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

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 8

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, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \cos y, z \cdot \sin y\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return fma(x, cos(y), (z * sin(y)));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y + z \cdot \sin y \]
2. Step-by-step derivation

   1. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(x, \cos y, z \cdot \sin y\right) \]

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 81.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+158} \lor \neg \left(x \leq 10^{+182}\right):\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e+158) (not (<= x 1e+182)))
   (+ (* x (cos y)) (* y z))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e+158) || !(x <= 1e+182)) {
		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 <= (-2d+158)) .or. (.not. (x <= 1d+182))) 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 <= -2e+158) || !(x <= 1e+182)) {
		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 <= -2e+158) or not (x <= 1e+182):
		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 <= -2e+158) || !(x <= 1e+182))
		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 <= -2e+158) || ~((x <= 1e+182)))
		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, -2e+158], N[Not[LessEqual[x, 1e+182]], $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 < -1.99999999999999991e158 or 1.0000000000000001e182 < x

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 83.1%

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

   if -1.99999999999999991e158 < x < 1.0000000000000001e182

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 86.5%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+158} \lor \neg \left(x \leq 10^{+182}\right):\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]

Alternative 4: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12000 \lor \neg \left(y \leq 0.0029\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + -0.5 \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -12000.0) (not (<= y 0.0029)))
   (* z (sin y))
   (+ (* y z) (+ x (* -0.5 (* y (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -12000.0) || !(y <= 0.0029)) {
		tmp = z * sin(y);
	} else {
		tmp = (y * z) + (x + (-0.5 * (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 ((y <= (-12000.0d0)) .or. (.not. (y <= 0.0029d0))) then
        tmp = z * sin(y)
    else
        tmp = (y * z) + (x + ((-0.5d0) * (y * (x * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -12000.0) || !(y <= 0.0029)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = (y * z) + (x + (-0.5 * (y * (x * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -12000.0) or not (y <= 0.0029):
		tmp = z * math.sin(y)
	else:
		tmp = (y * z) + (x + (-0.5 * (y * (x * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -12000.0) || !(y <= 0.0029))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(Float64(y * z) + Float64(x + Float64(-0.5 * Float64(y * Float64(x * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -12000.0) || ~((y <= 0.0029)))
		tmp = z * sin(y);
	else
		tmp = (y * z) + (x + (-0.5 * (y * (x * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -12000.0], N[Not[LessEqual[y, 0.0029]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x + N[(-0.5 * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -12000 or 0.0029 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 55.4%

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

   if -12000 < y < 0.0029

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. fma-def 99.3%

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

      2. unpow2 99.3%

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

      3. associate-*l* 99.3%

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

   5. Simplified 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.5, y \cdot \left(y \cdot x\right), x\right)} + z \cdot y \]
   6. Step-by-step derivation

      1. fma-udef 99.3%

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

   7. Applied egg-rr 99.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12000 \lor \neg \left(y \leq 0.0029\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + -0.5 \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 5: 76.8% 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. Taylor expanded in y around 0 78.9%

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

3. Final simplification 78.9%

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

Alternative 6: 40.9% accurate, 40.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 7.5e+167) x (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+167) {
		tmp = x;
	} else {
		tmp = 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 (z <= 7.5d+167) then
        tmp = x
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 7.5e+167) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7.5e+167:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7.5e+167)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 7.5e+167)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7.5e+167], x, N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.4999999999999995e167

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 53.5%

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

   3. Taylor expanded in y around 0 43.9%

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

   if 7.4999999999999995e167 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.8%

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

   3. Taylor expanded in y around 0 38.6%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+167}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7: 52.8% 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 53.0%

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

3. Final simplification 53.0%

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

Alternative 8: 39.5% 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 53.0%

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

3. Taylor expanded in y around 0 39.7%

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

4. Final simplification 39.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023199 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))