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

Percentage Accurate: 99.8% → 99.8%

Time: 8.7s

Alternatives: 5

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: 85.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-42} \lor \neg \left(z \leq 118000000000\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-42) (not (<= z 118000000000.0)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-42) || !(z <= 118000000000.0)) {
		tmp = x + (z * sin(y));
	} else {
		tmp = x * cos(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 ((z <= (-4.4d-42)) .or. (.not. (z <= 118000000000.0d0))) then
        tmp = x + (z * sin(y))
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-42) || !(z <= 118000000000.0)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-42) or not (z <= 118000000000.0):
		tmp = x + (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e-42) || !(z <= 118000000000.0))
		tmp = Float64(x + Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.4e-42) || ~((z <= 118000000000.0)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-42], N[Not[LessEqual[z, 118000000000.0]], $MachinePrecision]], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000001e-42 or 1.18e11 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 88.9%

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

   if -4.4000000000000001e-42 < z < 1.18e11

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.0%

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

   3. Taylor expanded in x around inf 84.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-42} \lor \neg \left(z \leq 118000000000\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 3: 74.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27} \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+27) (not (<= y 0.015)))
   (* x (cos y))
   (+ x (* y (+ z (* y (* x -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+27) || !(y <= 0.015)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	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 <= (-2.4d+27)) .or. (.not. (y <= 0.015d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+27) || !(y <= 0.015)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+27) or not (y <= 0.015):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * (x * -0.5))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+27) || !(y <= 0.015))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+27) || ~((y <= 0.015)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * (x * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+27], N[Not[LessEqual[y, 0.015]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999998e27 or 0.014999999999999999 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 30.6%

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

   3. Taylor expanded in x around inf 48.7%

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

   if -2.39999999999999998e27 < y < 0.014999999999999999

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.5%

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

   3. Taylor expanded in y around 0 97.5%

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

      1. *-commutative 97.5%

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

      2. *-commutative 97.5%

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

      3. associate-*r* 97.5%

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

      4. *-lft-identity 97.5%

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

      5. pow-base-1 97.5%

         \[\leadsto x + \left({y}^{2} \cdot \left(\left(\color{blue}{{1}^{0.3333333333333333}} \cdot x\right) \cdot -0.5\right) + y \cdot z\right) \]

      6. metadata-eval 97.5%

         \[\leadsto x + \left({y}^{2} \cdot \left(\left({1}^{0.3333333333333333} \cdot x\right) \cdot \color{blue}{\left(-0.3333333333333333 + -0.16666666666666666\right)}\right) + y \cdot z\right) \]

      7. distribute-rgt-out 97.5%

         \[\leadsto x + \left({y}^{2} \cdot \color{blue}{\left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right)} + y \cdot z\right) \]

      8. unpow2 97.5%

         \[\leadsto x + \left(\color{blue}{\left(y \cdot y\right)} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) + y \cdot z\right) \]

      9. associate-*l* 97.5%

         \[\leadsto x + \left(\color{blue}{y \cdot \left(y \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right)\right)} + y \cdot z\right) \]

      10. distribute-lft-out 97.5%

          \[\leadsto x + \color{blue}{y \cdot \left(y \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot x\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot x\right)\right) + z\right)} \]

      11. distribute-rgt-out 97.5%

          \[\leadsto x + y \cdot \left(y \cdot \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot x\right) \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)} + z\right) \]

      12. pow-base-1 97.5%

          \[\leadsto x + y \cdot \left(y \cdot \left(\left(\color{blue}{1} \cdot x\right) \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right) + z\right) \]

      13. *-lft-identity 97.5%

          \[\leadsto x + y \cdot \left(y \cdot \left(\color{blue}{x} \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right) + z\right) \]

      14. metadata-eval 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+27} \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \]

Alternative 4: 52.5% 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 60.4%

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

3. Taylor expanded in y around 0 46.0%

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

   1. *-commutative 46.0%

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

5. Simplified 46.0%

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

6. Final simplification 46.0%

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

Alternative 5: 39.0% accurate, 207.0× 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

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

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

2. Taylor expanded in y around 0 60.4%

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

3. Taylor expanded in y around 0 37.1%

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

4. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023334 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))