tan-example (used to crash)

Percentage Accurate: 79.3% → 99.7%

Time: 6.2s

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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, 0.2× speedup

Math

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

FPCore

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) / (1.0d0 - (tan(y) * tan(z)))) + (tan(z) / (1.0d0 - (sin(y) * (sin(z) / (cos(z) * 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) / (1.0 - (Math.tan(y) * Math.tan(z)))) + (Math.tan(z) / (1.0 - (Math.sin(y) * (Math.sin(z) / (Math.cos(z) * 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) / (1.0 - (math.tan(y) * math.tan(z)))) + (math.tan(z) / (1.0 - (math.sin(y) * (math.sin(z) / (math.cos(z) * 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) / Float64(1.0 - Float64(tan(y) * tan(z)))) + Float64(tan(z) / Float64(1.0 - Float64(sin(y) * Float64(sin(z) / Float64(cos(z) * 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) / (1.0 - (tan(y) * tan(z)))) + (tan(z) / (1.0 - (sin(y) * (sin(z) / (cos(z) * 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[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Tan[z], $MachinePrecision] / N[(1.0 - N[(N[Sin[y], $MachinePrecision] * N[(N[Sin[z], $MachinePrecision] / N[(N[Cos[z], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.3%

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

   1. lift-+.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. tan-sum N/A

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

   4. quot-tan N/A

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

   5. quot-tan N/A

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

   6. div-add N/A

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

   7. lower-+.f64 N/A

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

4. Applied rewrites 99.7%

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

   1. lift-*.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. lift-tan.f64 N/A

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

   4. tan-quot N/A

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

   5. tan-quot N/A

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

   6. times-frac N/A

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

   7. associate-/l* N/A

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

   8. lower-*.f64 N/A

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

   9. lower-sin.f64 N/A

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

   10. lower-/.f64 N/A

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

   11. lower-sin.f64 N/A

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

   12. *-commutative N/A

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

   13. lower-*.f64 N/A

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

   14. lower-cos.f64 N/A

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

   15. lower-cos.f64 99.7

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

6. Applied rewrites 99.7%

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

Alternative 2: 99.7% accurate, 0.2× speedup

Math

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

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

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) / (1.0d0 - (tan(y) * (sin(z) / cos(z))))) + (tan(z) / (1.0d0 - (tan(y) * tan(z))))) - tan(a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

   1. lift-+.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. tan-sum N/A

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

   4. quot-tan N/A

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

   5. quot-tan N/A

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

   6. div-add N/A

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

   7. lower-+.f64 N/A

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

4. Applied rewrites 99.7%

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

   1. lift-tan.f64 N/A

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

   2. tan-quot N/A

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

   3. lower-/.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. lower-cos.f64 99.7

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

6. Applied rewrites 99.7%

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

Alternative 3: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.05:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \mathsf{fma}\left(a \cdot a, 0.3333333333333333, 1\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} - \tan a\right)\\ \end{array} \end{array} \]

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 (<= (tan a) -0.05)
   (+ x (- (tan (+ y z)) (tan a)))
   (if (<= (tan a) 2e-5)
     (+
      x
      (-
       (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y))))
       (* (fma (* a a) 0.3333333333333333 1.0) a)))
     (+ x (- (/ (sin (+ z y)) (cos (+ z y))) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.05) {
		tmp = x + (tan((y + z)) - tan(a));
	} else if (tan(a) <= 2e-5) {
		tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - (fma((a * a), 0.3333333333333333, 1.0) * a));
	} else {
		tmp = x + ((sin((z + y)) / cos((z + y))) - tan(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) <= -0.05)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	elseif (tan(a) <= 2e-5)
		tmp = Float64(x + Float64(Float64(Float64(tan(z) + tan(y)) / Float64(1.0 - Float64(tan(z) * tan(y)))) - Float64(fma(Float64(a * a), 0.3333333333333333, 1.0) * a)));
	else
		tmp = Float64(x + Float64(Float64(sin(Float64(z + y)) / cos(Float64(z + y))) - tan(a)));
	end
	return 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[Tan[a], $MachinePrecision], -0.05], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 2e-5], 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[(N[(N[(a * a), $MachinePrecision] * 0.3333333333333333 + 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[Sin[N[(z + y), $MachinePrecision]], $MachinePrecision] / N[Cos[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.050000000000000003

   1. Initial program 83.6%

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

   if -0.050000000000000003 < (tan.f64 a) < 2.00000000000000016e-5

   1. Initial program 74.8%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. +-commutative N/A

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

      4. tan-sum N/A

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

      5. lower-/.f64 N/A

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

      6. quot-tan N/A

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

      7. quot-tan N/A

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

      8. lower-+.f64 N/A

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

      9. quot-tan N/A

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

      10. lower-tan.f64 N/A

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

      11. quot-tan N/A

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

      12. lower-tan.f64 N/A

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

      13. lower--.f64 N/A

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

      14. quot-tan N/A

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

      15. quot-tan N/A

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

      16. lower-*.f64 N/A

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

      17. quot-tan N/A

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

      18. lower-tan.f64 N/A

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

      19. quot-tan N/A

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

      20. lower-tan.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

      \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \color{blue}{a \cdot \left(1 + \frac{1}{3} \cdot {a}^{2}\right)}\right) \]
   6. Step-by-step derivation

      1. tan-quot N/A

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \color{blue}{a} \cdot \left(1 + \frac{1}{3} \cdot {a}^{2}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \left(1 + \frac{1}{3} \cdot {a}^{2}\right) \cdot \color{blue}{a}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \left(1 + \frac{1}{3} \cdot {a}^{2}\right) \cdot \color{blue}{a}\right) \]

      4. +-commutative N/A

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \left(\frac{1}{3} \cdot {a}^{2} + 1\right) \cdot a\right) \]

      5. *-commutative N/A

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \left({a}^{2} \cdot \frac{1}{3} + 1\right) \cdot a\right) \]

      6. lower-fma.f64 N/A

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

      7. unpow2 N/A

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \mathsf{fma}\left(a \cdot a, \frac{1}{3}, 1\right) \cdot a\right) \]

      8. lower-*.f64 99.7

         \[\leadsto x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - \mathsf{fma}\left(a \cdot a, 0.3333333333333333, 1\right) \cdot a\right) \]

   7. Applied rewrites 99.7%

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

   if 2.00000000000000016e-5 < (tan.f64 a)

   1. Initial program 83.5%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-quot N/A

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

      4. lower-/.f64 N/A

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

      5. lower-sin.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-cos.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 83.6

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

   4. Applied rewrites 83.6%

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

Alternative 4: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.05:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x + \left(\frac{\tan z + \tan y}{1 - \tan z \cdot \tan y} - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} - \tan a\right)\\ \end{array} \end{array} \]

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 (<= (tan a) -0.05)
   (+ x (- (tan (+ y z)) (tan a)))
   (if (<= (tan a) 2e-5)
     (+ x (- (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y)))) a))
     (+ x (- (/ (sin (+ z y)) (cos (+ z y))) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.05) {
		tmp = x + (tan((y + z)) - tan(a));
	} else if (tan(a) <= 2e-5) {
		tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - a);
	} else {
		tmp = x + ((sin((z + y)) / cos((z + y))) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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) <= (-0.05d0)) then
        tmp = x + (tan((y + z)) - tan(a))
    else if (tan(a) <= 2d-5) then
        tmp = x + (((tan(z) + tan(y)) / (1.0d0 - (tan(z) * tan(y)))) - a)
    else
        tmp = x + ((sin((z + y)) / cos((z + y))) - 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 (Math.tan(a) <= -0.05) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else if (Math.tan(a) <= 2e-5) {
		tmp = x + (((Math.tan(z) + Math.tan(y)) / (1.0 - (Math.tan(z) * Math.tan(y)))) - a);
	} else {
		tmp = x + ((Math.sin((z + y)) / Math.cos((z + y))) - Math.tan(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) <= -0.05:
		tmp = x + (math.tan((y + z)) - math.tan(a))
	elif math.tan(a) <= 2e-5:
		tmp = x + (((math.tan(z) + math.tan(y)) / (1.0 - (math.tan(z) * math.tan(y)))) - a)
	else:
		tmp = x + ((math.sin((z + y)) / math.cos((z + y))) - 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 (tan(a) <= -0.05)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	elseif (tan(a) <= 2e-5)
		tmp = Float64(x + Float64(Float64(Float64(tan(z) + tan(y)) / Float64(1.0 - Float64(tan(z) * tan(y)))) - a));
	else
		tmp = Float64(x + Float64(Float64(sin(Float64(z + y)) / cos(Float64(z + y))) - 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 (tan(a) <= -0.05)
		tmp = x + (tan((y + z)) - tan(a));
	elseif (tan(a) <= 2e-5)
		tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - a);
	else
		tmp = x + ((sin((z + y)) / cos((z + y))) - 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[Tan[a], $MachinePrecision], -0.05], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 2e-5], 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], N[(x + N[(N[(N[Sin[N[(z + y), $MachinePrecision]], $MachinePrecision] / N[Cos[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.050000000000000003

   1. Initial program 83.6%

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

   if -0.050000000000000003 < (tan.f64 a) < 2.00000000000000016e-5

   1. Initial program 74.8%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. +-commutative N/A

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

      4. tan-sum N/A

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

      5. lower-/.f64 N/A

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

      6. quot-tan N/A

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

      7. quot-tan N/A

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

      8. lower-+.f64 N/A

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

      9. quot-tan N/A

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

      10. lower-tan.f64 N/A

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

      11. quot-tan N/A

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

      12. lower-tan.f64 N/A

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

      13. lower--.f64 N/A

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

      14. quot-tan N/A

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

      15. quot-tan N/A

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

      16. lower-*.f64 N/A

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

      17. quot-tan N/A

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

      18. lower-tan.f64 N/A

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

      19. quot-tan N/A

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

      20. lower-tan.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

      1. tan-quot 99.7

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

   7. Applied rewrites 99.7%

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

   if 2.00000000000000016e-5 < (tan.f64 a)

   1. Initial program 83.5%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-quot N/A

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

      4. lower-/.f64 N/A

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

      5. lower-sin.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-cos.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 83.6

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

   4. Applied rewrites 83.6%

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

Alternative 5: 99.7% accurate, 0.3× speedup

Math

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

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
  (- (/ (+ (/ (sin z) (cos 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 + ((((sin(z) / cos(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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((((sin(z) / cos(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.sin(z) / Math.cos(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.sin(z) / math.cos(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(Float64(sin(z) / cos(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 + ((((sin(z) / cos(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[(N[Sin[z], $MachinePrecision] / N[Cos[z], $MachinePrecision]), $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 79.3%

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

   1. lift-+.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. +-commutative N/A

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

   4. tan-sum N/A

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

   5. lower-/.f64 N/A

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

   6. quot-tan N/A

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

   7. quot-tan N/A

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

   8. lower-+.f64 N/A

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

   9. quot-tan N/A

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

   10. lower-tan.f64 N/A

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

   11. quot-tan N/A

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

   12. lower-tan.f64 N/A

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

   13. lower--.f64 N/A

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

   14. quot-tan N/A

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

   15. quot-tan N/A

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

   16. lower-*.f64 N/A

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

   17. quot-tan N/A

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

   18. lower-tan.f64 N/A

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

   19. quot-tan N/A

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

   20. lower-tan.f64 99.6

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

4. Applied rewrites 99.6%

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

   1. lift-tan.f64 N/A

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

   2. tan-quot N/A

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

   3. lower-/.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. lower-cos.f64 99.6

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

6. Applied rewrites 99.6%

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

Alternative 6: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;\tan a \leq -0.05:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \tan a\right)\\ \mathbf{elif}\;\tan a \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{\tan z + \tan y}{1 - \tan z \cdot \tan y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{\sin \left(z + y\right)}{\cos \left(z + y\right)} - \tan a\right)\\ \end{array} \end{array} \]

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 (<= (tan a) -0.05)
   (+ x (- (tan (+ y z)) (tan a)))
   (if (<= (tan a) 2e-5)
     (+ x (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y)))))
     (+ x (- (/ (sin (+ z y)) (cos (+ z y))) (tan a))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (tan(a) <= -0.05) {
		tmp = x + (tan((y + z)) - tan(a));
	} else if (tan(a) <= 2e-5) {
		tmp = x + ((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y))));
	} else {
		tmp = x + ((sin((z + y)) / cos((z + y))) - tan(a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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) <= (-0.05d0)) then
        tmp = x + (tan((y + z)) - tan(a))
    else if (tan(a) <= 2d-5) then
        tmp = x + ((tan(z) + tan(y)) / (1.0d0 - (tan(z) * tan(y))))
    else
        tmp = x + ((sin((z + y)) / cos((z + y))) - 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 (Math.tan(a) <= -0.05) {
		tmp = x + (Math.tan((y + z)) - Math.tan(a));
	} else if (Math.tan(a) <= 2e-5) {
		tmp = x + ((Math.tan(z) + Math.tan(y)) / (1.0 - (Math.tan(z) * Math.tan(y))));
	} else {
		tmp = x + ((Math.sin((z + y)) / Math.cos((z + y))) - Math.tan(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) <= -0.05:
		tmp = x + (math.tan((y + z)) - math.tan(a))
	elif math.tan(a) <= 2e-5:
		tmp = x + ((math.tan(z) + math.tan(y)) / (1.0 - (math.tan(z) * math.tan(y))))
	else:
		tmp = x + ((math.sin((z + y)) / math.cos((z + y))) - 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 (tan(a) <= -0.05)
		tmp = Float64(x + Float64(tan(Float64(y + z)) - tan(a)));
	elseif (tan(a) <= 2e-5)
		tmp = Float64(x + Float64(Float64(tan(z) + tan(y)) / Float64(1.0 - Float64(tan(z) * tan(y)))));
	else
		tmp = Float64(x + Float64(Float64(sin(Float64(z + y)) / cos(Float64(z + y))) - 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 (tan(a) <= -0.05)
		tmp = x + (tan((y + z)) - tan(a));
	elseif (tan(a) <= 2e-5)
		tmp = x + ((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y))));
	else
		tmp = x + ((sin((z + y)) / cos((z + y))) - 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[Tan[a], $MachinePrecision], -0.05], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Tan[a], $MachinePrecision], 2e-5], N[(x + 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]), $MachinePrecision], N[(x + N[(N[(N[Sin[N[(z + y), $MachinePrecision]], $MachinePrecision] / N[Cos[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (tan.f64 a) < -0.050000000000000003

   1. Initial program 83.6%

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

   if -0.050000000000000003 < (tan.f64 a) < 2.00000000000000016e-5

   1. Initial program 74.8%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-sum N/A

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

      4. quot-tan N/A

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

      5. quot-tan N/A

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

      6. div-add N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 74.8%

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

      1. lift-+.f64 N/A

         \[\leadsto x + \tan \left(z + y\right) \]

      2. lift-tan.f64 N/A

         \[\leadsto x + \tan \left(z + y\right) \]

      3. tan-sum-rev N/A

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

      4. lower-/.f64 N/A

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

      5. tan-quot N/A

         \[\leadsto x + \frac{\frac{\sin z}{\cos z} + \tan y}{1 - \tan z \cdot \tan y} \]

      6. tan-quot N/A

         \[\leadsto x + \frac{\frac{\sin z}{\cos z} + \frac{\sin y}{\cos y}}{1 - \tan z \cdot \tan y} \]

      7. lower-+.f64 N/A

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

      8. tan-quot N/A

         \[\leadsto x + \frac{\tan z + \frac{\sin y}{\cos y}}{1 - \tan z \cdot \tan y} \]

      9. lift-tan.f64 N/A

         \[\leadsto x + \frac{\tan z + \frac{\sin y}{\cos y}}{1 - \tan z \cdot \tan y} \]

      10. tan-quot N/A

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

      11. lift-tan.f64 N/A

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

      12. lift-tan.f64 N/A

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

      13. lift-tan.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. lift--.f64 99.1

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

   9. Applied rewrites 99.1%

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

   if 2.00000000000000016e-5 < (tan.f64 a)

   1. Initial program 83.5%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-quot N/A

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

      4. lower-/.f64 N/A

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

      5. lower-sin.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-cos.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 83.6

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

   4. Applied rewrites 83.6%

      \[\leadsto x + \left(\color{blue}{\frac{\sin \left(z + y\right)}{\cos \left(z + y\right)}} - \tan a\right) \]
3. Recombined 3 regimes into one program.
4. 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 79.3%

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

   1. lift-+.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. +-commutative N/A

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

   4. tan-sum N/A

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

   5. lower-/.f64 N/A

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

   6. quot-tan N/A

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

   7. quot-tan N/A

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

   8. lower-+.f64 N/A

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

   9. quot-tan N/A

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

   10. lower-tan.f64 N/A

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

   11. quot-tan N/A

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

   12. lower-tan.f64 N/A

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

   13. lower--.f64 N/A

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

   14. quot-tan N/A

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

   15. quot-tan N/A

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

   16. lower-*.f64 N/A

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

   17. quot-tan N/A

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

   18. lower-tan.f64 N/A

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

   19. quot-tan N/A

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

   20. lower-tan.f64 99.6

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

4. Applied rewrites 99.6%

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

Alternative 8: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\left(\tan y + x\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \end{array} \]

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-7) (- (+ (tan y) x) (tan a)) (+ x (tan (+ z y)))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 5e-7) {
		tmp = (tan(y) + x) - tan(a);
	} else {
		tmp = x + tan((z + y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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-7) then
        tmp = (tan(y) + x) - tan(a)
    else
        tmp = x + tan((z + y))
    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-7) {
		tmp = (Math.tan(y) + x) - Math.tan(a);
	} else {
		tmp = x + Math.tan((z + y));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= 5e-7:
		tmp = (math.tan(y) + x) - math.tan(a)
	else:
		tmp = x + math.tan((z + y))
	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-7)
		tmp = Float64(Float64(tan(y) + x) - tan(a));
	else
		tmp = Float64(x + tan(Float64(z + y)));
	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-7)
		tmp = (tan(y) + x) - tan(a);
	else
		tmp = x + tan((z + y));
	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-7], N[(N[(N[Tan[y], $MachinePrecision] + x), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < 4.99999999999999977e-7

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. quot-tan N/A

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

      5. lower-tan.f64 N/A

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

      6. tan-quot N/A

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

      7. lift-tan.f64 72.8

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

   5. Applied rewrites 72.8%

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

   if 4.99999999999999977e-7 < (+.f64 y z)

   1. Initial program 71.3%

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

   3. Taylor expanded in a around 0

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

      1. tan-quot N/A

         \[\leadsto x + \tan \left(y + z\right) \]

      2. lift-tan.f64 N/A

         \[\leadsto x + \tan \left(y + z\right) \]

      3. +-commutative N/A

         \[\leadsto x + \tan \left(z + y\right) \]

      4. lower-+.f64 41.4

         \[\leadsto x + \tan \left(z + y\right) \]

   5. Applied rewrites 41.4%

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

Alternative 9: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

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 -7.5e-11) (+ 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 <= -7.5e-11) {
		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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 <= (-7.5d-11)) 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 <= -7.5e-11) {
		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 <= -7.5e-11:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -7.5e-11)
		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 <= -7.5e-11)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -7.5e-11], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e-11

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 61.1%

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

   if -7.5e-11 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 72.2%

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

Alternative 10: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\tan z + x\right) - \tan a\\ \end{array} \end{array} \]

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 (<= y -7.5e-11) (+ x (- (tan y) (tan a))) (- (+ (tan z) x) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -7.5e-11) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = (tan(z) + x) - tan(a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 <= (-7.5d-11)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = (tan(z) + x) - tan(a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -7.5e-11) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = (Math.tan(z) + x) - Math.tan(a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if y <= -7.5e-11:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = (math.tan(z) + x) - math.tan(a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -7.5e-11)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(Float64(tan(z) + x) - tan(a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -7.5e-11)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = (tan(z) + x) - tan(a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -7.5e-11], N[(x + N[(N[Tan[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Tan[z], $MachinePrecision] + x), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e-11

   1. Initial program 61.6%

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

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 61.1%

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

   if -7.5e-11 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. quot-tan N/A

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

      5. lower-tan.f64 N/A

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

      6. tan-quot N/A

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

      7. lift-tan.f64 72.1

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

   5. Applied rewrites 72.1%

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

Alternative 11: 79.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-11}:\\ \;\;\;\;\left(\tan y + x\right) - \tan a\\ \mathbf{else}:\\ \;\;\;\;\left(\tan z + x\right) - \tan a\\ \end{array} \end{array} \]

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 (<= y -7.5e-11) (- (+ (tan y) x) (tan a)) (- (+ (tan z) x) (tan a))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -7.5e-11) {
		tmp = (tan(y) + x) - tan(a);
	} else {
		tmp = (tan(z) + x) - tan(a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 <= (-7.5d-11)) then
        tmp = (tan(y) + x) - tan(a)
    else
        tmp = (tan(z) + x) - tan(a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -7.5e-11) {
		tmp = (Math.tan(y) + x) - Math.tan(a);
	} else {
		tmp = (Math.tan(z) + x) - Math.tan(a);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if y <= -7.5e-11:
		tmp = (math.tan(y) + x) - math.tan(a)
	else:
		tmp = (math.tan(z) + x) - math.tan(a)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -7.5e-11)
		tmp = Float64(Float64(tan(y) + x) - tan(a));
	else
		tmp = Float64(Float64(tan(z) + x) - tan(a));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -7.5e-11)
		tmp = (tan(y) + x) - tan(a);
	else
		tmp = (tan(z) + x) - tan(a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -7.5e-11], N[(N[(N[Tan[y], $MachinePrecision] + x), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(N[(N[Tan[z], $MachinePrecision] + x), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e-11

   1. Initial program 61.6%

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

   3. Taylor expanded in z around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. quot-tan N/A

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

      5. lower-tan.f64 N/A

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

      6. tan-quot N/A

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

      7. lift-tan.f64 61.0

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

   5. Applied rewrites 61.0%

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

   if -7.5e-11 < y

   1. Initial program 86.4%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. quot-tan N/A

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

      5. lower-tan.f64 N/A

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

      6. tan-quot N/A

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

      7. lift-tan.f64 72.1

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

   5. Applied rewrites 72.1%

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

Alternative 12: 79.3% 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 79.3%

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

Alternative 13: 59.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -1000000:\\ \;\;\;\;x + \tan y\\ \mathbf{elif}\;y + z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x + \left(\left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \end{array} \]

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) -1000000.0)
   (+ x (tan y))
   (if (<= (+ y z) 5e-7) (+ x (- (+ y z) (tan a))) (+ x (tan (+ z y))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -1000000.0) {
		tmp = x + tan(y);
	} else if ((y + z) <= 5e-7) {
		tmp = x + ((y + z) - tan(a));
	} else {
		tmp = x + tan((z + y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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) <= (-1000000.0d0)) then
        tmp = x + tan(y)
    else if ((y + z) <= 5d-7) then
        tmp = x + ((y + z) - tan(a))
    else
        tmp = x + tan((z + y))
    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) <= -1000000.0) {
		tmp = x + Math.tan(y);
	} else if ((y + z) <= 5e-7) {
		tmp = x + ((y + z) - Math.tan(a));
	} else {
		tmp = x + Math.tan((z + y));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -1000000.0:
		tmp = x + math.tan(y)
	elif (y + z) <= 5e-7:
		tmp = x + ((y + z) - math.tan(a))
	else:
		tmp = x + math.tan((z + y))
	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) <= -1000000.0)
		tmp = Float64(x + tan(y));
	elseif (Float64(y + z) <= 5e-7)
		tmp = Float64(x + Float64(Float64(y + z) - tan(a)));
	else
		tmp = Float64(x + tan(Float64(z + y)));
	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) <= -1000000.0)
		tmp = x + tan(y);
	elseif ((y + z) <= 5e-7)
		tmp = x + ((y + z) - tan(a));
	else
		tmp = x + tan((z + y));
	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], -1000000.0], N[(x + N[Tan[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y + z), $MachinePrecision], 5e-7], N[(x + N[(N[(y + z), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 y z) < -1e6

   1. Initial program 75.5%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-sum N/A

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

      4. quot-tan N/A

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

      5. quot-tan N/A

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

      6. div-add N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 49.8%

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

   8. Taylor expanded in y around inf

      \[\leadsto x + \tan y \]
   9. Step-by-step derivation

   10. Applied rewrites 38.1%

       \[\leadsto x + \tan y \]

   if -1e6 < (+.f64 y z) < 4.99999999999999977e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto x + \left(\color{blue}{\left(y \cdot \left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}\right) + \frac{\sin z}{\cos z}\right)} - \tan a\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \left(\left(\left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}\right) \cdot y + \frac{\color{blue}{\sin z}}{\cos z}\right) - \tan a\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}, \color{blue}{y}, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}, y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      4. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(\mathsf{neg}\left(\frac{{\sin z}^{2}}{{\cos z}^{2}}\right)\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      5. unpow2 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(\mathsf{neg}\left(\frac{\sin z \cdot \sin z}{{\cos z}^{2}}\right)\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      6. unpow2 N/A

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

      7. frac-times N/A

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

      8. lower-neg.f64 N/A

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

      9. pow2 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\left(\frac{\sin z}{\cos z}\right)}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      10. lower-pow.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\left(\frac{\sin z}{\cos z}\right)}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      11. quot-tan N/A

          \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\tan z}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      12. lower-tan.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\tan z}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

   5. Applied rewrites 98.5%

      \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(1 - \left(-{\tan z}^{2}\right), y, \tan z\right)} - \tan a\right) \]

   6. Taylor expanded in z around 0

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

      1. lower-+.f64 97.5

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

   8. Applied rewrites 97.5%

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

   if 4.99999999999999977e-7 < (+.f64 y z)

   1. Initial program 71.3%

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

   3. Taylor expanded in a around 0

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

      1. tan-quot N/A

         \[\leadsto x + \tan \left(y + z\right) \]

      2. lift-tan.f64 N/A

         \[\leadsto x + \tan \left(y + z\right) \]

      3. +-commutative N/A

         \[\leadsto x + \tan \left(z + y\right) \]

      4. lower-+.f64 41.4

         \[\leadsto x + \tan \left(z + y\right) \]

   5. Applied rewrites 41.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -1000000:\\ \;\;\;\;x + \tan y\\ \mathbf{elif}\;y + z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x + \left(\left(y + z\right) - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y + z \leq -1000000:\\ \;\;\;\;x + \tan y\\ \mathbf{elif}\;y + z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \end{array} \]

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) -1000000.0)
   (+ x (tan y))
   (if (<= (+ y z) 5e-7) (+ x (- y (tan a))) (+ x (tan (+ z y))))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -1000000.0) {
		tmp = x + tan(y);
	} else if ((y + z) <= 5e-7) {
		tmp = x + (y - tan(a));
	} else {
		tmp = x + tan((z + y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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) <= (-1000000.0d0)) then
        tmp = x + tan(y)
    else if ((y + z) <= 5d-7) then
        tmp = x + (y - tan(a))
    else
        tmp = x + tan((z + y))
    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) <= -1000000.0) {
		tmp = x + Math.tan(y);
	} else if ((y + z) <= 5e-7) {
		tmp = x + (y - Math.tan(a));
	} else {
		tmp = x + Math.tan((z + y));
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -1000000.0:
		tmp = x + math.tan(y)
	elif (y + z) <= 5e-7:
		tmp = x + (y - math.tan(a))
	else:
		tmp = x + math.tan((z + y))
	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) <= -1000000.0)
		tmp = Float64(x + tan(y));
	elseif (Float64(y + z) <= 5e-7)
		tmp = Float64(x + Float64(y - tan(a)));
	else
		tmp = Float64(x + tan(Float64(z + y)));
	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) <= -1000000.0)
		tmp = x + tan(y);
	elseif ((y + z) <= 5e-7)
		tmp = x + (y - tan(a));
	else
		tmp = x + tan((z + y));
	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], -1000000.0], N[(x + N[Tan[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y + z), $MachinePrecision], 5e-7], N[(x + N[(y - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 y z) < -1e6

   1. Initial program 75.5%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-sum N/A

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

      4. quot-tan N/A

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

      5. quot-tan N/A

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

      6. div-add N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 99.5%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 49.8%

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

   8. Taylor expanded in y around inf

      \[\leadsto x + \tan y \]
   9. Step-by-step derivation

   10. Applied rewrites 38.1%

       \[\leadsto x + \tan y \]

   if -1e6 < (+.f64 y z) < 4.99999999999999977e-7

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto x + \left(\color{blue}{\left(y \cdot \left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}\right) + \frac{\sin z}{\cos z}\right)} - \tan a\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \left(\left(\left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}\right) \cdot y + \frac{\color{blue}{\sin z}}{\cos z}\right) - \tan a\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}, \color{blue}{y}, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      3. lower--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - -1 \cdot \frac{{\sin z}^{2}}{{\cos z}^{2}}, y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      4. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(\mathsf{neg}\left(\frac{{\sin z}^{2}}{{\cos z}^{2}}\right)\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      5. unpow2 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(\mathsf{neg}\left(\frac{\sin z \cdot \sin z}{{\cos z}^{2}}\right)\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      6. unpow2 N/A

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

      7. frac-times N/A

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

      8. lower-neg.f64 N/A

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

      9. pow2 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\left(\frac{\sin z}{\cos z}\right)}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      10. lower-pow.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\left(\frac{\sin z}{\cos z}\right)}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      11. quot-tan N/A

          \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\tan z}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

      12. lower-tan.f64 N/A

          \[\leadsto x + \left(\mathsf{fma}\left(1 - \left(-{\tan z}^{2}\right), y, \frac{\sin z}{\cos z}\right) - \tan a\right) \]

   5. Applied rewrites 98.5%

      \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(1 - \left(-{\tan z}^{2}\right), y, \tan z\right)} - \tan a\right) \]

   6. Taylor expanded in z around 0

      \[\leadsto x + \left(y - \tan a\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 96.5%

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

   if 4.99999999999999977e-7 < (+.f64 y z)

   1. Initial program 71.3%

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

   3. Taylor expanded in a around 0

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

      1. tan-quot N/A

         \[\leadsto x + \tan \left(y + z\right) \]

      2. lift-tan.f64 N/A

         \[\leadsto x + \tan \left(y + z\right) \]

      3. +-commutative N/A

         \[\leadsto x + \tan \left(z + y\right) \]

      4. lower-+.f64 41.4

         \[\leadsto x + \tan \left(z + y\right) \]

   5. Applied rewrites 41.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + z \leq -1000000:\\ \;\;\;\;x + \tan y\\ \mathbf{elif}\;y + z \leq 5 \cdot 10^{-7}:\\ \;\;\;\;x + \left(y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, a] = \mathsf{sort}([x, y, z, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-6}:\\ \;\;\;\;x + \tan y\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
(FPCore (x y z a)
 :precision binary64
 (if (<= y -3.4e-6) (+ x (tan y)) (+ x (tan z))))

C

assert(x < y && y < z && z < a);
double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -3.4e-6) {
		tmp = x + tan(y);
	} else {
		tmp = x + tan(z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 <= (-3.4d-6)) then
        tmp = x + tan(y)
    else
        tmp = x + tan(z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < a;
public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -3.4e-6) {
		tmp = x + Math.tan(y);
	} else {
		tmp = x + Math.tan(z);
	}
	return tmp;
}

Python

[x, y, z, a] = sort([x, y, z, a])
def code(x, y, z, a):
	tmp = 0
	if y <= -3.4e-6:
		tmp = x + math.tan(y)
	else:
		tmp = x + math.tan(z)
	return tmp

Julia

x, y, z, a = sort([x, y, z, a])
function code(x, y, z, a)
	tmp = 0.0
	if (y <= -3.4e-6)
		tmp = Float64(x + tan(y));
	else
		tmp = Float64(x + tan(z));
	end
	return tmp
end

MATLAB

x, y, z, a = num2cell(sort([x, y, z, a])){:}
function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -3.4e-6)
		tmp = x + tan(y);
	else
		tmp = x + tan(z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, a_] := If[LessEqual[y, -3.4e-6], N[(x + N[Tan[y], $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[z], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000006e-6

   1. Initial program 61.5%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-sum N/A

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

      4. quot-tan N/A

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

      5. quot-tan N/A

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

      6. div-add N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 40.2%

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

   8. Taylor expanded in y around inf

      \[\leadsto x + \tan y \]
   9. Step-by-step derivation

   10. Applied rewrites 40.6%

       \[\leadsto x + \tan y \]

   if -3.40000000000000006e-6 < y

   1. Initial program 86.3%

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

      1. lift-+.f64 N/A

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

      2. lift-tan.f64 N/A

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

      3. tan-sum N/A

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

      4. quot-tan N/A

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

      5. quot-tan N/A

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

      6. div-add N/A

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

      7. lower-+.f64 N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 51.3%

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

   8. Taylor expanded in y around 0

      \[\leadsto x + \tan z \]
   9. Step-by-step derivation

   10. Applied rewrites 44.6%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-6}:\\ \;\;\;\;x + \tan y\\ \mathbf{else}:\\ \;\;\;\;x + \tan z\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

3. Taylor expanded in a around 0

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

   1. tan-quot N/A

      \[\leadsto x + \tan \left(y + z\right) \]

   2. lift-tan.f64 N/A

      \[\leadsto x + \tan \left(y + z\right) \]

   3. +-commutative N/A

      \[\leadsto x + \tan \left(z + y\right) \]

   4. lower-+.f64 48.2

      \[\leadsto x + \tan \left(z + y\right) \]

5. Applied rewrites 48.2%

   \[\leadsto x + \color{blue}{\tan \left(z + y\right)} \]
6. Add Preprocessing

Alternative 17: 40.5% accurate, 2.0× speedup

Math

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

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)))

C

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

Fortran

NOTE: x, y, z, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + tan(y)
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);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

   1. lift-+.f64 N/A

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

   2. lift-tan.f64 N/A

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

   3. tan-sum N/A

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

   4. quot-tan N/A

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

   5. quot-tan N/A

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

   6. div-add N/A

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

   7. lower-+.f64 N/A

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

4. Applied rewrites 99.7%

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

5. Taylor expanded in a around 0

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

7. Applied rewrites 48.2%

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

8. Taylor expanded in y around inf

   \[\leadsto x + \tan y \]
9. Step-by-step derivation

10. Applied rewrites 40.4%

    \[\leadsto x + \tan y \]

11. Final simplification 40.4%

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

Alternative 18: 31.5% accurate, 210.0× 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.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, a)
use fmin_fmax_functions
    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 79.3%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 30.7%

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

Reproduce

herbie shell --seed 2025083 
(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))))