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

Percentage Accurate: 99.8% → 99.8%

Time: 7.6s

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 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 75.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -72000000 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -72000000.0) (not (<= y 0.035)))
   (* x (cos y))
   (+ x (* y (+ z (* y (* x -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -72000000.0) || !(y <= 0.035)) {
		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 <= (-72000000.0d0)) .or. (.not. (y <= 0.035d0))) 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 <= -72000000.0) || !(y <= 0.035)) {
		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 <= -72000000.0) or not (y <= 0.035):
		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 <= -72000000.0) || !(y <= 0.035))
		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 <= -72000000.0) || ~((y <= 0.035)))
		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, -72000000.0], N[Not[LessEqual[y, 0.035]], $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 < -7.2e7 or 0.035000000000000003 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 53.5%

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

   if -7.2e7 < y < 0.035000000000000003

   1. Initial program 100.0%

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

   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%

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

      2. *-commutative 97.5%

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

      3. associate-*r* 97.5%

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

      4. unpow2 97.5%

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

      5. associate-*r* 97.5%

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

      6. distribute-rgt-out 97.5%

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

      7. *-commutative 97.5%

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

      8. *-commutative 97.5%

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

   5. Simplified 97.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -72000000 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+61} \lor \neg \left(z \leq 3.35 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.2e+61) (not (<= z 3.35e+22))) (* z (sin y)) (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.2e+61) || !(z <= 3.35e+22)) {
		tmp = 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 <= (-2.2d+61)) .or. (.not. (z <= 3.35d+22))) then
        tmp = 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 <= -2.2e+61) || !(z <= 3.35e+22)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.2e+61) or not (z <= 3.35e+22):
		tmp = z * math.sin(y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.2e+61) || !(z <= 3.35e+22))
		tmp = 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 <= -2.2e+61) || ~((z <= 3.35e+22)))
		tmp = z * sin(y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.2e+61], N[Not[LessEqual[z, 3.35e+22]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e61 or 3.3500000000000001e22 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 71.4%

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

   if -2.2e61 < z < 3.3500000000000001e22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 85.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+61} \lor \neg \left(z \leq 3.35 \cdot 10^{+22}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.6% 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 99.9%

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

3. Taylor expanded in y around 0 48.5%

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

   1. +-commutative 48.5%

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

5. Simplified 48.5%

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

6. Final simplification 48.5%

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

Alternative 5: 17.2% 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 99.9%

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

3. Taylor expanded in y around 0 48.5%

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

   1. +-commutative 48.5%

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

5. Simplified 48.5%

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

6. Taylor expanded in y around inf 15.9%

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

7. Final simplification 15.9%

   \[\leadsto y \cdot z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024048 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))