tan-example (used to crash)

Percentage Accurate: 79.5% → 99.7%

Time: 10.6s

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: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \tan y \cdot \tan z\\ t_1 := \frac{\tan z}{t\_0}\\ t_2 := \frac{\tan y}{t\_0}\\ x + \left(\frac{{t\_2}^{2} - {t\_1}^{2}}{t\_2 - t\_1} - \tan a\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (tan y) (tan z))))
        (t_1 (/ (tan z) t_0))
        (t_2 (/ (tan y) t_0)))
   (+ x (- (/ (- (pow t_2 2.0) (pow t_1 2.0)) (- t_2 t_1)) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = 1.0 - (tan(y) * tan(z));
	double t_1 = tan(z) / t_0;
	double t_2 = tan(y) / t_0;
	return x + (((pow(t_2, 2.0) - pow(t_1, 2.0)) / (t_2 - t_1)) - 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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = 1.0d0 - (tan(y) * tan(z))
    t_1 = tan(z) / t_0
    t_2 = tan(y) / t_0
    code = x + ((((t_2 ** 2.0d0) - (t_1 ** 2.0d0)) / (t_2 - t_1)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = 1.0 - (Math.tan(y) * Math.tan(z));
	double t_1 = Math.tan(z) / t_0;
	double t_2 = Math.tan(y) / t_0;
	return x + (((Math.pow(t_2, 2.0) - Math.pow(t_1, 2.0)) / (t_2 - t_1)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	t_0 = 1.0 - (math.tan(y) * math.tan(z))
	t_1 = math.tan(z) / t_0
	t_2 = math.tan(y) / t_0
	return x + (((math.pow(t_2, 2.0) - math.pow(t_1, 2.0)) / (t_2 - t_1)) - math.tan(a))

Julia

function code(x, y, z, a)
	t_0 = Float64(1.0 - Float64(tan(y) * tan(z)))
	t_1 = Float64(tan(z) / t_0)
	t_2 = Float64(tan(y) / t_0)
	return Float64(x + Float64(Float64(Float64((t_2 ^ 2.0) - (t_1 ^ 2.0)) / Float64(t_2 - t_1)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	t_0 = 1.0 - (tan(y) * tan(z));
	t_1 = tan(z) / t_0;
	t_2 = tan(y) / t_0;
	tmp = x + ((((t_2 ^ 2.0) - (t_1 ^ 2.0)) / (t_2 - t_1)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Tan[z], $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Tan[y], $MachinePrecision] / t$95$0), $MachinePrecision]}, N[(x + N[(N[(N[(N[Power[t$95$2, 2.0], $MachinePrecision] - N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] / N[(t$95$2 - t$95$1), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Initial program 79.5%

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

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

   1. lift-+.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift-tan.f64 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-tan.f64 N/A

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

   7. lift-tan.f64 N/A

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

   8. lift-/.f64 N/A

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

   9. lift-tan.f64 N/A

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

   10. lift--.f64 N/A

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

   11. lift-*.f64 N/A

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

   12. lift-tan.f64 N/A

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

   13. lift-tan.f64 N/A

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

6. Applied rewrites 99.7%

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

8. Applied rewrites 99.7%

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

Alternative 2: 99.7% accurate, 0.2× speedup

Math

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

FPCore

(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 y) (cos z)))))))
   (tan a))))

C

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(y) * cos(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) / (1.0d0 - (tan(y) * tan(z)))) + (tan(z) / (1.0d0 - (sin(y) * (sin(z) / (cos(y) * cos(z))))))) - tan(a))
end function

Java

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(y) * Math.cos(z))))))) - Math.tan(a));
}

Python

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(y) * math.cos(z))))))) - math.tan(a))

Julia

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(y) * cos(z))))))) - tan(a)))
end

MATLAB

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(y) * cos(z))))))) - tan(a));
end

Wolfram

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[y], $MachinePrecision] * N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

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

   \[\leadsto x + \left(\color{blue}{\left(\frac{\tan y}{1 - \tan y \cdot \tan z} + \frac{\tan z}{1 - \tan y \cdot \tan z}\right)} - \tan a\right) \]
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. lower-*.f64 N/A

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

   13. lower-cos.f64 N/A

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

   14. lower-cos.f64 99.7

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

6. Applied rewrites 99.7%

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

Alternative 3: 99.7% accurate, 0.2× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+
  x
  (-
   (+
    (/ (tan y) (- 1.0 (* (tan y) (tan z))))
    (/ (tan z) (- 1.0 (* (tan y) (/ (sin z) (cos z))))))
   (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (((tan(y) / (1.0 - (tan(y) * tan(z)))) + (tan(z) / (1.0 - (tan(y) * (sin(z) / cos(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) / (1.0d0 - (tan(y) * tan(z)))) + (tan(z) / (1.0d0 - (tan(y) * (sin(z) / cos(z)))))) - tan(a))
end function

Java

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

Python

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.tan(y) * (math.sin(z) / math.cos(z)))))) - math.tan(a))

Julia

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(tan(y) * Float64(sin(z) / cos(z)))))) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) / (1.0 - (tan(y) * tan(z)))) + (tan(z) / (1.0 - (tan(y) * (sin(z) / cos(z)))))) - tan(a));
end

Wolfram

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[Tan[y], $MachinePrecision] * N[(N[Sin[z], $MachinePrecision] / N[Cos[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

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

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

   1. lift-tan.f64 N/A

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

   2. tan-quot N/A

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

   3. lower-/.f64 N/A

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

   4. lower-sin.f64 N/A

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

   5. lower-cos.f64 99.7

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

6. Applied rewrites 99.7%

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

Alternative 4: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \tan y \cdot \tan z\\ x + \left(\left(\frac{\tan y}{t\_0} + \frac{\tan z}{t\_0}\right) - \tan a\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (let* ((t_0 (- 1.0 (* (tan y) (tan z)))))
   (+ x (- (+ (/ (tan y) t_0) (/ (tan z) t_0)) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double t_0 = 1.0 - (tan(y) * tan(z));
	return x + (((tan(y) / t_0) + (tan(z) / t_0)) - 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
    real(8) :: t_0
    t_0 = 1.0d0 - (tan(y) * tan(z))
    code = x + (((tan(y) / t_0) + (tan(z) / t_0)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	double t_0 = 1.0 - (Math.tan(y) * Math.tan(z));
	return x + (((Math.tan(y) / t_0) + (Math.tan(z) / t_0)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	t_0 = 1.0 - (math.tan(y) * math.tan(z))
	return x + (((math.tan(y) / t_0) + (math.tan(z) / t_0)) - math.tan(a))

Julia

function code(x, y, z, a)
	t_0 = Float64(1.0 - Float64(tan(y) * tan(z)))
	return Float64(x + Float64(Float64(Float64(tan(y) / t_0) + Float64(tan(z) / t_0)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	t_0 = 1.0 - (tan(y) * tan(z));
	tmp = x + (((tan(y) / t_0) + (tan(z) / t_0)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := Block[{t$95$0 = N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] / t$95$0), $MachinePrecision] + N[(N[Tan[z], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 79.5%

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

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

Alternative 5: 99.7% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan z) (tan y)) (- 1.0 (* (tan z) (tan y)))) (tan a))))

C

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

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

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

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

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

function tmp = code(x, y, z, a)
	tmp = x + (((tan(z) + tan(y)) / (1.0 - (tan(z) * tan(y)))) - tan(a));
end

Wolfram

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 79.5%

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

Alternative 6: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\tan y + \left(x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) 2e-12) (+ (tan y) (- x (tan a))) (+ x (tan (+ z y)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 2e-12) {
		tmp = tan(y) + (x - tan(a));
	} else {
		tmp = x + tan((z + y));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y + z) <= 2d-12) then
        tmp = tan(y) + (x - tan(a))
    else
        tmp = x + tan((z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= 2e-12) {
		tmp = Math.tan(y) + (x - Math.tan(a));
	} else {
		tmp = x + Math.tan((z + y));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= 2e-12:
		tmp = math.tan(y) + (x - math.tan(a))
	else:
		tmp = x + math.tan((z + y))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= 2e-12)
		tmp = Float64(tan(y) + Float64(x - tan(a)));
	else
		tmp = Float64(x + tan(Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= 2e-12)
		tmp = tan(y) + (x - tan(a));
	else
		tmp = x + tan((z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], 2e-12], N[(N[Tan[y], $MachinePrecision] + N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 y z) < 1.99999999999999996e-12

   1. Initial program 83.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 70.0

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

   5. Applied rewrites 70.0%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-tan.f64 N/A

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

      4. tan-quot N/A

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

      5. lift-tan.f64 N/A

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

      6. tan-quot N/A

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

      7. associate--l+ N/A

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

      8. lower-+.f64 N/A

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

      9. tan-quot N/A

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

      10. lift-tan.f64 N/A

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

      11. lower--.f64 N/A

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

      12. tan-quot N/A

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

      13. lift-tan.f64 70.0

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

   7. Applied rewrites 70.0%

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

   if 1.99999999999999996e-12 < (+.f64 y z)

   1. Initial program 72.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 45.9

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

   5. Applied rewrites 45.9%

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

Alternative 7: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00145:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= y -0.00145) (+ x (- (tan y) (tan a))) (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -0.00145) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-0.00145d0)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -0.00145) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if y <= -0.00145:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (y <= -0.00145)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -0.00145)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[y, -0.00145], 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 < -0.00145

   1. Initial program 59.4%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 59.6%

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

   if -0.00145 < y

   1. Initial program 86.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 74.3%

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

Alternative 8: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00145:\\ \;\;\;\;x + \left(\tan y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\tan z + x\right) - \tan a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= y -0.00145) (+ x (- (tan y) (tan a))) (- (+ (tan z) x) (tan a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -0.00145) {
		tmp = x + (tan(y) - tan(a));
	} else {
		tmp = (tan(z) + x) - tan(a);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-0.00145d0)) then
        tmp = x + (tan(y) - tan(a))
    else
        tmp = (tan(z) + x) - tan(a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -0.00145) {
		tmp = x + (Math.tan(y) - Math.tan(a));
	} else {
		tmp = (Math.tan(z) + x) - Math.tan(a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if y <= -0.00145:
		tmp = x + (math.tan(y) - math.tan(a))
	else:
		tmp = (math.tan(z) + x) - math.tan(a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (y <= -0.00145)
		tmp = Float64(x + Float64(tan(y) - tan(a)));
	else
		tmp = Float64(Float64(tan(z) + x) - tan(a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -0.00145)
		tmp = x + (tan(y) - tan(a));
	else
		tmp = (tan(z) + x) - tan(a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[y, -0.00145], 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 < -0.00145

   1. Initial program 59.4%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 59.6%

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

   if -0.00145 < y

   1. Initial program 86.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 74.2

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

   5. Applied rewrites 74.2%

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

Alternative 9: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00145:\\ \;\;\;\;\tan y + \left(x - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\tan z + x\right) - \tan a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= y -0.00145) (+ (tan y) (- x (tan a))) (- (+ (tan z) x) (tan a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -0.00145) {
		tmp = tan(y) + (x - tan(a));
	} else {
		tmp = (tan(z) + x) - tan(a);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (y <= (-0.00145d0)) then
        tmp = tan(y) + (x - tan(a))
    else
        tmp = (tan(z) + x) - tan(a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -0.00145) {
		tmp = Math.tan(y) + (x - Math.tan(a));
	} else {
		tmp = (Math.tan(z) + x) - Math.tan(a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if y <= -0.00145:
		tmp = math.tan(y) + (x - math.tan(a))
	else:
		tmp = (math.tan(z) + x) - math.tan(a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (y <= -0.00145)
		tmp = Float64(tan(y) + Float64(x - tan(a)));
	else
		tmp = Float64(Float64(tan(z) + x) - tan(a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -0.00145)
		tmp = tan(y) + (x - tan(a));
	else
		tmp = (tan(z) + x) - tan(a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[y, -0.00145], N[(N[Tan[y], $MachinePrecision] + N[(x - 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 < -0.00145

   1. Initial program 59.4%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 59.6

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

   5. Applied rewrites 59.6%

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

      1. lift--.f64 N/A

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

      2. lift-+.f64 N/A

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

      3. lift-tan.f64 N/A

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

      4. tan-quot N/A

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

      5. lift-tan.f64 N/A

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

      6. tan-quot N/A

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

      7. associate--l+ N/A

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

      8. lower-+.f64 N/A

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

      9. tan-quot N/A

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

      10. lift-tan.f64 N/A

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

      11. lower--.f64 N/A

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

      12. tan-quot N/A

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

      13. lift-tan.f64 59.6

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

   7. Applied rewrites 59.6%

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

   if -0.00145 < y

   1. Initial program 86.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 74.2

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

   5. Applied rewrites 74.2%

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

Alternative 10: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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]

Derivation

1. Initial program 79.5%

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

Alternative 11: 61.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.27 \lor \neg \left(a \leq 0.00035\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \mathsf{fma}\left(0.3333333333333333, a \cdot a, 1\right) \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.27) (not (<= a 0.00035)))
   (- x (tan a))
   (+ x (- (tan (+ y z)) (* (fma 0.3333333333333333 (* a a) 1.0) a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.27) || !(a <= 0.00035)) {
		tmp = x - tan(a);
	} else {
		tmp = x + (tan((y + z)) - (fma(0.3333333333333333, (a * a), 1.0) * a));
	}
	return tmp;
}

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.27) || !(a <= 0.00035))
		tmp = Float64(x - tan(a));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - Float64(fma(0.3333333333333333, Float64(a * a), 1.0) * a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.27], N[Not[LessEqual[a, 0.00035]], $MachinePrecision]], N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[(N[(0.3333333333333333 * N[(a * a), $MachinePrecision] + 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.27000000000000002 or 3.49999999999999996e-4 < a

   1. Initial program 78.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto x - \tan \color{blue}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.7%

      \[\leadsto x - \tan \color{blue}{a} \]

   if -0.27000000000000002 < a < 3.49999999999999996e-4

   1. Initial program 80.4%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. unpow2 N/A

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

      6. lower-*.f64 80.4

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

   5. Applied rewrites 80.4%

      \[\leadsto x + \left(\tan \left(y + z\right) - \color{blue}{\mathsf{fma}\left(0.3333333333333333, a \cdot a, 1\right) \cdot a}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.27 \lor \neg \left(a \leq 0.00035\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - \mathsf{fma}\left(0.3333333333333333, a \cdot a, 1\right) \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 56.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -2:\\ \;\;\;\;x + \tan y\\ \mathbf{elif}\;y + z \leq 2 \cdot 10^{-12}:\\ \;\;\;\;x + \left(z - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -2.0)
   (+ x (tan y))
   (if (<= (+ y z) 2e-12) (+ x (- z (tan a))) (+ x (tan (+ z y))))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -2.0) {
		tmp = x + tan(y);
	} else if ((y + z) <= 2e-12) {
		tmp = x + (z - tan(a));
	} else {
		tmp = x + tan((z + y));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((y + z) <= (-2.0d0)) then
        tmp = x + tan(y)
    else if ((y + z) <= 2d-12) then
        tmp = x + (z - tan(a))
    else
        tmp = x + tan((z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((y + z) <= -2.0) {
		tmp = x + Math.tan(y);
	} else if ((y + z) <= 2e-12) {
		tmp = x + (z - Math.tan(a));
	} else {
		tmp = x + Math.tan((z + y));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (y + z) <= -2.0:
		tmp = x + math.tan(y)
	elif (y + z) <= 2e-12:
		tmp = x + (z - math.tan(a))
	else:
		tmp = x + math.tan((z + y))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (Float64(y + z) <= -2.0)
		tmp = Float64(x + tan(y));
	elseif (Float64(y + z) <= 2e-12)
		tmp = Float64(x + Float64(z - tan(a)));
	else
		tmp = Float64(x + tan(Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -2.0)
		tmp = x + tan(y);
	elseif ((y + z) <= 2e-12)
		tmp = x + (z - tan(a));
	else
		tmp = x + tan((z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -2.0], N[(x + N[Tan[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y + z), $MachinePrecision], 2e-12], N[(x + N[(z - 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) < -2

   1. Initial program 72.2%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{\sin y}{\cos y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. tan-quot N/A

         \[\leadsto x + \tan y \]

      3. lift-tan.f64 37.3

         \[\leadsto x + \tan y \]

   8. Applied rewrites 37.3%

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

   if -2 < (+.f64 y z) < 1.99999999999999996e-12

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower--.f64 N/A

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

      4. mul-1-neg N/A

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

      5. unpow2 N/A

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

      6. unpow2 N/A

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

      7. frac-times N/A

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

      8. lower-neg.f64 N/A

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

      9. pow2 N/A

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

      10. lower-pow.f64 N/A

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

      11. quot-tan N/A

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

      12. lower-tan.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 99.7%

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

   if 1.99999999999999996e-12 < (+.f64 y z)

   1. Initial program 72.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 45.9

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

   5. Applied rewrites 45.9%

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

Alternative 13: 61.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.146 \lor \neg \left(a \leq 0.00035\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.146) (not (<= a 0.00035)))
   (- x (tan a))
   (- (+ x (tan (+ y z))) a)))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.146) || !(a <= 0.00035)) {
		tmp = x - tan(a);
	} else {
		tmp = (x + tan((y + z))) - a;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-0.146d0)) .or. (.not. (a <= 0.00035d0))) then
        tmp = x - tan(a)
    else
        tmp = (x + tan((y + z))) - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.146) || !(a <= 0.00035)) {
		tmp = x - Math.tan(a);
	} else {
		tmp = (x + Math.tan((y + z))) - a;
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.146) or not (a <= 0.00035):
		tmp = x - math.tan(a)
	else:
		tmp = (x + math.tan((y + z))) - a
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.146) || !(a <= 0.00035))
		tmp = Float64(x - tan(a));
	else
		tmp = Float64(Float64(x + tan(Float64(y + z))) - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.146) || ~((a <= 0.00035)))
		tmp = x - tan(a);
	else
		tmp = (x + tan((y + z))) - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.146], N[Not[LessEqual[a, 0.00035]], $MachinePrecision]], N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.145999999999999991 or 3.49999999999999996e-4 < a

   1. Initial program 78.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto x - \tan \color{blue}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.7%

      \[\leadsto x - \tan \color{blue}{a} \]

   if -0.145999999999999991 < a < 3.49999999999999996e-4

   1. Initial program 80.4%

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

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

   7. Applied rewrites 99.5%

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

   9. Applied rewrites 80.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.146 \lor \neg \left(a \leq 0.00035\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;\left(x + \tan \left(y + z\right)\right) - a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.146 \lor \neg \left(a \leq 0.00035\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.146) (not (<= a 0.00035)))
   (- x (tan a))
   (+ x (- (tan (+ y z)) a))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.146) || !(a <= 0.00035)) {
		tmp = x - tan(a);
	} else {
		tmp = x + (tan((y + z)) - a);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-0.146d0)) .or. (.not. (a <= 0.00035d0))) then
        tmp = x - tan(a)
    else
        tmp = x + (tan((y + z)) - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.146) || !(a <= 0.00035)) {
		tmp = x - Math.tan(a);
	} else {
		tmp = x + (Math.tan((y + z)) - a);
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.146) or not (a <= 0.00035):
		tmp = x - math.tan(a)
	else:
		tmp = x + (math.tan((y + z)) - a)
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.146) || !(a <= 0.00035))
		tmp = Float64(x - tan(a));
	else
		tmp = Float64(x + Float64(tan(Float64(y + z)) - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.146) || ~((a <= 0.00035)))
		tmp = x - tan(a);
	else
		tmp = x + (tan((y + z)) - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.146], N[Not[LessEqual[a, 0.00035]], $MachinePrecision]], N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -0.145999999999999991 or 3.49999999999999996e-4 < a

   1. Initial program 78.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 56.6

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

   5. Applied rewrites 56.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto x - \tan \color{blue}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.7%

      \[\leadsto x - \tan \color{blue}{a} \]

   if -0.145999999999999991 < a < 3.49999999999999996e-4

   1. Initial program 80.4%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 80.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.146 \lor \neg \left(a \leq 0.00035\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan \left(y + z\right) - a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.000345 \lor \neg \left(a \leq 2.9 \cdot 10^{-9}\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (or (<= a -0.000345) (not (<= a 2.9e-9)))
   (- x (tan a))
   (+ x (tan (+ z y)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.000345) || !(a <= 2.9e-9)) {
		tmp = x - tan(a);
	} else {
		tmp = x + tan((z + y));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((a <= (-0.000345d0)) .or. (.not. (a <= 2.9d-9))) then
        tmp = x - tan(a)
    else
        tmp = x + tan((z + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if ((a <= -0.000345) || !(a <= 2.9e-9)) {
		tmp = x - Math.tan(a);
	} else {
		tmp = x + Math.tan((z + y));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if (a <= -0.000345) or not (a <= 2.9e-9):
		tmp = x - math.tan(a)
	else:
		tmp = x + math.tan((z + y))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if ((a <= -0.000345) || !(a <= 2.9e-9))
		tmp = Float64(x - tan(a));
	else
		tmp = Float64(x + tan(Float64(z + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((a <= -0.000345) || ~((a <= 2.9e-9)))
		tmp = x - tan(a);
	else
		tmp = x + tan((z + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[Or[LessEqual[a, -0.000345], N[Not[LessEqual[a, 2.9e-9]], $MachinePrecision]], N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision], N[(x + N[Tan[N[(z + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.44999999999999983e-4 or 2.89999999999999991e-9 < a

   1. Initial program 79.2%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 57.5

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

   5. Applied rewrites 57.5%

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

   6. Taylor expanded in x around inf

      \[\leadsto x - \tan \color{blue}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.4%

      \[\leadsto x - \tan \color{blue}{a} \]

   if -3.44999999999999983e-4 < a < 2.89999999999999991e-9

   1. Initial program 79.9%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 79.0

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

   5. Applied rewrites 79.0%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.000345 \lor \neg \left(a \leq 2.9 \cdot 10^{-9}\right):\\ \;\;\;\;x - \tan a\\ \mathbf{else}:\\ \;\;\;\;x + \tan \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + z \leq -2:\\ \;\;\;\;x + \tan y\\ \mathbf{else}:\\ \;\;\;\;x - \tan a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= (+ y z) -2.0) (+ x (tan y)) (- x (tan a))))

C

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

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
    real(8) :: tmp
    if ((y + z) <= (-2.0d0)) then
        tmp = x + tan(y)
    else
        tmp = x - tan(a)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if ((y + z) <= -2.0)
		tmp = x + tan(y);
	else
		tmp = x - tan(a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[N[(y + z), $MachinePrecision], -2.0], N[(x + N[Tan[y], $MachinePrecision]), $MachinePrecision], N[(x - N[Tan[a], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 72.2%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 48.9

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

   5. Applied rewrites 48.9%

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

   6. Taylor expanded in a around 0

      \[\leadsto x + \color{blue}{\frac{\sin y}{\cos y}} \]
   7. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. tan-quot N/A

         \[\leadsto x + \tan y \]

      3. lift-tan.f64 37.3

         \[\leadsto x + \tan y \]

   8. Applied rewrites 37.3%

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

   if -2 < (+.f64 y z)

   1. Initial program 83.7%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   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 68.0

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

   5. Applied rewrites 68.0%

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

   6. Taylor expanded in x around inf

      \[\leadsto x - \tan \color{blue}{a} \]
   7. Step-by-step derivation

   8. Applied rewrites 54.0%

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

Alternative 17: 41.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ x + \tan y \end{array} \]

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.5%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
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 61.1

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

5. Applied rewrites 61.1%

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

6. Taylor expanded in a around 0

   \[\leadsto x + \color{blue}{\frac{\sin y}{\cos y}} \]
7. Step-by-step derivation

   1. lower-+.f64 N/A

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

   2. tan-quot N/A

      \[\leadsto x + \tan y \]

   3. lift-tan.f64 42.9

      \[\leadsto x + \tan y \]

8. Applied rewrites 42.9%

   \[\leadsto x + \color{blue}{\tan y} \]
9. Add Preprocessing

Alternative 18: 32.0% accurate, 210.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z, a):
	return x

Julia

function code(x, y, z, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, a_] := x

Derivation

1. Initial program 79.5%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 32.5%

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

Reproduce

herbie shell --seed 2025064 
(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))))