Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B

Percentage Accurate: 99.9% → 99.9%

Time: 5.3s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + cos(y)) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + Math.cos(y)) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + math.cos(y)) - (z * math.sin(y))

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Add Preprocessing

Alternative 2: 99.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + 1\right) - z \cdot \sin y\\ \mathbf{if}\;z \leq -0.81:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(1 + \frac{\cos y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x 1.0) (* z (sin y)))))
   (if (<= z -0.81) t_0 (if (<= z 5e-17) (* x (+ 1.0 (/ (cos y) x))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * sin(y));
	double tmp;
	if (z <= -0.81) {
		tmp = t_0;
	} else if (z <= 5e-17) {
		tmp = x * (1.0 + (cos(y) / x));
	} else {
		tmp = t_0;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + 1.0d0) - (z * sin(y))
    if (z <= (-0.81d0)) then
        tmp = t_0
    else if (z <= 5d-17) then
        tmp = x * (1.0d0 + (cos(y) / x))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * Math.sin(y));
	double tmp;
	if (z <= -0.81) {
		tmp = t_0;
	} else if (z <= 5e-17) {
		tmp = x * (1.0 + (Math.cos(y) / x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + 1.0) - (z * math.sin(y))
	tmp = 0
	if z <= -0.81:
		tmp = t_0
	elif z <= 5e-17:
		tmp = x * (1.0 + (math.cos(y) / x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + 1.0) - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -0.81)
		tmp = t_0;
	elseif (z <= 5e-17)
		tmp = Float64(x * Float64(1.0 + Float64(cos(y) / x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + 1.0) - (z * sin(y));
	tmp = 0.0;
	if (z <= -0.81)
		tmp = t_0;
	elseif (z <= 5e-17)
		tmp = x * (1.0 + (cos(y) / x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.81], t$95$0, If[LessEqual[z, 5e-17], N[(x * N[(1.0 + N[(N[Cos[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.81000000000000005 or 4.9999999999999999e-17 < z

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 88.3%

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

   if -0.81000000000000005 < z < 4.9999999999999999e-17

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 91.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto x \cdot \left(1 + \color{blue}{\frac{1}{x}}\right) \]

   7. Applied rewrites 62.3%

      \[\leadsto x \cdot \left(1 + \color{blue}{\frac{1}{x}}\right) \]

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 73.2%

       \[\leadsto x \cdot \left(1 + \color{blue}{\frac{\cos y}{x}}\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -100:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.98:\\ \;\;\;\;\cos y - 1 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y)))
        (t_1 (- (+ x (cos y)) t_0))
        (t_2 (- (+ x 1.0) t_0)))
   (if (<= t_1 -100.0) t_2 (if (<= t_1 0.98) (- (cos y) (* 1.0 z)) t_2))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = (x + cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -100.0) {
		tmp = t_2;
	} else if (t_1 <= 0.98) {
		tmp = cos(y) - (1.0 * z);
	} else {
		tmp = t_2;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = (x + cos(y)) - t_0
    t_2 = (x + 1.0d0) - t_0
    if (t_1 <= (-100.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.98d0) then
        tmp = cos(y) - (1.0d0 * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double t_1 = (x + Math.cos(y)) - t_0;
	double t_2 = (x + 1.0) - t_0;
	double tmp;
	if (t_1 <= -100.0) {
		tmp = t_2;
	} else if (t_1 <= 0.98) {
		tmp = Math.cos(y) - (1.0 * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = (x + math.cos(y)) - t_0
	t_2 = (x + 1.0) - t_0
	tmp = 0
	if t_1 <= -100.0:
		tmp = t_2
	elif t_1 <= 0.98:
		tmp = math.cos(y) - (1.0 * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	t_2 = Float64(Float64(x + 1.0) - t_0)
	tmp = 0.0
	if (t_1 <= -100.0)
		tmp = t_2;
	elseif (t_1 <= 0.98)
		tmp = Float64(cos(y) - Float64(1.0 * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = (x + cos(y)) - t_0;
	t_2 = (x + 1.0) - t_0;
	tmp = 0.0;
	if (t_1 <= -100.0)
		tmp = t_2;
	elseif (t_1 <= 0.98)
		tmp = cos(y) - (1.0 * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -100.0], t$95$2, If[LessEqual[t$95$1, 0.98], N[(N[Cos[y], $MachinePrecision] - N[(1.0 * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -100 or 0.97999999999999998 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 88.3%

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

   if -100 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.97999999999999998

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 69.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   7. Applied rewrites 35.2%

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   9. Applied rewrites 27.8%

      \[\leadsto \cos y - \color{blue}{1 \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 0\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -100:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.98:\\ \;\;\;\;\cos y - 1 \cdot z\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;1 + x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y)))
        (t_1 (- (+ x (cos y)) t_0))
        (t_2 (- (+ x 0.0) t_0)))
   (if (<= t_1 -100.0)
     t_2
     (if (<= t_1 0.98)
       (- (cos y) (* 1.0 z))
       (if (<= t_1 5.0) (+ 1.0 x) t_2)))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = (x + cos(y)) - t_0;
	double t_2 = (x + 0.0) - t_0;
	double tmp;
	if (t_1 <= -100.0) {
		tmp = t_2;
	} else if (t_1 <= 0.98) {
		tmp = cos(y) - (1.0 * z);
	} else if (t_1 <= 5.0) {
		tmp = 1.0 + x;
	} else {
		tmp = t_2;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = z * sin(y)
    t_1 = (x + cos(y)) - t_0
    t_2 = (x + 0.0d0) - t_0
    if (t_1 <= (-100.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.98d0) then
        tmp = cos(y) - (1.0d0 * z)
    else if (t_1 <= 5.0d0) then
        tmp = 1.0d0 + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double t_1 = (x + Math.cos(y)) - t_0;
	double t_2 = (x + 0.0) - t_0;
	double tmp;
	if (t_1 <= -100.0) {
		tmp = t_2;
	} else if (t_1 <= 0.98) {
		tmp = Math.cos(y) - (1.0 * z);
	} else if (t_1 <= 5.0) {
		tmp = 1.0 + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = (x + math.cos(y)) - t_0
	t_2 = (x + 0.0) - t_0
	tmp = 0
	if t_1 <= -100.0:
		tmp = t_2
	elif t_1 <= 0.98:
		tmp = math.cos(y) - (1.0 * z)
	elif t_1 <= 5.0:
		tmp = 1.0 + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	t_2 = Float64(Float64(x + 0.0) - t_0)
	tmp = 0.0
	if (t_1 <= -100.0)
		tmp = t_2;
	elseif (t_1 <= 0.98)
		tmp = Float64(cos(y) - Float64(1.0 * z));
	elseif (t_1 <= 5.0)
		tmp = Float64(1.0 + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = (x + cos(y)) - t_0;
	t_2 = (x + 0.0) - t_0;
	tmp = 0.0;
	if (t_1 <= -100.0)
		tmp = t_2;
	elseif (t_1 <= 0.98)
		tmp = cos(y) - (1.0 * z);
	elseif (t_1 <= 5.0)
		tmp = 1.0 + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + 0.0), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -100.0], t$95$2, If[LessEqual[t$95$1, 0.98], N[(N[Cos[y], $MachinePrecision] - N[(1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5.0], N[(1.0 + x), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -100 or 5 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 88.3%

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

   6. Applied rewrites 68.3%

      \[\leadsto \left(x + 0\right) - z \cdot \sin y \]

   if -100 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.97999999999999998

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 69.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   7. Applied rewrites 35.2%

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   9. Applied rewrites 27.8%

      \[\leadsto \cos y - \color{blue}{1 \cdot z} \]

   if 0.97999999999999998 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 5

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 74.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + \cos y\right) - z \cdot \sin y\\ t_1 := \left(x + 1\right) - z \cdot y\\ \mathbf{if}\;t\_0 \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 0.98:\\ \;\;\;\;\cos y - 1 \cdot z\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x (cos y)) (* z (sin y)))) (t_1 (- (+ x 1.0) (* z y))))
   (if (<= t_0 -100.0)
     t_1
     (if (<= t_0 0.98)
       (- (cos y) (* 1.0 z))
       (if (<= t_0 5e+149) t_1 (+ 1.0 x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + cos(y)) - (z * sin(y));
	double t_1 = (x + 1.0) - (z * y);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = cos(y) - (1.0 * z);
	} else if (t_0 <= 5e+149) {
		tmp = t_1;
	} else {
		tmp = 1.0 + x;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x + cos(y)) - (z * sin(y))
    t_1 = (x + 1.0d0) - (z * y)
    if (t_0 <= (-100.0d0)) then
        tmp = t_1
    else if (t_0 <= 0.98d0) then
        tmp = cos(y) - (1.0d0 * z)
    else if (t_0 <= 5d+149) then
        tmp = t_1
    else
        tmp = 1.0d0 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + Math.cos(y)) - (z * Math.sin(y));
	double t_1 = (x + 1.0) - (z * y);
	double tmp;
	if (t_0 <= -100.0) {
		tmp = t_1;
	} else if (t_0 <= 0.98) {
		tmp = Math.cos(y) - (1.0 * z);
	} else if (t_0 <= 5e+149) {
		tmp = t_1;
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + math.cos(y)) - (z * math.sin(y))
	t_1 = (x + 1.0) - (z * y)
	tmp = 0
	if t_0 <= -100.0:
		tmp = t_1
	elif t_0 <= 0.98:
		tmp = math.cos(y) - (1.0 * z)
	elif t_0 <= 5e+149:
		tmp = t_1
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
	t_1 = Float64(Float64(x + 1.0) - Float64(z * y))
	tmp = 0.0
	if (t_0 <= -100.0)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = Float64(cos(y) - Float64(1.0 * z));
	elseif (t_0 <= 5e+149)
		tmp = t_1;
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + cos(y)) - (z * sin(y));
	t_1 = (x + 1.0) - (z * y);
	tmp = 0.0;
	if (t_0 <= -100.0)
		tmp = t_1;
	elseif (t_0 <= 0.98)
		tmp = cos(y) - (1.0 * z);
	elseif (t_0 <= 5e+149)
		tmp = t_1;
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -100.0], t$95$1, If[LessEqual[t$95$0, 0.98], N[(N[Cos[y], $MachinePrecision] - N[(1.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+149], t$95$1, N[(1.0 + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -100 or 0.97999999999999998 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 4.9999999999999999e149

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 88.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 64.2%

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

   if -100 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 0.97999999999999998

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 69.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   7. Applied rewrites 35.2%

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   9. Applied rewrites 27.8%

      \[\leadsto \cos y - \color{blue}{1 \cdot z} \]

   if 4.9999999999999999e149 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 73.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00112:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-13}:\\ \;\;\;\;\cos y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.00112)
   (+ 1.0 x)
   (if (<= x 7.6e-13) (- (cos y) (* y z)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00112) {
		tmp = 1.0 + x;
	} else if (x <= 7.6e-13) {
		tmp = cos(y) - (y * z);
	} else {
		tmp = 1.0 + x;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-0.00112d0)) then
        tmp = 1.0d0 + x
    else if (x <= 7.6d-13) then
        tmp = cos(y) - (y * z)
    else
        tmp = 1.0d0 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.00112) {
		tmp = 1.0 + x;
	} else if (x <= 7.6e-13) {
		tmp = Math.cos(y) - (y * z);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.00112:
		tmp = 1.0 + x
	elif x <= 7.6e-13:
		tmp = math.cos(y) - (y * z)
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.00112)
		tmp = Float64(1.0 + x);
	elseif (x <= 7.6e-13)
		tmp = Float64(cos(y) - Float64(y * z));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.00112)
		tmp = 1.0 + x;
	elseif (x <= 7.6e-13)
		tmp = cos(y) - (y * z);
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.00112], N[(1.0 + x), $MachinePrecision], If[LessEqual[x, 7.6e-13], N[(N[Cos[y], $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0011199999999999999 or 7.5999999999999999e-13 < x

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{1 + x} \]

   if -0.0011199999999999999 < x < 7.5999999999999999e-13

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 69.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]

   7. Applied rewrites 35.2%

      \[\leadsto \color{blue}{\cos y} - y \cdot z \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 71.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+19}:\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{elif}\;y \leq 3.6:\\ \;\;\;\;1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(\frac{\mathsf{fma}\left(1, -0.5, z\right)}{x}, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.4e+19)
   (* (- z) (sin y))
   (if (<= y 3.6)
     (+ 1.0 (+ x (* y (- (* -0.5 y) z))))
     (+ 1.0 (fma (/ (fma 1.0 -0.5 z) x) x x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.4e+19) {
		tmp = -z * sin(y);
	} else if (y <= 3.6) {
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)));
	} else {
		tmp = 1.0 + fma((fma(1.0, -0.5, z) / x), x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.4e+19)
		tmp = Float64(Float64(-z) * sin(y));
	elseif (y <= 3.6)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(-0.5 * y) - z))));
	else
		tmp = Float64(1.0 + fma(Float64(fma(1.0, -0.5, z) / x), x, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.4e+19], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6], N[(1.0 + N[(x + N[(y * N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(N[(1.0 * -0.5 + z), $MachinePrecision] / x), $MachinePrecision] * x + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4e19

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 28.0%

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

   6. Applied rewrites 28.0%

      \[\leadsto \color{blue}{\left(-z\right) \cdot \sin y} \]

   if -7.4e19 < y < 3.60000000000000009

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   if 3.60000000000000009 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 53.7%

      \[\leadsto 1 + x \cdot \color{blue}{\left(1 + \frac{y \cdot \left(-0.5 \cdot y - z\right)}{x}\right)} \]

   9. Applied rewrites 42.4%

      \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(1, -0.5, z\right)}{x}, x, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 71.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+19}:\\ \;\;\;\;1 + x \cdot \left(1 + \frac{1 \cdot \left(-0.5 \cdot 1 - z\right)}{x}\right)\\ \mathbf{elif}\;y \leq 3.6:\\ \;\;\;\;1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(\frac{\mathsf{fma}\left(1, -0.5, z\right)}{x}, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+19)
   (+ 1.0 (* x (+ 1.0 (/ (* 1.0 (- (* -0.5 1.0) z)) x))))
   (if (<= y 3.6)
     (+ 1.0 (+ x (* y (- (* -0.5 y) z))))
     (+ 1.0 (fma (/ (fma 1.0 -0.5 z) x) x x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+19) {
		tmp = 1.0 + (x * (1.0 + ((1.0 * ((-0.5 * 1.0) - z)) / x)));
	} else if (y <= 3.6) {
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)));
	} else {
		tmp = 1.0 + fma((fma(1.0, -0.5, z) / x), x, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+19)
		tmp = Float64(1.0 + Float64(x * Float64(1.0 + Float64(Float64(1.0 * Float64(Float64(-0.5 * 1.0) - z)) / x))));
	elseif (y <= 3.6)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(-0.5 * y) - z))));
	else
		tmp = Float64(1.0 + fma(Float64(fma(1.0, -0.5, z) / x), x, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+19], N[(1.0 + N[(x * N[(1.0 + N[(N[(1.0 * N[(N[(-0.5 * 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6], N[(1.0 + N[(x + N[(y * N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(N[(1.0 * -0.5 + z), $MachinePrecision] / x), $MachinePrecision] * x + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e19

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 53.7%

      \[\leadsto 1 + x \cdot \color{blue}{\left(1 + \frac{y \cdot \left(-0.5 \cdot y - z\right)}{x}\right)} \]

   9. Applied rewrites 42.3%

      \[\leadsto 1 + x \cdot \left(1 + \frac{1 \cdot \left(-0.5 \cdot 1 - z\right)}{x}\right) \]

   if -1.65e19 < y < 3.60000000000000009

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   if 3.60000000000000009 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 53.7%

      \[\leadsto 1 + x \cdot \color{blue}{\left(1 + \frac{y \cdot \left(-0.5 \cdot y - z\right)}{x}\right)} \]

   9. Applied rewrites 42.4%

      \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(1, -0.5, z\right)}{x}, x, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 70.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \mathsf{fma}\left(\frac{\mathsf{fma}\left(1, -0.5, z\right)}{x}, x, x\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.6:\\ \;\;\;\;1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (fma (/ (fma 1.0 -0.5 z) x) x x))))
   (if (<= y -9.2e+14)
     t_0
     (if (<= y 3.6) (+ 1.0 (+ x (* y (- (* -0.5 y) z)))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + fma((fma(1.0, -0.5, z) / x), x, x);
	double tmp;
	if (y <= -9.2e+14) {
		tmp = t_0;
	} else if (y <= 3.6) {
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + fma(Float64(fma(1.0, -0.5, z) / x), x, x))
	tmp = 0.0
	if (y <= -9.2e+14)
		tmp = t_0;
	elseif (y <= 3.6)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(-0.5 * y) - z))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(N[(N[(1.0 * -0.5 + z), $MachinePrecision] / x), $MachinePrecision] * x + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+14], t$95$0, If[LessEqual[y, 3.6], N[(1.0 + N[(x + N[(y * N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.2e14 or 3.60000000000000009 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 53.7%

      \[\leadsto 1 + x \cdot \color{blue}{\left(1 + \frac{y \cdot \left(-0.5 \cdot y - z\right)}{x}\right)} \]

   9. Applied rewrites 42.4%

      \[\leadsto 1 + \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(1, -0.5, z\right)}{x}, x, x\right)} \]

   if -9.2e14 < y < 3.60000000000000009

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 70.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+19}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-16}:\\ \;\;\;\;1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e+19)
   (+ 1.0 x)
   (if (<= y 1.15e-16) (+ 1.0 (+ x (* y (- (* -0.5 y) z)))) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+19) {
		tmp = 1.0 + x;
	} else if (y <= 1.15e-16) {
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)));
	} else {
		tmp = 1.0 + x;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.65d+19)) then
        tmp = 1.0d0 + x
    else if (y <= 1.15d-16) then
        tmp = 1.0d0 + (x + (y * (((-0.5d0) * y) - z)))
    else
        tmp = 1.0d0 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.65e+19) {
		tmp = 1.0 + x;
	} else if (y <= 1.15e-16) {
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)));
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.65e+19:
		tmp = 1.0 + x
	elif y <= 1.15e-16:
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)))
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.65e+19)
		tmp = Float64(1.0 + x);
	elseif (y <= 1.15e-16)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(-0.5 * y) - z))));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.65e+19)
		tmp = 1.0 + x;
	elseif (y <= 1.15e-16)
		tmp = 1.0 + (x + (y * ((-0.5 * y) - z)));
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.65e+19], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 1.15e-16], N[(1.0 + N[(x + N[(y * N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e19 or 1.15e-16 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{1 + x} \]

   if -1.65e19 < y < 1.15e-16

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 69.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+19}:\\ \;\;\;\;1 + x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;\left(x + 1\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+19)
   (+ 1.0 x)
   (if (<= y 8.5e+58) (- (+ x 1.0) (* z y)) (+ 1.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+19) {
		tmp = 1.0 + x;
	} else if (y <= 8.5e+58) {
		tmp = (x + 1.0) - (z * y);
	} else {
		tmp = 1.0 + x;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.95d+19)) then
        tmp = 1.0d0 + x
    else if (y <= 8.5d+58) then
        tmp = (x + 1.0d0) - (z * y)
    else
        tmp = 1.0d0 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+19) {
		tmp = 1.0 + x;
	} else if (y <= 8.5e+58) {
		tmp = (x + 1.0) - (z * y);
	} else {
		tmp = 1.0 + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+19:
		tmp = 1.0 + x
	elif y <= 8.5e+58:
		tmp = (x + 1.0) - (z * y)
	else:
		tmp = 1.0 + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+19)
		tmp = Float64(1.0 + x);
	elseif (y <= 8.5e+58)
		tmp = Float64(Float64(x + 1.0) - Float64(z * y));
	else
		tmp = Float64(1.0 + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+19)
		tmp = 1.0 + x;
	elseif (y <= 8.5e+58)
		tmp = (x + 1.0) - (z * y);
	else
		tmp = 1.0 + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+19], N[(1.0 + x), $MachinePrecision], If[LessEqual[y, 8.5e+58], N[(N[(x + 1.0), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(1.0 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.95e19 or 8.50000000000000015e58 < y

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{1 + x} \]

   if -1.95e19 < y < 8.50000000000000015e58

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 88.3%

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

   5. Taylor expanded in y around 0

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

   7. Applied rewrites 64.2%

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

Alternative 12: 62.3% accurate, 19.5× speedup

Math

\[\begin{array}{l} \\ 1 + x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ 1.0 x))

C

double code(double x, double y, double z) {
	return 1.0 + 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + x
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + x;
}

Python

def code(x, y, z):
	return 1.0 + x

Julia

function code(x, y, z)
	return Float64(1.0 + x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + x;
end

Wolfram

code[x_, y_, z_] := N[(1.0 + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]

4. Applied rewrites 62.3%

   \[\leadsto \color{blue}{1 + x} \]
5. Add Preprocessing

Alternative 13: 24.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -0.04:\\ \;\;\;\;-0.5\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- (+ x (cos y)) (* z (sin y))) -0.04) -0.5 1.0))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x + cos(y)) - (z * sin(y))) <= -0.04) {
		tmp = -0.5;
	} else {
		tmp = 1.0;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((x + cos(y)) - (z * sin(y))) <= (-0.04d0)) then
        tmp = -0.5d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x + Math.cos(y)) - (z * Math.sin(y))) <= -0.04) {
		tmp = -0.5;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x + math.cos(y)) - (z * math.sin(y))) <= -0.04:
		tmp = -0.5
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x + cos(y)) - Float64(z * sin(y))) <= -0.04)
		tmp = -0.5;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x + cos(y)) - (z * sin(y))) <= -0.04)
		tmp = -0.5;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -0.04], -0.5, 1.0]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -0.0400000000000000008

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 55.8%

      \[\leadsto \color{blue}{1 + \left(x + y \cdot \left(-0.5 \cdot y - z\right)\right)} \]

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 6.4%

      \[\leadsto {y}^{2} \cdot \color{blue}{\left(-1 \cdot \frac{z}{y} - 0.5\right)} \]

   9. Applied rewrites 4.6%

      \[\leadsto \left(\frac{z \cdot z}{1} - 0.5 \cdot 0.5\right) \cdot \frac{1}{\color{blue}{0.5 - \frac{z}{1}}} \]

   10. Taylor expanded in z around 0

       \[\leadsto \frac{-1}{2} \]

   12. Applied rewrites 3.8%

       \[\leadsto -0.5 \]

   if -0.0400000000000000008 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]

   4. Applied rewrites 62.3%

      \[\leadsto \color{blue}{1 + x} \]

   5. Taylor expanded in x around 0

      \[\leadsto 1 \]

   7. Applied rewrites 22.1%

      \[\leadsto 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 22.1% accurate, 72.9× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]

4. Applied rewrites 62.3%

   \[\leadsto \color{blue}{1 + x} \]

5. Taylor expanded in x around 0

   \[\leadsto 1 \]

7. Applied rewrites 22.1%

   \[\leadsto 1 \]
8. Add Preprocessing

Alternative 15: 2.5% accurate, 72.9× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 0.0)

C

double code(double x, double y, double z) {
	return 0.0;
}

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 0.0;
}

Python

def code(x, y, z):
	return 0.0

Julia

function code(x, y, z)
	return 0.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_] := 0.0

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]

4. Applied rewrites 62.3%

   \[\leadsto \color{blue}{1 + x} \]

5. Taylor expanded in x around 0

   \[\leadsto 1 \]

7. Applied rewrites 22.1%

   \[\leadsto 1 \]

9. Applied rewrites 2.5%

   \[\leadsto 0 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025159 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))