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

Percentage Accurate: 99.8% → 99.8%

Time: 7.6s

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 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 80.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.4e+116) (+ (* x (sin y)) z) (+ (* z (cos y)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.4e+116) {
		tmp = (x * sin(y)) + z;
	} else {
		tmp = (z * cos(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 (z <= 3.4d+116) then
        tmp = (x * sin(y)) + z
    else
        tmp = (z * cos(y)) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.4e+116) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = (z * Math.cos(y)) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.4e+116:
		tmp = (x * math.sin(y)) + z
	else:
		tmp = (z * math.cos(y)) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.4e+116)
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = Float64(Float64(z * cos(y)) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.4e+116)
		tmp = (x * sin(y)) + z;
	else
		tmp = (z * cos(y)) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.4e+116], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.40000000000000023e116

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.7%

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

   if 3.40000000000000023e116 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 84.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.4 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \]

Alternative 3: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-6} \lor \neg \left(y \leq 520000000000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot \left(y \cdot z\right)\right) + \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e-6) (not (<= y 520000000000.0)))
   (* x (sin y))
   (+ (* -0.5 (* y (* y z))) (+ z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-6) || !(y <= 520000000000.0)) {
		tmp = x * sin(y);
	} else {
		tmp = (-0.5 * (y * (y * z))) + (z + (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 <= (-2.3d-6)) .or. (.not. (y <= 520000000000.0d0))) then
        tmp = x * sin(y)
    else
        tmp = ((-0.5d0) * (y * (y * z))) + (z + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-6) || !(y <= 520000000000.0)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = (-0.5 * (y * (y * z))) + (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e-6) or not (y <= 520000000000.0):
		tmp = x * math.sin(y)
	else:
		tmp = (-0.5 * (y * (y * z))) + (z + (x * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e-6) || !(y <= 520000000000.0))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(Float64(-0.5 * Float64(y * Float64(y * z))) + Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.3e-6) || ~((y <= 520000000000.0)))
		tmp = x * sin(y);
	else
		tmp = (-0.5 * (y * (y * z))) + (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e-6], N[Not[LessEqual[y, 520000000000.0]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 * N[(y * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e-6 or 5.2e11 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 63.5%

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

   3. Taylor expanded in x around inf 60.8%

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

   if -2.3e-6 < y < 5.2e11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.9%

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

      1. expm1-log1p-u 96.0%

         \[\leadsto -0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({y}^{2} \cdot z\right)\right)} + \left(y \cdot x + z\right) \]

      2. expm1-udef 95.8%

         \[\leadsto -0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({y}^{2} \cdot z\right)} - 1\right)} + \left(y \cdot x + z\right) \]

      3. unpow2 95.8%

         \[\leadsto -0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot y\right)} \cdot z\right)} - 1\right) + \left(y \cdot x + z\right) \]

      4. associate-*l* 95.8%

         \[\leadsto -0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(y \cdot z\right)}\right)} - 1\right) + \left(y \cdot x + z\right) \]

   4. Applied egg-rr 95.8%

      \[\leadsto -0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(y \cdot z\right)\right)} - 1\right)} + \left(y \cdot x + z\right) \]
   5. Step-by-step derivation

      1. expm1-def 96.0%

         \[\leadsto -0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(y \cdot z\right)\right)\right)} + \left(y \cdot x + z\right) \]

      2. expm1-log1p 98.9%

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

   6. Simplified 98.9%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-6} \lor \neg \left(y \leq 520000000000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(y \cdot \left(y \cdot z\right)\right) + \left(z + x \cdot y\right)\\ \end{array} \]

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 99.9%

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

2. Taylor expanded in y around 0 82.9%

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

3. Final simplification 82.9%

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

Alternative 5: 52.3% 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 99.9%

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

2. Taylor expanded in y around 0 56.8%

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

3. Final simplification 56.8%

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

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 99.9%

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

2. Taylor expanded in y around 0 56.8%

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

3. Taylor expanded in y around inf 17.1%

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

4. Final simplification 17.1%

   \[\leadsto x \cdot y \]

Reproduce

herbie shell --seed 2023238 
(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))))