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

Percentage Accurate: 99.8% → 99.8%

Time: 16.3s

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 99.7%

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

2. Final simplification 99.7%

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

Alternative 2: 71.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+51} \lor \neg \left(x \leq -5.4 \cdot 10^{-39}\right) \land \left(x \leq -6.8 \cdot 10^{-123} \lor \neg \left(x \leq 4.2 \cdot 10^{-113}\right)\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+51)
         (and (not (<= x -5.4e-39))
              (or (<= x -6.8e-123) (not (<= x 4.2e-113)))))
   (* x (cos y))
   (* z (- (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+51) || (!(x <= -5.4e-39) && ((x <= -6.8e-123) || !(x <= 4.2e-113)))) {
		tmp = x * cos(y);
	} else {
		tmp = 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 <= (-1.05d+51)) .or. (.not. (x <= (-5.4d-39))) .and. (x <= (-6.8d-123)) .or. (.not. (x <= 4.2d-113))) then
        tmp = x * cos(y)
    else
        tmp = z * -sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+51) || (!(x <= -5.4e-39) && ((x <= -6.8e-123) || !(x <= 4.2e-113)))) {
		tmp = x * Math.cos(y);
	} else {
		tmp = z * -Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+51) or (not (x <= -5.4e-39) and ((x <= -6.8e-123) or not (x <= 4.2e-113))):
		tmp = x * math.cos(y)
	else:
		tmp = z * -math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+51) || (!(x <= -5.4e-39) && ((x <= -6.8e-123) || !(x <= 4.2e-113))))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(z * Float64(-sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e+51) || (~((x <= -5.4e-39)) && ((x <= -6.8e-123) || ~((x <= 4.2e-113)))))
		tmp = x * cos(y);
	else
		tmp = z * -sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+51], And[N[Not[LessEqual[x, -5.4e-39]], $MachinePrecision], Or[LessEqual[x, -6.8e-123], N[Not[LessEqual[x, 4.2e-113]], $MachinePrecision]]]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0500000000000001e51 or -5.4000000000000001e-39 < x < -6.8000000000000001e-123 or 4.2e-113 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 83.3%

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

   if -1.0500000000000001e51 < x < -5.4000000000000001e-39 or -6.8000000000000001e-123 < x < 4.2e-113

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 82.0%

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

      1. associate-*r* 82.0%

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

      2. neg-mul-1 82.0%

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

   4. Simplified 82.0%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+51} \lor \neg \left(x \leq -5.4 \cdot 10^{-39}\right) \land \left(x \leq -6.8 \cdot 10^{-123} \lor \neg \left(x \leq 4.2 \cdot 10^{-113}\right)\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]

Alternative 3: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-27} \lor \neg \left(z \leq 7800000000\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3e-27) (not (<= z 7800000000.0)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3e-27) || !(z <= 7800000000.0)) {
		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 <= (-3d-27)) .or. (.not. (z <= 7800000000.0d0))) 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 <= -3e-27) || !(z <= 7800000000.0)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3e-27) or not (z <= 7800000000.0):
		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 <= -3e-27) || !(z <= 7800000000.0))
		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 <= -3e-27) || ~((z <= 7800000000.0)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3e-27], N[Not[LessEqual[z, 7800000000.0]], $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 < -3.0000000000000001e-27 or 7.8e9 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 90.9%

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

   if -3.0000000000000001e-27 < z < 7.8e9

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 91.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-27} \lor \neg \left(z \leq 7800000000\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 4: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9000000 \lor \neg \left(y \leq 2.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(-0.5 \cdot \left(y \cdot \left(x \cdot y\right)\right) - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9000000.0) (not (<= y 2.5e-8)))
   (* x (cos y))
   (+ x (- (* -0.5 (* y (* x y))) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9000000.0) || !(y <= 2.5e-8)) {
		tmp = x * cos(y);
	} else {
		tmp = x + ((-0.5 * (y * (x * y))) - (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 <= (-9000000.0d0)) .or. (.not. (y <= 2.5d-8))) then
        tmp = x * cos(y)
    else
        tmp = x + (((-0.5d0) * (y * (x * y))) - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9000000.0) || !(y <= 2.5e-8)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + ((-0.5 * (y * (x * y))) - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9000000.0) or not (y <= 2.5e-8):
		tmp = x * math.cos(y)
	else:
		tmp = x + ((-0.5 * (y * (x * y))) - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9000000.0) || !(y <= 2.5e-8))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(Float64(-0.5 * Float64(y * Float64(x * y))) - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9000000.0) || ~((y <= 2.5e-8)))
		tmp = x * cos(y);
	else
		tmp = x + ((-0.5 * (y * (x * y))) - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9000000.0], N[Not[LessEqual[y, 2.5e-8]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(-0.5 * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e6 or 2.4999999999999999e-8 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 47.8%

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

   if -9e6 < y < 2.4999999999999999e-8

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.0%

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

      1. +-commutative 99.0%

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

      2. mul-1-neg 99.0%

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

      3. unsub-neg 99.0%

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

      4. *-commutative 99.0%

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

      5. unpow2 99.0%

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

      6. associate-*l* 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9000000 \lor \neg \left(y \leq 2.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(-0.5 \cdot \left(y \cdot \left(x \cdot y\right)\right) - y \cdot z\right)\\ \end{array} \]

Alternative 5: 52.4% 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 99.7%

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

2. Taylor expanded in y around 0 46.3%

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

   1. mul-1-neg 46.3%

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

   2. unsub-neg 46.3%

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

4. Simplified 46.3%

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

5. Final simplification 46.3%

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

Alternative 6: 38.7% 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 99.7%

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

2. Taylor expanded in y around 0 76.3%

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

3. Taylor expanded in x around inf 35.3%

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

4. Final simplification 35.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023285 
(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))))