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

Percentage Accurate: 99.9% → 99.9%

Time: 10.2s

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

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

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
3. Add Preprocessing

Alternative 2: 98.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ t_1 := \left(x + \cos y\right) - t\_0\\ \mathbf{if}\;t\_1 \leq -2000000 \lor \neg \left(t\_1 \leq 200\right):\\ \;\;\;\;x - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))) (t_1 (- (+ x (cos y)) t_0)))
   (if (or (<= t_1 -2000000.0) (not (<= t_1 200.0))) (- x t_0) (+ (cos y) x))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double t_1 = (x + cos(y)) - t_0;
	double tmp;
	if ((t_1 <= -2000000.0) || !(t_1 <= 200.0)) {
		tmp = x - t_0;
	} else {
		tmp = cos(y) + 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 = z * sin(y)
    t_1 = (x + cos(y)) - t_0
    if ((t_1 <= (-2000000.0d0)) .or. (.not. (t_1 <= 200.0d0))) then
        tmp = x - t_0
    else
        tmp = cos(y) + x
    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 tmp;
	if ((t_1 <= -2000000.0) || !(t_1 <= 200.0)) {
		tmp = x - t_0;
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	t_1 = (x + math.cos(y)) - t_0
	tmp = 0
	if (t_1 <= -2000000.0) or not (t_1 <= 200.0):
		tmp = x - t_0
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	t_1 = Float64(Float64(x + cos(y)) - t_0)
	tmp = 0.0
	if ((t_1 <= -2000000.0) || !(t_1 <= 200.0))
		tmp = Float64(x - t_0);
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	t_1 = (x + cos(y)) - t_0;
	tmp = 0.0;
	if ((t_1 <= -2000000.0) || ~((t_1 <= 200.0)))
		tmp = x - t_0;
	else
		tmp = cos(y) + x;
	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]}, If[Or[LessEqual[t$95$1, -2000000.0], N[Not[LessEqual[t$95$1, 200.0]], $MachinePrecision]], N[(x - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < -2e6 or 200 < (-.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.4%

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

   if -2e6 < (-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))) < 200

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 98.2

         \[\leadsto \cos y + x \]

   5. Applied rewrites 98.2%

      \[\leadsto \color{blue}{\cos y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + \cos y\right) - z \cdot \sin y \leq -2000000 \lor \neg \left(\left(x + \cos y\right) - z \cdot \sin y \leq 200\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \lor \neg \left(z \leq 4.5 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7) (not (<= z 4.5e-28)))
   (- (+ x 1.0) (* z (sin y)))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7) || !(z <= 4.5e-28)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = cos(y) + 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 ((z <= (-3.7d0)) .or. (.not. (z <= 4.5d-28))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7) || !(z <= 4.5e-28)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7) or not (z <= 4.5e-28):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7) || !(z <= 4.5e-28))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7) || ~((z <= 4.5e-28)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7], N[Not[LessEqual[z, 4.5e-28]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.7000000000000002 or 4.4999999999999998e-28 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 99.6%

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

   if -3.7000000000000002 < z < 4.4999999999999998e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 100.0

         \[\leadsto \cos y + x \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\cos y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \lor \neg \left(z \leq 4.5 \cdot 10^{-28}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+80} \lor \neg \left(z \leq 1.3 \cdot 10^{+165}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.9e+80) (not (<= z 1.3e+165)))
   (* (- z) (sin y))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.9e+80) || !(z <= 1.3e+165)) {
		tmp = -z * sin(y);
	} else {
		tmp = cos(y) + 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 ((z <= (-3.9d+80)) .or. (.not. (z <= 1.3d+165))) then
        tmp = -z * sin(y)
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.9e+80) || !(z <= 1.3e+165)) {
		tmp = -z * Math.sin(y);
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.9e+80) or not (z <= 1.3e+165):
		tmp = -z * math.sin(y)
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.9e+80) || !(z <= 1.3e+165))
		tmp = Float64(Float64(-z) * sin(y));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.9e+80) || ~((z <= 1.3e+165)))
		tmp = -z * sin(y);
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.9e+80], N[Not[LessEqual[z, 1.3e+165]], $MachinePrecision]], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999999e80 or 1.3000000000000001e165 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lift-sin.f64 72.2

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

   5. Applied rewrites 72.2%

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

   if -3.89999999999999999e80 < z < 1.3000000000000001e165

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 92.1

         \[\leadsto \cos y + x \]

   5. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\cos y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+80} \lor \neg \left(z \leq 1.3 \cdot 10^{+165}\right):\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+17} \lor \neg \left(y \leq 2.45 \cdot 10^{+29}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.8e+17) (not (<= y 2.45e+29)))
   (+ (cos y) x)
   (fma (- (* -0.5 y) z) y (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.8e+17) || !(y <= 2.45e+29)) {
		tmp = cos(y) + x;
	} else {
		tmp = fma(((-0.5 * y) - z), y, (x - -1.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.8e+17) || !(y <= 2.45e+29))
		tmp = Float64(cos(y) + x);
	else
		tmp = fma(Float64(Float64(-0.5 * y) - z), y, Float64(x - -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.8e+17], N[Not[LessEqual[y, 2.45e+29]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8e17 or 2.4500000000000001e29 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. lift-cos.f64 62.9

         \[\leadsto \cos y + x \]

   5. Applied rewrites 62.9%

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

   if -8.8e17 < y < 2.4500000000000001e29

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. +-commutative N/A

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

      10. metadata-eval N/A

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

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

          \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot y - z, y, x - \left(\mathsf{neg}\left(1\right)\right) \cdot 1\right) \]

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 98.5

          \[\leadsto \mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right) \]

   5. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+17} \lor \neg \left(y \leq 2.45 \cdot 10^{+29}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+53} \lor \neg \left(y \leq 2.6 \cdot 10^{+61}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.82e+53) (not (<= y 2.6e+61)))
   (- x -1.0)
   (fma (- (* (- (* 0.16666666666666666 (* z y)) 0.5) y) z) y (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.82e+53) || !(y <= 2.6e+61)) {
		tmp = x - -1.0;
	} else {
		tmp = fma(((((0.16666666666666666 * (z * y)) - 0.5) * y) - z), y, (x - -1.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.82e+53) || !(y <= 2.6e+61))
		tmp = Float64(x - -1.0);
	else
		tmp = fma(Float64(Float64(Float64(Float64(0.16666666666666666 * Float64(z * y)) - 0.5) * y) - z), y, Float64(x - -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.82e+53], N[Not[LessEqual[y, 2.6e+61]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(N[(N[(N[(N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.81999999999999999e53 or 2.59999999999999973e61 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 43.6

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

   5. Applied rewrites 43.6%

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

   if -1.81999999999999999e53 < y < 2.59999999999999973e61

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

         \[\leadsto \left(x + y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right)\right) + \color{blue}{1} \]

      2. +-commutative N/A

         \[\leadsto \left(y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + x\right) + 1 \]

      3. associate-+l+ N/A

         \[\leadsto y \cdot \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) + \color{blue}{\left(x + 1\right)} \]

      4. *-commutative N/A

         \[\leadsto \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) \cdot y + \left(\color{blue}{x} + 1\right) \]

      5. +-commutative N/A

         \[\leadsto \left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z\right) \cdot y + \left(1 + \color{blue}{x}\right) \]

      6. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z, \color{blue}{y}, 1 + x\right) \]

      7. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y \cdot \left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) - z, y, 1 + x\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(y \cdot z\right) - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      13. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, 1 + x\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, x + 1\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, x + 1 \cdot 1\right) \]

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

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, x - \left(\mathsf{neg}\left(1\right)\right) \cdot 1\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, x - -1 \cdot 1\right) \]

      18. metadata-eval N/A

          \[\leadsto \mathsf{fma}\left(\left(\frac{1}{6} \cdot \left(z \cdot y\right) - \frac{1}{2}\right) \cdot y - z, y, x - -1\right) \]

   5. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+53} \lor \neg \left(y \leq 2.6 \cdot 10^{+61}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\left(0.16666666666666666 \cdot \left(z \cdot y\right) - 0.5\right) \cdot y - z, y, x - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 7.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+78} \lor \neg \left(y \leq 3.3 \cdot 10^{+47}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4e+78) (not (<= y 3.3e+47)))
   (- x -1.0)
   (fma (- (* -0.5 y) z) y (- x -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e+78) || !(y <= 3.3e+47)) {
		tmp = x - -1.0;
	} else {
		tmp = fma(((-0.5 * y) - z), y, (x - -1.0));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4e+78) || !(y <= 3.3e+47))
		tmp = Float64(x - -1.0);
	else
		tmp = fma(Float64(Float64(-0.5 * y) - z), y, Float64(x - -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4e+78], N[Not[LessEqual[y, 3.3e+47]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(N[(N[(-0.5 * y), $MachinePrecision] - z), $MachinePrecision] * y + N[(x - -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.40000000000000009e78 or 3.2999999999999999e47 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 42.8

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

   5. Applied rewrites 42.8%

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

   if -5.40000000000000009e78 < y < 3.2999999999999999e47

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. *-commutative N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. +-commutative N/A

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

      10. metadata-eval N/A

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

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

          \[\leadsto \mathsf{fma}\left(\frac{-1}{2} \cdot y - z, y, x - \left(\mathsf{neg}\left(1\right)\right) \cdot 1\right) \]

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 88.8

          \[\leadsto \mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right) \]

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+78} \lor \neg \left(y \leq 3.3 \cdot 10^{+47}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot y - z, y, x - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.7% accurate, 9.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+66} \lor \neg \left(y \leq 3.2 \cdot 10^{+30}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+66) (not (<= y 3.2e+30)))
   (- x -1.0)
   (- x (fma z y -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+66) || !(y <= 3.2e+30)) {
		tmp = x - -1.0;
	} else {
		tmp = x - fma(z, y, -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+66) || !(y <= 3.2e+30))
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(x - fma(z, y, -1.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+66], N[Not[LessEqual[y, 3.2e+30]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(x - N[(z * y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e66 or 3.19999999999999973e30 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 42.1

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

   5. Applied rewrites 42.1%

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

   if -1.4e66 < y < 3.19999999999999973e30

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 91.6

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

   5. Applied rewrites 91.6%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 91.6

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

   7. Applied rewrites 91.6%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+66} \lor \neg \left(y \leq 3.2 \cdot 10^{+30}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(z, y, -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 10.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -155 \lor \neg \left(x \leq 5.4 \cdot 10^{-69}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -155.0) (not (<= x 5.4e-69))) (- x -1.0) (- 1.0 (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -155.0) || !(x <= 5.4e-69)) {
		tmp = x - -1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-155.0d0)) .or. (.not. (x <= 5.4d-69))) then
        tmp = x - (-1.0d0)
    else
        tmp = 1.0d0 - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -155.0) || !(x <= 5.4e-69)) {
		tmp = x - -1.0;
	} else {
		tmp = 1.0 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -155.0) or not (x <= 5.4e-69):
		tmp = x - -1.0
	else:
		tmp = 1.0 - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -155.0) || !(x <= 5.4e-69))
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(1.0 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -155.0) || ~((x <= 5.4e-69)))
		tmp = x - -1.0;
	else
		tmp = 1.0 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -155.0], N[Not[LessEqual[x, 5.4e-69]], $MachinePrecision]], N[(x - -1.0), $MachinePrecision], N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -155 or 5.3999999999999995e-69 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 79.5

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

   5. Applied rewrites 79.5%

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

   if -155 < x < 5.3999999999999995e-69

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 47.3

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

   5. Applied rewrites 47.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 - \color{blue}{y \cdot z} \]
   7. Step-by-step derivation

      1. lower--.f64 N/A

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

      2. *-commutative N/A

         \[\leadsto 1 - z \cdot y \]

      3. lift-*.f64 47.1

         \[\leadsto 1 - z \cdot y \]

   8. Applied rewrites 47.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -155 \lor \neg \left(x \leq 5.4 \cdot 10^{-69}\right):\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;1 - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.7% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+202}:\\ \;\;\;\;x - -1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 9.5e+202) (- x -1.0) (- x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 9.5e+202) {
		tmp = x - -1.0;
	} else {
		tmp = x - (z * y);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 9.5d+202) then
        tmp = x - (-1.0d0)
    else
        tmp = x - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 9.5e+202) {
		tmp = x - -1.0;
	} else {
		tmp = x - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 9.5e+202:
		tmp = x - -1.0
	else:
		tmp = x - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 9.5e+202)
		tmp = Float64(x - -1.0);
	else
		tmp = Float64(x - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 9.5e+202)
		tmp = x - -1.0;
	else
		tmp = x - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 9.5e+202], N[(x - -1.0), $MachinePrecision], N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 9.50000000000000059e202

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto x - -1 \cdot 1 \]

      5. metadata-eval N/A

         \[\leadsto x - -1 \]

      6. lower--.f64 65.6

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

   5. Applied rewrites 65.6%

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

   if 9.50000000000000059e202 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. metadata-eval N/A

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

      6. lower--.f64 N/A

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

      7. metadata-eval N/A

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

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

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

      9. *-lft-identity N/A

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

      10. lower--.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 40.2

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

   5. Applied rewrites 40.2%

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

      1. lift--.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate--l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lower-fma.f64 40.2

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

   7. Applied rewrites 40.2%

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

   8. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto x - z \cdot y \]

      2. lower-*.f64 40.2

         \[\leadsto x - z \cdot y \]

   10. Applied rewrites 40.2%

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

Alternative 11: 61.8% accurate, 53.0× 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. Add Preprocessing

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. metadata-eval N/A

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

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

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

   4. metadata-eval N/A

      \[\leadsto x - -1 \cdot 1 \]

   5. metadata-eval N/A

      \[\leadsto x - -1 \]

   6. lower--.f64 61.5

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

5. Applied rewrites 61.5%

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

Alternative 12: 43.4% accurate, 212.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 42.8%

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

Reproduce

herbie shell --seed 2025043 
(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))))