tan-example (used to crash)

Percentage Accurate: 79.5% → 99.7%

Time: 47.4s

Alternatives: 18

Speedup: 1.0×

Specification

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

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

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

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

C

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

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(a) + ((tan(y) + tan(z)) * (1.0d0 / ((tan(z) * (sin(y) / cos(y))) + (-1.0d0)))))
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(a) + ((Math.tan(y) + Math.tan(z)) * (1.0 / ((Math.tan(z) * (Math.sin(y) / Math.cos(y))) + -1.0))));
}

Python

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

Julia

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

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp = code(x, y, z, a)
	tmp = x - (tan(a) + ((tan(y) + tan(z)) * (1.0 / ((tan(z) * (sin(y) / cos(y))) + -1.0))));
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[a], $MachinePrecision] + N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(N[Tan[z], $MachinePrecision] * N[(N[Sin[y], $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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. tan-quot 99.7%

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

   2. frac-2neg 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 2: 99.7% accurate, 0.3× speedup

Math

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

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 79.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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. expm1-log1p-u 94.3%

      \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

   2. expm1-undefine 94.3%

      \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\tan y \cdot \tan z\right)} - 1\right)}} - \tan a\right) \]

   3. log1p-undefine 94.2%

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

   4. add-exp-log 99.7%

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

6. Applied egg-rr 99.7%

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

   1. associate--l+ 99.7%

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

   2. fma-neg 99.7%

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

   3. metadata-eval 99.7%

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

8. Simplified 99.7%

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

9. Final simplification 99.7%

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

Alternative 3: 99.7% accurate, 0.3× speedup

Math

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

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 y) (tan z)) (- 1.0 (/ (* (tan z) (sin y)) (cos y)))) (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(z) * sin(y)) / cos(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(y) + tan(z)) / (1.0d0 - ((tan(z) * sin(y)) / cos(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(y) + Math.tan(z)) / (1.0 - ((Math.tan(z) * Math.sin(y)) / Math.cos(y)))) - 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(z) * math.sin(y)) / math.cos(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(y) + tan(z)) / Float64(1.0 - Float64(Float64(tan(z) * sin(y)) / cos(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(y) + tan(z)) / (1.0 - ((tan(z) * sin(y)) / cos(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[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[(N[Tan[z], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision] / N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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. tan-quot 99.7%

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

   2. frac-2neg 99.7%

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

6. Applied egg-rr 99.7%

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

   1. sub-neg 99.7%

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

   2. un-div-inv 99.7%

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

   3. +-commutative 99.7%

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

   4. associate-*l/ 99.7%

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

8. Applied egg-rr 99.7%

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

   1. sub-neg 99.7%

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

   2. sub-neg 99.7%

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

   3. distribute-frac-neg2 99.7%

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

   4. remove-double-neg 99.7%

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

   5. distribute-lft-neg-out 99.7%

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

   6. distribute-rgt-neg-in 99.7%

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

10. Simplified 99.7%

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

11. Final simplification 99.7%

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

Alternative 4: 99.7% accurate, 0.4× speedup

Math

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

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

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x - (tan(a) - ((tan(y) + tan(z)) * (1.0 / (1.0 - (tan(y) * 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(a) - ((tan(y) + tan(z)) * (1.0d0 / (1.0d0 - (tan(y) * 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(a) - ((Math.tan(y) + Math.tan(z)) * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z))))));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 79.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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%

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

Alternative 5: 99.7% accurate, 0.4× speedup

Math

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

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

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	return x - (tan(a) + ((tan(y) + tan(z)) / (-1.0 + (tan(y) * 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(a) + ((tan(y) + tan(z)) / ((-1.0d0) + (tan(y) * 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(a) + ((Math.tan(y) + Math.tan(z)) / (-1.0 + (Math.tan(y) * Math.tan(z)))));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 79.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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%

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

Alternative 6: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-5} \lor \neg \left(a \leq 1.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + \left(t\_0 - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(t\_0 \cdot \frac{1}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= a -1.3e-5) (not (<= a 1.6e-9)))
     (+ x (- t_0 (tan a)))
     (+ x (- (* t_0 (/ 1.0 (- 1.0 (* (tan y) (tan z))))) a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((a <= -1.3e-5) || !(a <= 1.6e-9)) {
		tmp = x + (t_0 - tan(a));
	} else {
		tmp = x + ((t_0 * (1.0 / (1.0 - (tan(y) * tan(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) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((a <= (-1.3d-5)) .or. (.not. (a <= 1.6d-9))) then
        tmp = x + (t_0 - tan(a))
    else
        tmp = x + ((t_0 * (1.0d0 / (1.0d0 - (tan(y) * tan(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 t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if ((a <= -1.3e-5) || !(a <= 1.6e-9)) {
		tmp = x + (t_0 - Math.tan(a));
	} else {
		tmp = x + ((t_0 * (1.0 / (1.0 - (Math.tan(y) * Math.tan(z))))) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (a <= -1.3e-5) or not (a <= 1.6e-9):
		tmp = x + (t_0 - math.tan(a))
	else:
		tmp = x + ((t_0 * (1.0 / (1.0 - (math.tan(y) * math.tan(z))))) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((a <= -1.3e-5) || !(a <= 1.6e-9))
		tmp = Float64(x + Float64(t_0 - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(t_0 * Float64(1.0 / Float64(1.0 - Float64(tan(y) * tan(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)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if ((a <= -1.3e-5) || ~((a <= 1.6e-9)))
		tmp = x + (t_0 - tan(a));
	else
		tmp = x + ((t_0 * (1.0 / (1.0 - (tan(y) * tan(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_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.3e-5], N[Not[LessEqual[a, 1.6e-9]], $MachinePrecision]], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t$95$0 * N[(1.0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.29999999999999992e-5 or 1.60000000000000006e-9 < a

   1. Initial program 79.7%

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

      1. tan-sum 99.6%

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

      2. div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. expm1-log1p-u 93.2%

         \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

      2. expm1-undefine 93.1%

         \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\tan y \cdot \tan z\right)} - 1\right)}} - \tan a\right) \]

      3. log1p-undefine 93.1%

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

      4. add-exp-log 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. associate--l+ 99.6%

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

      2. fma-neg 99.6%

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

      3. metadata-eval 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around 0 80.3%

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

   if -1.29999999999999992e-5 < a < 1.60000000000000006e-9

   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 80.0%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
   4. 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 99.8%

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

   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 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-5} \lor \neg \left(a \leq 1.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} t_0 := \tan y + \tan z\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{-5} \lor \neg \left(a \leq 1.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + \left(t\_0 - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t\_0}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (+ (tan y) (tan z))))
   (if (or (<= a -1.3e-5) (not (<= a 1.6e-9)))
     (+ x (- t_0 (tan a)))
     (+ x (- (/ t_0 (- 1.0 (* (tan y) (tan z)))) a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double t_0 = tan(y) + tan(z);
	double tmp;
	if ((a <= -1.3e-5) || !(a <= 1.6e-9)) {
		tmp = x + (t_0 - tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(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) :: t_0
    real(8) :: tmp
    t_0 = tan(y) + tan(z)
    if ((a <= (-1.3d-5)) .or. (.not. (a <= 1.6d-9))) then
        tmp = x + (t_0 - tan(a))
    else
        tmp = x + ((t_0 / (1.0d0 - (tan(y) * tan(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 t_0 = Math.tan(y) + Math.tan(z);
	double tmp;
	if ((a <= -1.3e-5) || !(a <= 1.6e-9)) {
		tmp = x + (t_0 - Math.tan(a));
	} else {
		tmp = x + ((t_0 / (1.0 - (Math.tan(y) * Math.tan(z)))) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	t_0 = math.tan(y) + math.tan(z)
	tmp = 0
	if (a <= -1.3e-5) or not (a <= 1.6e-9):
		tmp = x + (t_0 - math.tan(a))
	else:
		tmp = x + ((t_0 / (1.0 - (math.tan(y) * math.tan(z)))) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	t_0 = Float64(tan(y) + tan(z))
	tmp = 0.0
	if ((a <= -1.3e-5) || !(a <= 1.6e-9))
		tmp = Float64(x + Float64(t_0 - tan(a)));
	else
		tmp = Float64(x + Float64(Float64(t_0 / Float64(1.0 - Float64(tan(y) * tan(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)
	t_0 = tan(y) + tan(z);
	tmp = 0.0;
	if ((a <= -1.3e-5) || ~((a <= 1.6e-9)))
		tmp = x + (t_0 - tan(a));
	else
		tmp = x + ((t_0 / (1.0 - (tan(y) * tan(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_] := Block[{t$95$0 = N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.3e-5], N[Not[LessEqual[a, 1.6e-9]], $MachinePrecision]], N[(x + N[(t$95$0 - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t$95$0 / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.29999999999999992e-5 or 1.60000000000000006e-9 < a

   1. Initial program 79.7%

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

      1. tan-sum 99.6%

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

      2. div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

      1. expm1-log1p-u 93.2%

         \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

      2. expm1-undefine 93.1%

         \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\tan y \cdot \tan z\right)} - 1\right)}} - \tan a\right) \]

      3. log1p-undefine 93.1%

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

      4. add-exp-log 99.6%

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

   6. Applied egg-rr 99.6%

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

      1. associate--l+ 99.6%

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

      2. fma-neg 99.6%

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

      3. metadata-eval 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around 0 80.3%

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

   if -1.29999999999999992e-5 < a < 1.60000000000000006e-9

   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 80.0%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{a}\right) \]
   4. 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 99.8%

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

   5. Applied egg-rr 99.8%

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

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

   7. Simplified 99.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-5} \lor \neg \left(a \leq 1.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + \left(\left(\tan y + \tan z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \end{array} \]

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) 2e-9)))
   (+ 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) <= 2e-9)) {
		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) <= 2d-9))) 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) <= 2e-9)) {
		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) <= 2e-9):
		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) <= 2e-9))
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(Float64(x + 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) <= 2e-9)))
		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], 2e-9]], $MachinePrecision]], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (tan.f64 a) < -1e-3 or 2.00000000000000012e-9 < (tan.f64 a)

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 58.5%

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

   if -1e-3 < (tan.f64 a) < 2.00000000000000012e-9

   1. Initial program 80.3%

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

   3. Taylor expanded in a around 0 80.2%

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

      1. associate-+r- 80.2%

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

   5. Applied egg-rr 80.2%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\tan a \leq -0.001 \lor \neg \left(\tan a \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 79.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

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

3. Taylor expanded in a around inf 79.9%

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

Alternative 10: 79.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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. expm1-log1p-u 94.3%

      \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\tan y \cdot \tan z\right)\right)}} - \tan a\right) \]

   2. expm1-undefine 94.3%

      \[\leadsto x + \left(\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \color{blue}{\left(e^{\mathsf{log1p}\left(\tan y \cdot \tan z\right)} - 1\right)}} - \tan a\right) \]

   3. log1p-undefine 94.2%

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

   4. add-exp-log 99.7%

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

6. Applied egg-rr 99.7%

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

   1. associate--l+ 99.7%

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

   2. fma-neg 99.7%

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

   3. metadata-eval 99.7%

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

8. Simplified 99.7%

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

9. Taylor expanded in y around 0 80.2%

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

10. Final simplification 80.2%

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

Alternative 11: 79.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -5 \cdot 10^{-12}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -5e-12) (+ x (- (tan y) (tan a))) (+ x (- (tan z) (tan a)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -5e-12) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y + z) <= (-5d-12)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -5e-12) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -5e-12:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -5e-12)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -5e-12)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -5e-12], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < -4.9999999999999997e-12

   1. Initial program 76.3%

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

   3. Taylor expanded in y around inf 49.2%

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

   if -4.9999999999999997e-12 < (+.f64 y z)

   1. Initial program 82.6%

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

   3. Taylor expanded in y around 0 69.0%

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

Alternative 12: 79.5% accurate, 1.0× speedup

Math

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

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 (- (tan (+ -1.0 (+ 1.0 (+ 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((-1.0 + (1.0 + (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(((-1.0d0) + (1.0d0 + (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((-1.0 + (1.0 + (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((-1.0 + (1.0 + (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(-1.0 + Float64(1.0 + 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((-1.0 + (1.0 + (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[(-1.0 + N[(1.0 + N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.9%

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

   1. expm1-log1p-u 32.1%

      \[\leadsto x + \left(\tan \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(y + z\right)\right)\right)} - \tan a\right) \]

   2. expm1-undefine 32.1%

      \[\leadsto x + \left(\tan \color{blue}{\left(e^{\mathsf{log1p}\left(y + z\right)} - 1\right)} - \tan a\right) \]

4. Applied egg-rr 32.1%

   \[\leadsto x + \left(\tan \color{blue}{\left(e^{\mathsf{log1p}\left(y + z\right)} - 1\right)} - \tan a\right) \]
5. Step-by-step derivation

   1. expm1-define 32.1%

      \[\leadsto x + \left(\tan \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(y + z\right)\right)\right)} - \tan a\right) \]

   2. +-commutative 32.1%

      \[\leadsto x + \left(\tan \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{z + y}\right)\right)\right) - \tan a\right) \]

6. Simplified 32.1%

   \[\leadsto x + \left(\tan \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(z + y\right)\right)\right)} - \tan a\right) \]
7. Step-by-step derivation

   1. expm1-undefine 32.1%

      \[\leadsto x + \left(\tan \color{blue}{\left(e^{\mathsf{log1p}\left(z + y\right)} - 1\right)} - \tan a\right) \]

   2. log1p-expm1-u 32.1%

      \[\leadsto x + \left(\tan \left(e^{\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\mathsf{log1p}\left(z + y\right)\right)\right)}} - 1\right) - \tan a\right) \]

   3. log1p-undefine 32.1%

      \[\leadsto x + \left(\tan \left(e^{\color{blue}{\log \left(1 + \mathsf{expm1}\left(\mathsf{log1p}\left(z + y\right)\right)\right)}} - 1\right) - \tan a\right) \]

   4. rem-exp-log 32.1%

      \[\leadsto x + \left(\tan \left(\color{blue}{\left(1 + \mathsf{expm1}\left(\mathsf{log1p}\left(z + y\right)\right)\right)} - 1\right) - \tan a\right) \]

   5. expm1-log1p-u 79.9%

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

   6. +-commutative 79.9%

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

8. Applied egg-rr 79.9%

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

9. Final simplification 79.9%

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

Alternative 13: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.9%

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

Alternative 14: 50.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.56:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 11:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.56) x (if (<= a 11.0) (- (+ x (tan (+ y z))) a) x)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.56) {
		tmp = x;
	} else if (a <= 11.0) {
		tmp = (x + tan((y + z))) - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.56d0)) then
        tmp = x
    else if (a <= 11.0d0) then
        tmp = (x + tan((y + z))) - a
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.56) {
		tmp = x;
	} else if (a <= 11.0) {
		tmp = (x + Math.tan((y + z))) - a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.56:
		tmp = x
	elif a <= 11.0:
		tmp = (x + math.tan((y + z))) - a
	else:
		tmp = x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.56)
		tmp = x;
	elseif (a <= 11.0)
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.56)
		tmp = x;
	elseif (a <= 11.0)
		tmp = (x + tan((y + z))) - a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -1.56], x, If[LessEqual[a, 11.0], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5600000000000001 or 11 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 20.6%

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

   if -1.5600000000000001 < a < 11

   1. Initial program 80.4%

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

   3. Taylor expanded in a around 0 80.2%

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

      1. associate-+r- 80.2%

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

   5. Applied egg-rr 80.2%

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

Alternative 15: 50.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -2:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 11:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -2.0) x (if (<= a 11.0) (+ x (- (tan (+ y z)) a)) x)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.0) {
		tmp = x;
	} else if (a <= 11.0) {
		tmp = x + (tan((y + z)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.0d0)) then
        tmp = x
    else if (a <= 11.0d0) then
        tmp = x + (tan((y + z)) - a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -2.0) {
		tmp = x;
	} else if (a <= 11.0) {
		tmp = x + (Math.tan((y + z)) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -2.0:
		tmp = x
	elif a <= 11.0:
		tmp = x + (math.tan((y + z)) - a)
	else:
		tmp = x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -2.0)
		tmp = x;
	elseif (a <= 11.0)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -2.0)
		tmp = x;
	elseif (a <= 11.0)
		tmp = x + (tan((y + z)) - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -2.0], x, If[LessEqual[a, 11.0], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2 or 11 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in x around inf 20.6%

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

   if -2 < a < 11

   1. Initial program 80.4%

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

   3. Taylor expanded in a around 0 80.2%

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

Alternative 16: 40.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -1.56:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= a -1.56) x (if (<= a 1.6e-9) (+ x (- (tan y) a)) x)))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.56) {
		tmp = x;
	} else if (a <= 1.6e-9) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.56d0)) then
        tmp = x
    else if (a <= 1.6d-9) then
        tmp = x + (tan(y) - a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (a <= -1.56) {
		tmp = x;
	} else if (a <= 1.6e-9) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if a <= -1.56:
		tmp = x
	elif a <= 1.6e-9:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = x
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (a <= -1.56)
		tmp = x;
	elseif (a <= 1.6e-9)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (a <= -1.56)
		tmp = x;
	elseif (a <= 1.6e-9)
		tmp = x + (tan(y) - a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[a, -1.56], x, If[LessEqual[a, 1.6e-9], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.5600000000000001 or 1.60000000000000006e-9 < a

   1. Initial program 79.4%

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

   3. Taylor expanded in x around inf 20.6%

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

   if -1.5600000000000001 < a < 1.60000000000000006e-9

   1. Initial program 80.3%

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

   3. Taylor expanded in a around 0 80.1%

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

   4. Taylor expanded in y around inf 60.1%

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

Alternative 17: 41.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-17}:\\ \;\;\;\;x + \left(\tan y - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - a\right)\\ \end{array} \end{array} \]

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 1e-17) (+ x (- (tan y) a)) (+ x (- (tan z) a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (z <= 1e-17) {
		tmp = x + (tan(y) - a);
	} else {
		tmp = x + (tan(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 (z <= 1d-17) then
        tmp = x + (tan(y) - a)
    else
        tmp = x + (tan(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 (z <= 1e-17) {
		tmp = x + (Math.tan(y) - a);
	} else {
		tmp = x + (Math.tan(z) - a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if z <= 1e-17:
		tmp = x + (math.tan(y) - a)
	else:
		tmp = x + (math.tan(z) - a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (z <= 1e-17)
		tmp = Float64(x + Float64(tan(y) - a));
	else
		tmp = Float64(x + Float64(tan(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 (z <= 1e-17)
		tmp = x + (tan(y) - a);
	else
		tmp = x + (tan(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[LessEqual[z, 1e-17], N[(x + N[(N[Tan[y], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.00000000000000007e-17

   1. Initial program 84.9%

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

   3. Taylor expanded in a around 0 48.0%

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

   4. Taylor expanded in y around inf 39.4%

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

   if 1.00000000000000007e-17 < z

   1. Initial program 63.3%

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

   3. Taylor expanded in a around 0 31.5%

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

   4. Taylor expanded in y around 0 31.2%

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

Alternative 18: 31.6% 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 79.9%

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

3. Taylor expanded in x around inf 30.1%

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

Reproduce

herbie shell --seed 2024110 
(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))))