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

Percentage Accurate: 99.9% → 99.9%

Time: 9.8s

Alternatives: 12

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

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma(sin(y), -z, (cos(y) + x));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]
2. Step-by-step derivation

   1. lift--.f64 N/A

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

   2. sub-flip N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. distribute-rgt-neg-in N/A

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

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, \mathsf{neg}\left(z\right), x + \cos y\right)} \]

   8. lower-neg.f64 99.9

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

   9. lift-+.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 99.9

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

3. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, \cos y + x\right)} \]
4. Add Preprocessing

Alternative 2: 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 3: 99.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;\cos y - t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))) (t_1 (- (+ x 1.0) t_0)))
   (if (<= x -7.6e-10) t_1 (if (<= x 2.1e-16) (- (cos y) t_0) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = (x + 1.0) - t_0;
	double tmp;
	if (x <= -7.6e-10) {
		tmp = t_1;
	} else if (x <= 2.1e-16) {
		tmp = cos(y) - t_0;
	} else {
		tmp = t_1;
	}
	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 = z * sin(y)
    t_1 = (x + 1.0d0) - t_0
    if (x <= (-7.6d-10)) then
        tmp = t_1
    else if (x <= 2.1d-16) then
        tmp = cos(y) - t_0
    else
        tmp = t_1
    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 + 1.0) - t_0;
	double tmp;
	if (x <= -7.6e-10) {
		tmp = t_1;
	} else if (x <= 2.1e-16) {
		tmp = Math.cos(y) - t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = (x + 1.0) - t_0
	tmp = 0
	if x <= -7.6e-10:
		tmp = t_1
	elif x <= 2.1e-16:
		tmp = math.cos(y) - t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(Float64(x + 1.0) - t_0)
	tmp = 0.0
	if (x <= -7.6e-10)
		tmp = t_1;
	elseif (x <= 2.1e-16)
		tmp = Float64(cos(y) - t_0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = (x + 1.0) - t_0;
	tmp = 0.0;
	if (x <= -7.6e-10)
		tmp = t_1;
	elseif (x <= 2.1e-16)
		tmp = cos(y) - t_0;
	else
		tmp = t_1;
	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 + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[x, -7.6e-10], t$95$1, If[LessEqual[x, 2.1e-16], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5999999999999996e-10 or 2.1000000000000001e-16 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 87.7%

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

   if -7.5999999999999996e-10 < x < 2.1000000000000001e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]
   3. Step-by-step derivation

      1. lower-cos.f64 58.6

         \[\leadsto \cos y - z \cdot \sin y \]

   4. Applied rewrites 58.6%

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

Alternative 4: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ t_1 := z \cdot \sin y\\ t_2 := t\_0 - t\_1\\ t_3 := \left(x + 1\right) - t\_1\\ \mathbf{if}\;t\_2 \leq -0.999992:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 0.98:\\ \;\;\;\;\left(1 - \frac{y \cdot z}{1 + x}\right) \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y)))
        (t_1 (* z (sin y)))
        (t_2 (- t_0 t_1))
        (t_3 (- (+ x 1.0) t_1)))
   (if (<= t_2 -0.999992)
     t_3
     (if (<= t_2 0.98) (* (- 1.0 (/ (* y z) (+ 1.0 x))) t_0) t_3))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double t_1 = z * sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = (x + 1.0) - t_1;
	double tmp;
	if (t_2 <= -0.999992) {
		tmp = t_3;
	} else if (t_2 <= 0.98) {
		tmp = (1.0 - ((y * z) / (1.0 + x))) * t_0;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_0 = x + cos(y)
    t_1 = z * sin(y)
    t_2 = t_0 - t_1
    t_3 = (x + 1.0d0) - t_1
    if (t_2 <= (-0.999992d0)) then
        tmp = t_3
    else if (t_2 <= 0.98d0) then
        tmp = (1.0d0 - ((y * z) / (1.0d0 + x))) * t_0
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.cos(y);
	double t_1 = z * Math.sin(y);
	double t_2 = t_0 - t_1;
	double t_3 = (x + 1.0) - t_1;
	double tmp;
	if (t_2 <= -0.999992) {
		tmp = t_3;
	} else if (t_2 <= 0.98) {
		tmp = (1.0 - ((y * z) / (1.0 + x))) * t_0;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	t_1 = z * math.sin(y)
	t_2 = t_0 - t_1
	t_3 = (x + 1.0) - t_1
	tmp = 0
	if t_2 <= -0.999992:
		tmp = t_3
	elif t_2 <= 0.98:
		tmp = (1.0 - ((y * z) / (1.0 + x))) * t_0
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	t_1 = Float64(z * sin(y))
	t_2 = Float64(t_0 - t_1)
	t_3 = Float64(Float64(x + 1.0) - t_1)
	tmp = 0.0
	if (t_2 <= -0.999992)
		tmp = t_3;
	elseif (t_2 <= 0.98)
		tmp = Float64(Float64(1.0 - Float64(Float64(y * z) / Float64(1.0 + x))) * t_0);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	t_1 = z * sin(y);
	t_2 = t_0 - t_1;
	t_3 = (x + 1.0) - t_1;
	tmp = 0.0;
	if (t_2 <= -0.999992)
		tmp = t_3;
	elseif (t_2 <= 0.98)
		tmp = (1.0 - ((y * z) / (1.0 + x))) * t_0;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + 1.0), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -0.999992], t$95$3, If[LessEqual[t$95$2, 0.98], N[(N[(1.0 - N[(N[(y * z), $MachinePrecision] / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -0.99999199999999999 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

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

   4. Applied rewrites 87.7%

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

   if -0.99999199999999999 < (-.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. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-flip N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, \mathsf{neg}\left(z\right), x + \cos y\right)} \]

      8. lower-neg.f64 99.9

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

      9. lift-+.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 99.9

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

   3. Applied rewrites 99.9%

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

      1. lift-fma.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-+.f64 N/A

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

      4. +-commutative N/A

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

      5. lift-cos.f64 N/A

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

      6. *-commutative N/A

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

      7. lift-neg.f64 N/A

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

      8. fp-cancel-sub-sign-inv N/A

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

      9. lift-sin.f64 N/A

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

      10. lift-sin.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. sub-to-mult N/A

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 69.1

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

   8. Applied rewrites 69.1%

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

Alternative 5: 92.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + \cos y\right) - t\_0\\ t_2 := \left(x + 1\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.98:\\ \;\;\;\;\cos y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1000000.0) t_2 (if (<= t_1 0.98) (- (cos y) (* z y)) 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 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.98) {
		tmp = cos(y) - (z * y);
	} 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 <= (-1000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.98d0) then
        tmp = cos(y) - (z * y)
    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 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.98) {
		tmp = Math.cos(y) - (z * y);
	} 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 <= -1000000.0:
		tmp = t_2
	elif t_1 <= 0.98:
		tmp = math.cos(y) - (z * y)
	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 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.98)
		tmp = Float64(cos(y) - Float64(z * y));
	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 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 0.98)
		tmp = cos(y) - (z * y);
	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, -1000000.0], t$95$2, If[LessEqual[t$95$1, 0.98], N[(N[Cos[y], $MachinePrecision] - N[(z * y), $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))) < -1e6 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

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

   4. Applied rewrites 87.7%

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

   if -1e6 < (-.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 x around 0

      \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]
   3. Step-by-step derivation

      1. lower-cos.f64 58.6

         \[\leadsto \cos y - z \cdot \sin y \]

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in y around 0

      \[\leadsto \cos y - z \cdot \color{blue}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

Alternative 6: 72.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-10}:\\ \;\;\;\;x - -1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;\cos y - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e-10)
   (- x -1.0)
   (if (<= x 1.02e-14) (- (cos y) (* z y)) (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-10) {
		tmp = x - -1.0;
	} else if (x <= 1.02e-14) {
		tmp = cos(y) - (z * y);
	} else {
		tmp = x - -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 <= (-7.8d-10)) then
        tmp = x - (-1.0d0)
    else if (x <= 1.02d-14) then
        tmp = cos(y) - (z * y)
    else
        tmp = x - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-10) {
		tmp = x - -1.0;
	} else if (x <= 1.02e-14) {
		tmp = Math.cos(y) - (z * y);
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.8e-10:
		tmp = x - -1.0
	elif x <= 1.02e-14:
		tmp = math.cos(y) - (z * y)
	else:
		tmp = x - -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.8e-10)
		tmp = Float64(x - -1.0);
	elseif (x <= 1.02e-14)
		tmp = Float64(cos(y) - Float64(z * y));
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.8e-10)
		tmp = x - -1.0;
	elseif (x <= 1.02e-14)
		tmp = cos(y) - (z * y);
	else
		tmp = x - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.8e-10], N[(x - -1.0), $MachinePrecision], If[LessEqual[x, 1.02e-14], N[(N[Cos[y], $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x - -1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.7999999999999999e-10 or 1.02e-14 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. lower-+.f64 61.9

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

   4. Applied rewrites 61.9%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - -1 \]

      5. lower--.f64 61.9

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

   6. Applied rewrites 61.9%

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

   if -7.7999999999999999e-10 < x < 1.02e-14

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\cos y} - z \cdot \sin y \]
   3. Step-by-step derivation

      1. lower-cos.f64 58.6

         \[\leadsto \cos y - z \cdot \sin y \]

   4. Applied rewrites 58.6%

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

   5. Taylor expanded in y around 0

      \[\leadsto \cos y - z \cdot \color{blue}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 34.7%

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

Alternative 7: 70.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -8e+141) t_0 (if (<= z 1.15e+167) (- x -1.0) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -8e+141) {
		tmp = t_0;
	} else if (z <= 1.15e+167) {
		tmp = x - -1.0;
	} 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 = sin(y) * -z
    if (z <= (-8d+141)) then
        tmp = t_0
    else if (z <= 1.15d+167) then
        tmp = x - (-1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -8e+141) {
		tmp = t_0;
	} else if (z <= 1.15e+167) {
		tmp = x - -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -8e+141:
		tmp = t_0
	elif z <= 1.15e+167:
		tmp = x - -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -8e+141)
		tmp = t_0;
	elseif (z <= 1.15e+167)
		tmp = Float64(x - -1.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -8e+141)
		tmp = t_0;
	elseif (z <= 1.15e+167)
		tmp = x - -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -8e+141], t$95$0, If[LessEqual[z, 1.15e+167], N[(x - -1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.00000000000000014e141 or 1.14999999999999994e167 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-sin.f64 27.9

         \[\leadsto -1 \cdot \left(z \cdot \sin y\right) \]

   4. Applied rewrites 27.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \sin y\right) \]

      3. lift-*.f64 N/A

         \[\leadsto \mathsf{neg}\left(z \cdot \sin y\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\sin y \cdot z\right) \]

      5. distribute-rgt-neg-out N/A

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

      6. lift-neg.f64 N/A

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

      7. lower-*.f64 27.9

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

   6. Applied rewrites 27.9%

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

   if -8.00000000000000014e141 < z < 1.14999999999999994e167

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. lower-+.f64 61.9

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

   4. Applied rewrites 61.9%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - -1 \]

      5. lower--.f64 61.9

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

   6. Applied rewrites 61.9%

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

Alternative 8: 69.4% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+161}:\\ \;\;\;\;x - -1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+33}:\\ \;\;\;\;1 + \left(x + -1 \cdot \left(y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+161)
   (- x -1.0)
   (if (<= y 6e+33) (+ 1.0 (+ x (* -1.0 (* y z)))) (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+161) {
		tmp = x - -1.0;
	} else if (y <= 6e+33) {
		tmp = 1.0 + (x + (-1.0 * (y * z)));
	} else {
		tmp = x - -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 (y <= (-4.5d+161)) then
        tmp = x - (-1.0d0)
    else if (y <= 6d+33) then
        tmp = 1.0d0 + (x + ((-1.0d0) * (y * z)))
    else
        tmp = x - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+161) {
		tmp = x - -1.0;
	} else if (y <= 6e+33) {
		tmp = 1.0 + (x + (-1.0 * (y * z)));
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+161:
		tmp = x - -1.0
	elif y <= 6e+33:
		tmp = 1.0 + (x + (-1.0 * (y * z)))
	else:
		tmp = x - -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+161)
		tmp = Float64(x - -1.0);
	elseif (y <= 6e+33)
		tmp = Float64(1.0 + Float64(x + Float64(-1.0 * Float64(y * z))));
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.5e+161)
		tmp = x - -1.0;
	elseif (y <= 6e+33)
		tmp = 1.0 + (x + (-1.0 * (y * z)));
	else
		tmp = x - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+161], N[(x - -1.0), $MachinePrecision], If[LessEqual[y, 6e+33], N[(1.0 + N[(x + N[(-1.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - -1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999992e161 or 5.99999999999999967e33 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. lower-+.f64 61.9

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

   4. Applied rewrites 61.9%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - -1 \]

      5. lower--.f64 61.9

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

   6. Applied rewrites 61.9%

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

   if -4.49999999999999992e161 < y < 5.99999999999999967e33

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

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

      1. lower-+.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 63.5

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

   4. Applied rewrites 63.5%

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

Alternative 9: 67.3% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-10}:\\ \;\;\;\;x - -1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;1 + -1 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.5e-10)
   (- x -1.0)
   (if (<= x 1.02e-14) (+ 1.0 (* -1.0 (* y z))) (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-10) {
		tmp = x - -1.0;
	} else if (x <= 1.02e-14) {
		tmp = 1.0 + (-1.0 * (y * z));
	} else {
		tmp = x - -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 <= (-6.5d-10)) then
        tmp = x - (-1.0d0)
    else if (x <= 1.02d-14) then
        tmp = 1.0d0 + ((-1.0d0) * (y * z))
    else
        tmp = x - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.5e-10) {
		tmp = x - -1.0;
	} else if (x <= 1.02e-14) {
		tmp = 1.0 + (-1.0 * (y * z));
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.5e-10:
		tmp = x - -1.0
	elif x <= 1.02e-14:
		tmp = 1.0 + (-1.0 * (y * z))
	else:
		tmp = x - -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.5e-10)
		tmp = Float64(x - -1.0);
	elseif (x <= 1.02e-14)
		tmp = Float64(1.0 + Float64(-1.0 * Float64(y * z)));
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.5e-10)
		tmp = x - -1.0;
	elseif (x <= 1.02e-14)
		tmp = 1.0 + (-1.0 * (y * z));
	else
		tmp = x - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.5e-10], N[(x - -1.0), $MachinePrecision], If[LessEqual[x, 1.02e-14], N[(1.0 + N[(-1.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - -1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5000000000000003e-10 or 1.02e-14 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. lower-+.f64 61.9

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

   4. Applied rewrites 61.9%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - -1 \]

      5. lower--.f64 61.9

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

   6. Applied rewrites 61.9%

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

   if -6.5000000000000003e-10 < x < 1.02e-14

   1. Initial program 99.9%

      \[\left(x + \cos y\right) - z \cdot \sin y \]
   2. Step-by-step derivation

      1. lift--.f64 N/A

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

      2. sub-to-mult N/A

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

      3. lift-+.f64 N/A

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

      4. sum-to-mult N/A

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

      5. associate-*r* N/A

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

      6. lower-*.f64 N/A

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

   3. Applied rewrites 92.4%

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

   4. Taylor expanded in y around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-+.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-+.f64 N/A

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

      11. lower-/.f64 52.7

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

   6. Applied rewrites 52.7%

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

   7. Taylor expanded in x around 0

      \[\leadsto 1 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 29.4

         \[\leadsto 1 + -1 \cdot \left(y \cdot z\right) \]

   9. Applied rewrites 29.4%

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

Alternative 10: 62.3% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+210}:\\ \;\;\;\;-1 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.8e+210) (* -1.0 (* z y)) (- x -1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.8e+210) {
		tmp = -1.0 * (z * y);
	} else {
		tmp = x - -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 (z <= (-9.8d+210)) then
        tmp = (-1.0d0) * (z * y)
    else
        tmp = x - (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.8e+210) {
		tmp = -1.0 * (z * y);
	} else {
		tmp = x - -1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.8e+210:
		tmp = -1.0 * (z * y)
	else:
		tmp = x - -1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.8e+210)
		tmp = Float64(-1.0 * Float64(z * y));
	else
		tmp = Float64(x - -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.8e+210)
		tmp = -1.0 * (z * y);
	else
		tmp = x - -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.8e+210], N[(-1.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x - -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000013e210

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-sin.f64 27.9

         \[\leadsto -1 \cdot \left(z \cdot \sin y\right) \]

   4. Applied rewrites 27.9%

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

   5. Taylor expanded in y around 0

      \[\leadsto -1 \cdot \left(z \cdot y\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 10.8%

      \[\leadsto -1 \cdot \left(z \cdot y\right) \]

   if -9.80000000000000013e210 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 + x} \]
   3. Step-by-step derivation

      1. lower-+.f64 61.9

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

   4. Applied rewrites 61.9%

      \[\leadsto \color{blue}{1 + x} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - -1 \]

      5. lower--.f64 61.9

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

   6. Applied rewrites 61.9%

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

Alternative 11: 61.9% accurate, 20.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - -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 = x - (-1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0

   \[\leadsto \color{blue}{1 + x} \]
3. Step-by-step derivation

   1. lower-+.f64 61.9

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

4. Applied rewrites 61.9%

   \[\leadsto \color{blue}{1 + x} \]
5. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. add-flip N/A

      \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

   4. metadata-eval N/A

      \[\leadsto x - -1 \]

   5. lower--.f64 61.9

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

6. Applied rewrites 61.9%

   \[\leadsto x - \color{blue}{-1} \]
7. Add Preprocessing

Alternative 12: 21.7% 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

   \[\leadsto \color{blue}{1 + x} \]
3. Step-by-step derivation

   1. lower-+.f64 61.9

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

4. Applied rewrites 61.9%

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

5. Taylor expanded in x around 0

   \[\leadsto 1 \]
6. Step-by-step derivation

7. Applied rewrites 21.7%

   \[\leadsto 1 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025142 
(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))))