4%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{x + \frac{\sin z}{\cos z}}\right)}}^{3} \]
   7. Step-by-step derivation

      1. +-commutative 40.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin z}{\cos z} + x}}\right)}^{3} \]

   8. Simplified 40.4%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin z}{\cos z} + x}\right)}}^{3} \]
   9. Step-by-step derivation

      1. rem-cube-cbrt 40.9%

         \[\leadsto \color{blue}{\frac{\sin z}{\cos z} + x} \]

      2. tan-quot 40.8%

         \[\leadsto \color{blue}{\tan z} + x \]

   10. Applied egg-rr 40.8%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -2 \cdot 10^{-6}:\\ \;\;\;\;x + \tan \left(y + z\right)\\ \mathbf{elif}\;y + z \leq 0.2:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 0.13:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \end{array} \]

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 0.13) (+ x (- z (tan a))) (+ x (tan z))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 0.13) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + tan(z);
	}
	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 <= 0.13d0) then
        tmp = x + (z - tan(a))
    else
        tmp = x + tan(z)
    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 <= 0.13) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + Math.tan(z);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if z <= 0.13:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + math.tan(z)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (z <= 0.13)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + tan(z));
	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 <= 0.13)
		tmp = x + (z - tan(a));
	else
		tmp = x + tan(z);
	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, 0.13], N[(x + N[(z - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.13

   1. Initial program 88.1%

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

   3. Taylor expanded in y around 0 62.9%

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

   4. Taylor expanded in z around 0 38.3%

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

   if 0.13 < z

   1. Initial program 61.8%

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

   3. Taylor expanded in y around 0 61.7%

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

      1. add-cube-cbrt 60.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)} \cdot \sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}\right) \cdot \sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}} \]

      2. pow3 60.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}\right)}^{3}} \]

      3. tan-quot 60.9%

         \[\leadsto {\left(\sqrt[3]{x + \left(\color{blue}{\tan z} - \tan a\right)}\right)}^{3} \]

   5. Applied egg-rr 60.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\tan z - \tan a\right)}\right)}^{3}} \]

   6. Taylor expanded in a around 0 48.7%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{x + \frac{\sin z}{\cos z}}\right)}}^{3} \]
   7. Step-by-step derivation

      1. +-commutative 48.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin z}{\cos z} + x}}\right)}^{3} \]

   8. Simplified 48.7%

      \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin z}{\cos z} + x}\right)}}^{3} \]
   9. Step-by-step derivation

      1. rem-cube-cbrt 49.4%

         \[\leadsto \color{blue}{\frac{\sin z}{\cos z} + x} \]

      2. tan-quot 49.3%

         \[\leadsto \color{blue}{\tan z} + x \]

   10. Applied egg-rr 49.3%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.13:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 80.7%

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

3. Taylor expanded in y around 0 62.6%

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

   1. add-cube-cbrt 61.6%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)} \cdot \sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}\right) \cdot \sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}} \]

   2. pow3 61.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\frac{\sin z}{\cos z} - \tan a\right)}\right)}^{3}} \]

   3. tan-quot 61.7%

      \[\leadsto {\left(\sqrt[3]{x + \left(\color{blue}{\tan z} - \tan a\right)}\right)}^{3} \]

5. Applied egg-rr 61.7%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\tan z - \tan a\right)}\right)}^{3}} \]

6. Taylor expanded in a around 0 45.0%

   \[\leadsto {\color{blue}{\left(\sqrt[3]{x + \frac{\sin z}{\cos z}}\right)}}^{3} \]
7. Step-by-step derivation

   1. +-commutative 45.0%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\sin z}{\cos z} + x}}\right)}^{3} \]

8. Simplified 45.0%

   \[\leadsto {\color{blue}{\left(\sqrt[3]{\frac{\sin z}{\cos z} + x}\right)}}^{3} \]
9. Step-by-step derivation

   1. rem-cube-cbrt 45.6%

      \[\leadsto \color{blue}{\frac{\sin z}{\cos z} + x} \]

   2. tan-quot 45.6%

      \[\leadsto \color{blue}{\tan z} + x \]

10. Applied egg-rr 45.6%

    \[\leadsto \color{blue}{\tan z + x} \]

11. Final simplification 45.6%

    \[\leadsto x + \tan z \]
12. Add Preprocessing

Alternative 10: 31.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	return x

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	return x
end

MATLAB

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

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := x

Derivation

1. Initial program 80.7%

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

3. Taylor expanded in x around inf 32.1%

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

4. Final simplification 32.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(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))))