tan-example (used to crash)

Percentage Accurate: 79.7% → 99.7%

Time: 33.7s

Alternatives: 16

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

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

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
  (-
   (/
    1.0
    (/ (+ 1.0 (* (tan z) (/ -1.0 (/ (cos y) (sin y))))) (+ (tan z) (tan y))))
   (tan a))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. tan-sum 99.7%

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

   2. clear-num 99.7%

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

4. Applied egg-rr 99.7%

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

   1. tan-quot 99.7%

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

   2. frac-2neg 99.7%

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

6. Applied egg-rr 99.7%

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

   1. clear-num 99.7%

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

   2. inv-pow 99.7%

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

8. Applied egg-rr 99.7%

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

   1. unpow-1 99.7%

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

   2. distribute-frac-neg2 99.7%

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

   3. distribute-neg-frac 99.7%

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

   4. remove-double-neg 99.7%

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

10. Simplified 99.7%

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

11. Final simplification 99.7%

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

Alternative 2: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 10^{-32}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan z \cdot \tan y}{\tan z + \tan y}} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.001) (not (<= (tan a) 1e-32)))
   (+ x (- (tan (+ y z)) (tan a)))
   (+ x (- (/ 1.0 (/ (- 1.0 (* (tan z) (tan y))) (+ (tan z) (tan y)))) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.001) || !(tan(a) <= 1e-32)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = x + ((1.0 / ((1.0 - (tan(z) * tan(y))) / (tan(z) + tan(y)))) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((tan(a) <= (-0.001d0)) .or. (.not. (tan(a) <= 1d-32))) then
        tmp = x + (tan((y + z)) - tan(a))
    else
        tmp = x + ((1.0d0 / ((1.0d0 - (tan(z) * tan(y))) / (tan(z) + tan(y)))) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.001) || !(Math.tan(a) <= 1e-32)) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else {
		tmp = x + ((1.0 / ((1.0 - (Math.tan(z) * Math.tan(y))) / (Math.tan(z) + Math.tan(y)))) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.001) or not (math.tan(a) <= 1e-32):
		tmp = x + (math.tan((y + z)) - math.tan(a))
	else:
		tmp = x + ((1.0 / ((1.0 - (math.tan(z) * math.tan(y))) / (math.tan(z) + math.tan(y)))) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.001) || !(tan(a) <= 1e-32))
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(tan(z) * tan(y))) / Float64(tan(z) + tan(y)))) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.001) || ~((tan(a) <= 1e-32)))
		tmp = x + (tan((y + z)) - tan(a));
	else
		tmp = x + ((1.0 / ((1.0 - (tan(z) * tan(y))) / (tan(z) + tan(y)))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.001], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-32]], $MachinePrecision]], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -1e-3 or 1.00000000000000006e-32 < (tan.f64 a)

   1. Initial program 78.3%

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

   if -1e-3 < (tan.f64 a) < 1.00000000000000006e-32

   1. Initial program 78.8%

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

   3. Taylor expanded in a around 0 78.8%

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

      1. tan-sum 99.7%

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

      2. clear-num 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 10^{-32}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1}{\frac{1 - \tan z \cdot \tan y}{\tan z + \tan y}} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 10^{-32}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\tan z + \tan y\right) \cdot \frac{1}{1 - \tan z \cdot \tan y} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.001) (not (<= (tan a) 1e-32)))
   (+ x (- (tan (+ y z)) (tan a)))
   (+ x (- (* (+ (tan z) (tan y)) (/ 1.0 (- 1.0 (* (tan z) (tan y))))) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.001) || !(tan(a) <= 1e-32)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = x + (((tan(z) + tan(y)) * (1.0 / (1.0 - (tan(z) * tan(y))))) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((tan(a) <= (-0.001d0)) .or. (.not. (tan(a) <= 1d-32))) then
        tmp = x + (tan((y + z)) - tan(a))
    else
        tmp = x + (((tan(z) + tan(y)) * (1.0d0 / (1.0d0 - (tan(z) * tan(y))))) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.001) || !(Math.tan(a) <= 1e-32)) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else {
		tmp = x + (((Math.tan(z) + Math.tan(y)) * (1.0 / (1.0 - (Math.tan(z) * Math.tan(y))))) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.001) or not (math.tan(a) <= 1e-32):
		tmp = x + (math.tan((y + z)) - math.tan(a))
	else:
		tmp = x + (((math.tan(z) + math.tan(y)) * (1.0 / (1.0 - (math.tan(z) * math.tan(y))))) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.001) || !(tan(a) <= 1e-32))
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(Float64(tan(z) + tan(y)) * Float64(1.0 / Float64(1.0 - Float64(tan(z) * tan(y))))) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.001) || ~((tan(a) <= 1e-32)))
		tmp = x + (tan((y + z)) - tan(a));
	else
		tmp = x + (((tan(z) + tan(y)) * (1.0 / (1.0 - (tan(z) * tan(y))))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.001], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-32]], $MachinePrecision]], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -1e-3 or 1.00000000000000006e-32 < (tan.f64 a)

   1. Initial program 78.3%

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

   if -1e-3 < (tan.f64 a) < 1.00000000000000006e-32

   1. Initial program 78.8%

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

   3. Taylor expanded in a around 0 78.8%

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

      1. tan-sum 99.7%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 10^{-32}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\tan z + \tan y\right) \cdot \frac{1}{1 - \tan z \cdot \tan y} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 10^{-32}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.001) (not (<= (tan a) 1e-32)))
   (+ x (- (tan (+ y z)) (tan a)))
   (+ x (- (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y)))) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.001) || !(tan(a) <= 1e-32)) {
		tmp = x + (tan((y + z)) - tan(a));
	} else {
		tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((tan(a) <= (-0.001d0)) .or. (.not. (tan(a) <= 1d-32))) then
        tmp = x + (tan((y + z)) - tan(a))
    else
        tmp = x + (((tan(z) + tan(y)) / (1.0d0 - (tan(z) * tan(y)))) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((Math.tan(a) <= -0.001) || !(Math.tan(a) <= 1e-32)) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else {
		tmp = x + (((Math.tan(z) + Math.tan(y)) / (1.0 - (Math.tan(z) * Math.tan(y)))) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.001) or not (math.tan(a) <= 1e-32):
		tmp = x + (math.tan((y + z)) - math.tan(a))
	else:
		tmp = x + (((math.tan(z) + math.tan(y)) / (1.0 - (math.tan(z) * math.tan(y)))) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.001) || !(tan(a) <= 1e-32))
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(Float64(tan(z) + tan(y)) / Float64(1.0 - Float64(tan(z) * tan(y)))) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((tan(a) <= -0.001) || ~((tan(a) <= 1e-32)))
		tmp = x + (tan((y + z)) - tan(a));
	else
		tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.001], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 1e-32]], $MachinePrecision]], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[Tan[z], $MachinePrecision] + N[Tan[y], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[z], $MachinePrecision] * N[Tan[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -1e-3 or 1.00000000000000006e-32 < (tan.f64 a)

   1. Initial program 78.3%

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

   if -1e-3 < (tan.f64 a) < 1.00000000000000006e-32

   1. Initial program 78.8%

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

   3. Taylor expanded in a around 0 78.8%

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

      1. tan-sum 99.7%

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

      2. div-inv 99.8%

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

      3. fma-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

      1. fma-undefine 99.8%

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

      2. unsub-neg 99.8%

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

      3. associate-*r/ 99.7%

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

      4. *-rgt-identity 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 10^{-32}\right):\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 0.4× speedup

Math

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

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 (- (/ 1.0 (/ (- 1.0 (* (tan z) (tan y))) (+ (tan z) (tan y)))) (tan a))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. tan-sum 99.7%

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

   2. clear-num 99.7%

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

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 6: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 7: 99.7% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. tan-sum 99.7%

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

   2. div-inv 99.7%

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

4. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

6. Simplified 99.7%

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

7. Final simplification 99.7%

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

Alternative 8: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 0.005\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= (tan a) -0.001) (not (<= (tan a) 0.005)))
   (+ x (- (tan y) (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((tan(a) <= -0.001) || !(tan(a) <= 0.005)) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan((y + z)) - 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 ((tan(a) <= (-0.001d0)) .or. (.not. (tan(a) <= 0.005d0))) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan((y + z)) - 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 ((Math.tan(a) <= -0.001) || !(Math.tan(a) <= 0.005)) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (math.tan(a) <= -0.001) or not (math.tan(a) <= 0.005):
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((tan(a) <= -0.001) || !(tan(a) <= 0.005))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - 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 ((tan(a) <= -0.001) || ~((tan(a) <= 0.005)))
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[N[Tan[a], $MachinePrecision], -0.001], N[Not[LessEqual[N[Tan[a], $MachinePrecision], 0.005]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -1e-3 or 0.0050000000000000001 < (tan.f64 a)

   1. Initial program 77.4%

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

   3. Taylor expanded in y around inf 57.4%

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

   if -1e-3 < (tan.f64 a) < 0.0050000000000000001

   1. Initial program 79.8%

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

   3. Taylor expanded in a around 0 79.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 0.005\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -0.075 \lor \neg \left(a \leq 0.058\right):\\ \;\;\;\;x + \left(\sin z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.075) (not (<= a 0.058)))
   (+ x (- (sin z) (tan a)))
   (+ x (- (tan (+ y z)) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.075) || !(a <= 0.058)) {
		tmp = x + (sin(z) - tan(a));
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-0.075d0)) .or. (.not. (a <= 0.058d0))) then
        tmp = x + (sin(z) - tan(a))
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.075) || !(a <= 0.058)) {
		tmp = x + (Math.sin(z) - Math.tan(a));
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (a <= -0.075) or not (a <= 0.058):
		tmp = x + (math.sin(z) - math.tan(a))
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.075) || !(a <= 0.058))
		tmp = Float64(x + Float64(sin(z) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.075) || ~((a <= 0.058)))
		tmp = x + (sin(z) - tan(a));
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.075], N[Not[LessEqual[a, 0.058]], $MachinePrecision]], N[(x + N[(N[Sin[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.0749999999999999972 or 0.0580000000000000029 < a

   1. Initial program 77.2%

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

      1. +-commutative 77.2%

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

      2. sub-neg 77.2%

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

      3. associate-+l+ 77.1%

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

      4. tan-quot 77.1%

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

      5. div-inv 77.1%

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

      6. fma-define 77.1%

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

      7. neg-mul-1 77.1%

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

      8. fma-define 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. fma-undefine 77.1%

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

      2. fma-undefine 77.1%

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

      3. neg-mul-1 77.1%

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

      4. associate-*r/ 77.1%

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

      5. *-rgt-identity 77.1%

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

      6. +-commutative 77.1%

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

      7. +-commutative 77.1%

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

      8. +-commutative 77.1%

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

      9. sub-neg 77.1%

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

   6. Simplified 77.1%

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

   7. Taylor expanded in z around 0 58.0%

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

   8. Taylor expanded in y around 0 40.0%

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

      1. associate--l+ 40.0%

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

   10. Simplified 40.0%

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

       1. tan-quot 40.1%

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

       2. *-un-lft-identity 40.1%

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

   12. Applied egg-rr 40.1%

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

       1. *-lft-identity 40.1%

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

   14. Simplified 40.1%

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

   if -0.0749999999999999972 < a < 0.0580000000000000029

   1. Initial program 80.0%

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

   3. Taylor expanded in a around 0 79.4%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.075 \lor \neg \left(a \leq 0.058\right):\\ \;\;\;\;x + \left(\sin z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.6 \cdot 10^{-14}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

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 (<= z 5.6e-14) (+ 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 (z <= 5.6e-14) {
		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 (z <= 5.6d-14) 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 (z <= 5.6e-14) {
		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 z <= 5.6e-14:
		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 (z <= 5.6e-14)
		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 (z <= 5.6e-14)
		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[z, 5.6e-14], 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 z < 5.6000000000000001e-14

   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 72.6%

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

   if 5.6000000000000001e-14 < z

   1. Initial program 57.8%

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

   3. Taylor expanded in y around 0 56.6%

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

Alternative 11: 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 78.6%

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

Alternative 12: 50.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin z\\ \end{array} \end{array} \]

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 (<= a -1.9) x (if (<= a 1.55) (+ x (- (tan (+ y z)) a)) (+ x (sin z)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.9) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = x + sin(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 (a <= (-1.9d0)) then
        tmp = x
    else if (a <= 1.55d0) then
        tmp = x + (tan((y + z)) - a)
    else
        tmp = x + sin(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 (a <= -1.9) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = x + Math.sin(z);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.9:
		tmp = x
	elif a <= 1.55:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = x + math.sin(z)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.9)
		tmp = x;
	elseif (a <= 1.55)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = Float64(x + sin(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 (a <= -1.9)
		tmp = x;
	elseif (a <= 1.55)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = x + sin(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[a, -1.9], x, If[LessEqual[a, 1.55], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[z], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.8999999999999999

   1. Initial program 75.8%

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

   3. Taylor expanded in x around inf 22.9%

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

   if -1.8999999999999999 < a < 1.55000000000000004

   1. Initial program 80.0%

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

   3. Taylor expanded in a around 0 79.4%

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

   if 1.55000000000000004 < a

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. sub-neg 78.4%

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

      3. associate-+l+ 78.3%

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

      4. tan-quot 78.3%

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

      5. div-inv 78.3%

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

      6. fma-define 78.3%

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

      7. neg-mul-1 78.3%

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

      8. fma-define 78.3%

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

   4. Applied egg-rr 78.3%

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

      1. fma-undefine 78.3%

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

      2. fma-undefine 78.3%

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

      3. neg-mul-1 78.3%

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

      4. associate-*r/ 78.3%

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

      5. *-rgt-identity 78.3%

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

      6. +-commutative 78.3%

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

      7. +-commutative 78.3%

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

      8. +-commutative 78.3%

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

      9. sub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 58.6%

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

   8. Taylor expanded in y around 0 41.3%

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

      1. associate--l+ 41.3%

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

   10. Simplified 41.3%

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

   11. Taylor expanded in a around 0 21.9%

       \[\leadsto \color{blue}{x + \sin z} \]
   12. Step-by-step derivation

       1. +-commutative 21.9%

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

   13. Simplified 21.9%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin z\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -0.31:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7:\\ \;\;\;\;x + \left(a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin z\\ \end{array} \end{array} \]

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 (<= a -0.31) x (if (<= a 2.7) (+ x (+ a (tan (+ y z)))) (+ x (sin z)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -0.31) {
		tmp = x;
	} else if (a <= 2.7) {
		tmp = x + (a + tan((y + z)));
	} else {
		tmp = x + sin(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 (a <= (-0.31d0)) then
        tmp = x
    else if (a <= 2.7d0) then
        tmp = x + (a + tan((y + z)))
    else
        tmp = x + sin(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 (a <= -0.31) {
		tmp = x;
	} else if (a <= 2.7) {
		tmp = x + (a + Math.tan((y + z)));
	} else {
		tmp = x + Math.sin(z);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -0.31:
		tmp = x
	elif a <= 2.7:
		tmp = x + (a + math.tan((y + z)))
	else:
		tmp = x + math.sin(z)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -0.31)
		tmp = x;
	elseif (a <= 2.7)
		tmp = Float64(x + Float64(a + tan(Float64(y + z))));
	else
		tmp = Float64(x + sin(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 (a <= -0.31)
		tmp = x;
	elseif (a <= 2.7)
		tmp = x + (a + tan((y + z)));
	else
		tmp = x + sin(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[a, -0.31], x, If[LessEqual[a, 2.7], N[(x + N[(a + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[z], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.309999999999999998

   1. Initial program 75.8%

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

   3. Taylor expanded in x around inf 22.9%

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

   if -0.309999999999999998 < a < 2.7000000000000002

   1. Initial program 80.0%

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

   3. Taylor expanded in a around 0 79.4%

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

      1. add-sqr-sqrt 78.8%

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

      2. fma-define 78.9%

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

   5. Applied egg-rr 78.9%

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

      1. fma-undefine 78.8%

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

      2. add-sqr-sqrt 79.4%

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

      3. sub-neg 79.4%

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

      4. add-sqr-sqrt 36.7%

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

      5. sqrt-unprod 78.4%

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

      6. sqr-neg 78.4%

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

      7. sqrt-unprod 41.7%

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

      8. add-sqr-sqrt 78.1%

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

   7. Applied egg-rr 78.1%

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

   if 2.7000000000000002 < a

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. sub-neg 78.4%

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

      3. associate-+l+ 78.3%

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

      4. tan-quot 78.3%

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

      5. div-inv 78.3%

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

      6. fma-define 78.3%

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

      7. neg-mul-1 78.3%

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

      8. fma-define 78.3%

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

   4. Applied egg-rr 78.3%

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

      1. fma-undefine 78.3%

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

      2. fma-undefine 78.3%

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

      3. neg-mul-1 78.3%

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

      4. associate-*r/ 78.3%

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

      5. *-rgt-identity 78.3%

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

      6. +-commutative 78.3%

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

      7. +-commutative 78.3%

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

      8. +-commutative 78.3%

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

      9. sub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 58.6%

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

   8. Taylor expanded in y around 0 41.3%

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

      1. associate--l+ 41.3%

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

   10. Simplified 41.3%

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

   11. Taylor expanded in a around 0 21.9%

       \[\leadsto \color{blue}{x + \sin z} \]
   12. Step-by-step derivation

       1. +-commutative 21.9%

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

   13. Simplified 21.9%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.31:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.7:\\ \;\;\;\;x + \left(a + \tan \left(y + z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin z\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin z\\ \end{array} \end{array} \]

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 (<= a -1.35) x (if (<= a 1.55) (+ x (- (tan y) a)) (+ x (sin z)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.35) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = x + sin(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 (a <= (-1.35d0)) then
        tmp = x
    else if (a <= 1.55d0) then
        tmp = x + (tan(y) - a)
    else
        tmp = x + sin(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 (a <= -1.35) {
		tmp = x;
	} else if (a <= 1.55) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = x + Math.sin(z);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.35:
		tmp = x
	elif a <= 1.55:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = x + math.sin(z)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.35)
		tmp = x;
	elseif (a <= 1.55)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = Float64(x + sin(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 (a <= -1.35)
		tmp = x;
	elseif (a <= 1.55)
		tmp = x + (tan(y) - a);
	else
		tmp = x + sin(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[a, -1.35], x, If[LessEqual[a, 1.55], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[z], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.3500000000000001

   1. Initial program 75.8%

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

   3. Taylor expanded in x around inf 22.9%

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

   if -1.3500000000000001 < a < 1.55000000000000004

   1. Initial program 80.0%

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

   3. Taylor expanded in a around 0 79.4%

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

   4. Taylor expanded in y around inf 60.2%

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

   if 1.55000000000000004 < a

   1. Initial program 78.4%

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

      1. +-commutative 78.4%

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

      2. sub-neg 78.4%

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

      3. associate-+l+ 78.3%

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

      4. tan-quot 78.3%

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

      5. div-inv 78.3%

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

      6. fma-define 78.3%

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

      7. neg-mul-1 78.3%

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

      8. fma-define 78.3%

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

   4. Applied egg-rr 78.3%

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

      1. fma-undefine 78.3%

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

      2. fma-undefine 78.3%

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

      3. neg-mul-1 78.3%

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

      4. associate-*r/ 78.3%

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

      5. *-rgt-identity 78.3%

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

      6. +-commutative 78.3%

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

      7. +-commutative 78.3%

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

      8. +-commutative 78.3%

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

      9. sub-neg 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 58.6%

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

   8. Taylor expanded in y around 0 41.3%

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

      1. associate--l+ 41.3%

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

   10. Simplified 41.3%

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

   11. Taylor expanded in a around 0 21.9%

       \[\leadsto \color{blue}{x + \sin z} \]
   12. Step-by-step derivation

       1. +-commutative 21.9%

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

   13. Simplified 21.9%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.55:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin z\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.7% accurate, 2.0× speedup

Math

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

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 (sin z)))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 78.6%

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

   1. +-commutative 78.6%

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

   2. sub-neg 78.6%

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

   3. associate-+l+ 78.5%

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

   4. tan-quot 78.5%

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

   5. div-inv 78.5%

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

   6. fma-define 78.5%

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

   7. neg-mul-1 78.5%

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

   8. fma-define 78.5%

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

4. Applied egg-rr 78.5%

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

   1. fma-undefine 78.5%

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

   2. fma-undefine 78.5%

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

   3. neg-mul-1 78.5%

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

   4. associate-*r/ 78.5%

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

   5. *-rgt-identity 78.5%

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

   6. +-commutative 78.5%

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

   7. +-commutative 78.5%

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

   8. +-commutative 78.5%

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

   9. sub-neg 78.5%

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

6. Simplified 78.5%

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

7. Taylor expanded in z around 0 59.8%

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

8. Taylor expanded in y around 0 40.4%

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

   1. associate--l+ 40.4%

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

10. Simplified 40.4%

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

11. Taylor expanded in a around 0 30.9%

    \[\leadsto \color{blue}{x + \sin z} \]
12. Step-by-step derivation

    1. +-commutative 30.9%

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

13. Simplified 30.9%

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

14. Final simplification 30.9%

    \[\leadsto x + \sin z \]
15. Add Preprocessing

Alternative 16: 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 78.6%

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

3. Taylor expanded in x around inf 30.5%

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

Reproduce

herbie shell --seed 2024116 
(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))))