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

Percentage Accurate: 99.8% → 99.8%

Time: 7.3s

Alternatives: 5

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: 82.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+192} \lor \neg \left(z \leq 1.9 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e+192) (not (<= z 1.9e+118)))
   (+ (* z (cos y)) (* x y))
   (+ (* x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e+192) || !(z <= 1.9e+118)) {
		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 <= (-3.8d+192)) .or. (.not. (z <= 1.9d+118))) 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 <= -3.8e+192) || !(z <= 1.9e+118)) {
		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 <= -3.8e+192) or not (z <= 1.9e+118):
		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 <= -3.8e+192) || !(z <= 1.9e+118))
		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 <= -3.8e+192) || ~((z <= 1.9e+118)))
		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, -3.8e+192], N[Not[LessEqual[z, 1.9e+118]], $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 < -3.7999999999999999e192 or 1.90000000000000008e118 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 91.6%

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

   if -3.7999999999999999e192 < z < 1.90000000000000008e118

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 88.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+192} \lor \neg \left(z \leq 1.9 \cdot 10^{+118}\right):\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \]

Alternative 3: 77.3% 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 80.3%

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

3. Final simplification 80.3%

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

Alternative 4: 52.2% 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 80.3%

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

3. Taylor expanded in y around 0 55.6%

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

4. Final simplification 55.6%

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

Alternative 5: 16.5% 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. Step-by-step derivation

   1. add-cbrt-cube 75.0%

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

   2. pow3 75.0%

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

3. Applied egg-rr 75.0%

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

   1. *-commutative 75.0%

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

   2. unpow-prod-down 58.7%

      \[\leadsto \sqrt[3]{\color{blue}{{\sin y}^{3} \cdot {x}^{3}}} + z \cdot \cos y \]

5. Applied egg-rr 58.7%

   \[\leadsto \sqrt[3]{\color{blue}{{\sin y}^{3} \cdot {x}^{3}}} + z \cdot \cos y \]

6. Taylor expanded in y around 0 66.5%

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

   1. *-commutative 66.5%

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

8. Simplified 66.5%

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

9. Taylor expanded in y around inf 17.3%

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

    1. *-commutative 17.3%

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

11. Simplified 17.3%

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

12. Final simplification 17.3%

    \[\leadsto x \cdot y \]

Reproduce

herbie shell --seed 2023336 
(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))))