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

Percentage Accurate: 99.8% → 99.8%

Time: 8.5s

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. Add Preprocessing

3. Final simplification 99.8%

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

Alternative 2: 83.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+66} \lor \neg \left(x \leq 6 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \cos y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+66) (not (<= x 6e+58)))
   (- (* x (cos y)) (* y z))
   (- x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+66) || !(x <= 6e+58)) {
		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 <= (-2.8d+66)) .or. (.not. (x <= 6d+58))) 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 <= -2.8e+66) || !(x <= 6e+58)) {
		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 <= -2.8e+66) or not (x <= 6e+58):
		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 <= -2.8e+66) || !(x <= 6e+58))
		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 <= -2.8e+66) || ~((x <= 6e+58)))
		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, -2.8e+66], N[Not[LessEqual[x, 6e+58]], $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 < -2.8000000000000001e66 or 6.0000000000000005e58 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 84.0%

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

   if -2.8000000000000001e66 < x < 6.0000000000000005e58

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 90.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+66} \lor \neg \left(x \leq 6 \cdot 10^{+58}\right):\\ \;\;\;\;x \cdot \cos y - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14} \lor \neg \left(y \leq 0.0038\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+14) (not (<= y 0.0038))) (* z (- (sin y))) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+14) || !(y <= 0.0038)) {
		tmp = z * -sin(y);
	} else {
		tmp = x - (y * z);
	}
	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 <= (-4.4d+14)) .or. (.not. (y <= 0.0038d0))) then
        tmp = z * -sin(y)
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+14) || !(y <= 0.0038)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.4e+14) or not (y <= 0.0038):
		tmp = z * -math.sin(y)
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.4e+14) || !(y <= 0.0038))
		tmp = Float64(z * Float64(-sin(y)));
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.4e+14) || ~((y <= 0.0038)))
		tmp = z * -sin(y);
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.4e+14], N[Not[LessEqual[y, 0.0038]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e14 or 0.00379999999999999999 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 57.1%

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

      1. add-cube-cbrt 56.3%

         \[\leadsto x - \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}} \]

      2. pow3 56.3%

         \[\leadsto x - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   5. Applied egg-rr 56.3%

      \[\leadsto x - \color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{3}} \]

   6. Taylor expanded in x around 0 51.9%

      \[\leadsto \color{blue}{-1 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \sin y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 51.9%

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

      2. pow-base-1 51.9%

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

      3. *-lft-identity 51.9%

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

      4. distribute-rgt-neg-out 51.9%

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

   8. Simplified 51.9%

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

   if -4.4e14 < y < 0.00379999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

   4. Taylor expanded in y around 0 97.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14} \lor \neg \left(y \leq 0.0038\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% 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. Add Preprocessing

3. Taylor expanded in y around 0 78.1%

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

4. Final simplification 78.1%

   \[\leadsto x - z \cdot \sin y \]
5. Add Preprocessing

Alternative 5: 52.3% 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. Add Preprocessing

3. Taylor expanded in y around 0 78.1%

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

4. Taylor expanded in y around 0 53.9%

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

5. Final simplification 53.9%

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

Alternative 6: 17.7% accurate, 51.8× speedup

Math

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

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 * Float64(-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. Add Preprocessing

3. Taylor expanded in y around 0 68.1%

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

4. Taylor expanded in x around 0 15.2%

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

   1. associate-*r* 15.2%

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

   2. neg-mul-1 15.2%

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

   3. *-commutative 15.2%

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

6. Simplified 15.2%

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

7. Final simplification 15.2%

   \[\leadsto y \cdot \left(-z\right) \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))