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

Percentage Accurate: 99.8% → 99.8%

Time: 7.2s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 2: 82.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18} \lor \neg \left(z \leq 1.96 \cdot 10^{+149}\right):\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.9e+18) (not (<= z 1.96e+149)))
   (+ (* z (cos y)) (* x y))
   (+ (* x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+18) || !(z <= 1.96e+149)) {
		tmp = (z * cos(y)) + (x * y);
	} else {
		tmp = (x * sin(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 <= (-1.9d+18)) .or. (.not. (z <= 1.96d+149))) then
        tmp = (z * cos(y)) + (x * y)
    else
        tmp = (x * sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.9e+18) || !(z <= 1.96e+149)) {
		tmp = (z * Math.cos(y)) + (x * y);
	} else {
		tmp = (x * Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.9e+18) or not (z <= 1.96e+149):
		tmp = (z * math.cos(y)) + (x * y)
	else:
		tmp = (x * math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.9e+18) || !(z <= 1.96e+149))
		tmp = Float64(Float64(z * cos(y)) + Float64(x * y));
	else
		tmp = Float64(Float64(x * sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.9e+18) || ~((z <= 1.96e+149)))
		tmp = (z * cos(y)) + (x * y);
	else
		tmp = (x * sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.9e+18], N[Not[LessEqual[z, 1.96e+149]], $MachinePrecision]], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e18 or 1.96e149 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 78.5%

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

   if -1.9e18 < z < 1.96e149

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 84.8%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18} \lor \neg \left(z \leq 1.96 \cdot 10^{+149}\right):\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \]

Alternative 3: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \lor \neg \left(y \leq 0.057\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.5) (not (<= y 0.057)))
   (* x (sin y))
   (+ (* x y) (* z (+ 1.0 (* -0.5 (* y y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5) || !(y <= 0.057)) {
		tmp = x * sin(y);
	} else {
		tmp = (x * y) + (z * (1.0 + (-0.5 * (y * 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 <= (-8.5d0)) .or. (.not. (y <= 0.057d0))) then
        tmp = x * sin(y)
    else
        tmp = (x * y) + (z * (1.0d0 + ((-0.5d0) * (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5) || !(y <= 0.057)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = (x * y) + (z * (1.0 + (-0.5 * (y * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.5) or not (y <= 0.057):
		tmp = x * math.sin(y)
	else:
		tmp = (x * y) + (z * (1.0 + (-0.5 * (y * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.5) || !(y <= 0.057))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(Float64(x * y) + Float64(z * Float64(1.0 + Float64(-0.5 * Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.5) || ~((y <= 0.057)))
		tmp = x * sin(y);
	else
		tmp = (x * y) + (z * (1.0 + (-0.5 * (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.5], N[Not[LessEqual[y, 0.057]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5 or 0.0570000000000000021 < y

   1. Initial program 99.6%

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

   2. Taylor expanded in y around 0 18.3%

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

      1. unpow2 18.3%

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

   4. Simplified 18.3%

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

   5. Taylor expanded in x around inf 50.1%

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

   if -8.5 < y < 0.0570000000000000021

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.3%

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

      1. unpow2 99.3%

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

   4. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.3%

      \[\leadsto \color{blue}{y \cdot x} + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \lor \neg \left(y \leq 0.057\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(1 + -0.5 \cdot \left(y \cdot y\right)\right)\\ \end{array} \]

Alternative 4: 77.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 76.8%

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

3. Final simplification 76.8%

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

Alternative 5: 53.5% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	return z + (x * y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 53.1%

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

3. Final simplification 53.1%

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

Alternative 6: 17.1% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x y))

C

double code(double x, double y, double z) {
	return x * 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 * y
end function

Java

public static double code(double x, double y, double z) {
	return x * y;
}

Python

def code(x, y, z):
	return x * y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 53.1%

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

3. Taylor expanded in y around inf 19.2%

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

4. Final simplification 19.2%

   \[\leadsto x \cdot y \]

Reproduce

herbie shell --seed 2023214 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))