Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Percentage Accurate: 99.8% → 99.8%

Time: 7.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(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 * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(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 * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(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 * sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 82.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-136} \lor \neg \left(x \leq 2.3 \cdot 10^{-104}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e-136) (not (<= x 2.3e-104)))
   (+ (* x (sin y)) z)
   (+ (* z (cos y)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-136) || !(x <= 2.3e-104)) {
		tmp = (x * sin(y)) + z;
	} else {
		tmp = (z * cos(y)) + (x * 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 <= (-2.7d-136)) .or. (.not. (x <= 2.3d-104))) then
        tmp = (x * sin(y)) + z
    else
        tmp = (z * cos(y)) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-136) || !(x <= 2.3e-104)) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = (z * Math.cos(y)) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e-136) or not (x <= 2.3e-104):
		tmp = (x * math.sin(y)) + z
	else:
		tmp = (z * math.cos(y)) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e-136) || !(x <= 2.3e-104))
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = Float64(Float64(z * cos(y)) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.7e-136) || ~((x <= 2.3e-104)))
		tmp = (x * sin(y)) + z;
	else
		tmp = (z * cos(y)) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e-136], N[Not[LessEqual[x, 2.3e-104]], $MachinePrecision]], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6999999999999998e-136 or 2.2999999999999999e-104 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.5%

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

   if -2.6999999999999998e-136 < x < 2.2999999999999999e-104

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-136} \lor \neg \left(x \leq 2.3 \cdot 10^{-104}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-6} \lor \neg \left(y \leq 0.0195\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e-6) (not (<= y 0.0195))) (* x (sin y)) (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-6) || !(y <= 0.0195)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (x * 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 <= (-1.9d-6)) .or. (.not. (y <= 0.0195d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e-6) || !(y <= 0.0195)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e-6) or not (y <= 0.0195):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e-6) || !(y <= 0.0195))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e-6) || ~((y <= 0.0195)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e-6], N[Not[LessEqual[y, 0.0195]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e-6 or 0.0195 < y

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 60.4%

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

   4. Taylor expanded in x around inf 57.3%

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

   if -1.9e-6 < y < 0.0195

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.6%

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

   4. Taylor expanded in y around 0 98.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-6} \lor \neg \left(y \leq 0.0195\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 78.6%

   \[\leadsto x \cdot \sin y + \color{blue}{z} \]
4. Add Preprocessing

Alternative 5: 52.2% accurate, 41.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + (x * 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 = z + (x * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 78.6%

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

4. Taylor expanded in y around 0 50.4%

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

5. Final simplification 50.4%

   \[\leadsto z + x \cdot y \]
6. Add Preprocessing

Alternative 6: 38.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 78.6%

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

4. Taylor expanded in y around 0 49.7%

   \[\leadsto \color{blue}{y \cdot \left(x + -0.16666666666666666 \cdot \left(x \cdot {y}^{2}\right)\right)} + z \]

5. Taylor expanded in y around 0 38.5%

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

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))