Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.3s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \cos y + z \cdot \sin y \end{array} \]

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

real(8) function code(x, y, z)
    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: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos y + z \cdot \sin y \end{array} \]

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

real(8) function code(x, y, z)
    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: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos y + z \cdot \sin y \end{array} \]

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

real(8) function code(x, y, z)
    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 99.8%

   \[x \cdot \cos y + z \cdot \sin y \]

2. Final simplification 99.8%

   \[\leadsto x \cdot \cos y + z \cdot \sin y \]

Alternative 2: 83.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+90} \lor \neg \left(x \leq 2.9 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.1e+90) (not (<= x 2.9e+116)))
   (+ (* x (cos y)) (* y z))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.1e+90) || !(x <= 2.9e+116)) {
		tmp = (x * cos(y)) + (y * z);
	} else {
		tmp = x + (z * sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4.1d+90)) .or. (.not. (x <= 2.9d+116))) then
        tmp = (x * cos(y)) + (y * z)
    else
        tmp = x + (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.1e+90) || !(x <= 2.9e+116)) {
		tmp = (x * Math.cos(y)) + (y * z);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.1e+90) or not (x <= 2.9e+116):
		tmp = (x * math.cos(y)) + (y * z)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.1e+90) || !(x <= 2.9e+116))
		tmp = Float64(Float64(x * cos(y)) + Float64(y * z));
	else
		tmp = Float64(x + Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.1e+90) || ~((x <= 2.9e+116)))
		tmp = (x * cos(y)) + (y * z);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.1e+90], N[Not[LessEqual[x, 2.9e+116]], $MachinePrecision]], N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.10000000000000042e90 or 2.9000000000000001e116 < x

   1. Initial program 99.8%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in y around 0 84.7%

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

   if -4.10000000000000042e90 < x < 2.9000000000000001e116

   1. Initial program 99.8%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in y around 0 85.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+90} \lor \neg \left(x \leq 2.9 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]

Alternative 3: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -520 \lor \neg \left(y \leq 0.048\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -520.0) (not (<= y 0.048)))
   (* z (sin y))
   (+ (* y z) (* x (+ 1.0 (* -0.5 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -520.0) || !(y <= 0.048)) {
		tmp = z * sin(y);
	} else {
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-520.0d0)) .or. (.not. (y <= 0.048d0))) then
        tmp = z * sin(y)
    else
        tmp = (y * z) + (x * (1.0d0 + ((-0.5d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -520.0) || !(y <= 0.048)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -520.0) or not (y <= 0.048):
		tmp = z * math.sin(y)
	else:
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -520.0) || !(y <= 0.048))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(Float64(y * z) + Float64(x * Float64(1.0 + Float64(-0.5 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -520.0) || ~((y <= 0.048)))
		tmp = z * sin(y);
	else
		tmp = (y * z) + (x * (1.0 + (-0.5 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -520.0], N[Not[LessEqual[y, 0.048]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -520 or 0.048000000000000001 < y

   1. Initial program 99.6%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in x around 0 47.0%

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

   if -520 < y < 0.048000000000000001

   1. Initial program 100.0%

      \[x \cdot \cos y + z \cdot \sin y \]

   2. Taylor expanded in y around 0 99.3%

      \[\leadsto x \cdot \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)} + z \cdot \sin y \]
   3. Step-by-step derivation

      1. unpow2 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -520 \lor \neg \left(y \leq 0.048\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + x \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 76.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ x + z \cdot \sin y \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y + z \cdot \sin y \]

2. Taylor expanded in y around 0 77.0%

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

3. Final simplification 77.0%

   \[\leadsto x + z \cdot \sin y \]

Alternative 5: 52.2% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (y * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y + z \cdot \sin y \]

2. Taylor expanded in y around 0 56.2%

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

3. Final simplification 56.2%

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

Alternative 6: 17.0% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ y \cdot z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z)
	return Float64(y * z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * z), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y + z \cdot \sin y \]

2. Taylor expanded in y around 0 61.1%

   \[\leadsto x \cdot \color{blue}{\left(1 + -0.5 \cdot {y}^{2}\right)} + z \cdot \sin y \]
3. Step-by-step derivation

   1. unpow2 61.1%

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

4. Simplified 61.1%

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

5. Taylor expanded in y around 0 54.8%

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

6. Taylor expanded in x around 0 24.1%

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

7. Final simplification 24.1%

   \[\leadsto y \cdot z \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))