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

Percentage Accurate: 99.8% → 99.8%

Time: 8.2s

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. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto x \cdot \sin y + z \cdot \cos y \]
4. Add Preprocessing

Alternative 2: 80.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 9.5e+109) (+ (* x (sin y)) z) (+ (* z (cos y)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 9.5e+109) {
		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 <= 9.5d+109) 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 <= 9.5e+109) {
		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 <= 9.5e+109:
		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 <= 9.5e+109)
		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 <= 9.5e+109)
		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, 9.5e+109], 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 < 9.49999999999999972e109

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 86.5%

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

   if 9.49999999999999972e109 < z

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 91.4%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% 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. Add Preprocessing

3. Taylor expanded in y around 0 83.8%

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

4. Final simplification 83.8%

   \[\leadsto x \cdot \sin y + z \]
5. Add Preprocessing

Alternative 4: 40.9% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+137} \lor \neg \left(x \leq 9.6 \cdot 10^{+112}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e+137) (not (<= x 9.6e+112))) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+137) || !(x <= 9.6e+112)) {
		tmp = x * y;
	} else {
		tmp = 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 ((x <= (-1.02d+137)) .or. (.not. (x <= 9.6d+112))) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+137) || !(x <= 9.6e+112)) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.02e+137) or not (x <= 9.6e+112):
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.02e+137) || !(x <= 9.6e+112))
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.02e+137) || ~((x <= 9.6e+112)))
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.02e+137], N[Not[LessEqual[x, 9.6e+112]], $MachinePrecision]], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -1.02000000000000004e137 or 9.6e112 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.8%

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

   4. Taylor expanded in y around 0 45.6%

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

   5. Taylor expanded in x around inf 33.3%

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

      1. *-commutative 33.3%

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

   7. Simplified 33.3%

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

   if -1.02000000000000004e137 < x < 9.6e112

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.4%

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

   4. Taylor expanded in y around 0 56.7%

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

   5. Taylor expanded in z around -inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. *-commutative 56.5%

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

      3. distribute-rgt-neg-in 56.5%

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

      4. fma-neg 56.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{x \cdot y}{z}, -1\right)} \cdot \left(-z\right) \]

      5. *-commutative 56.5%

         \[\leadsto \mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot x}}{z}, -1\right) \cdot \left(-z\right) \]

      6. associate-/l* 55.9%

         \[\leadsto \mathsf{fma}\left(-1, \color{blue}{y \cdot \frac{x}{z}}, -1\right) \cdot \left(-z\right) \]

      7. metadata-eval 55.9%

         \[\leadsto \mathsf{fma}\left(-1, y \cdot \frac{x}{z}, \color{blue}{-1}\right) \cdot \left(-z\right) \]

   7. Simplified 55.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, y \cdot \frac{x}{z}, -1\right) \cdot \left(-z\right)} \]

   8. Taylor expanded in y around 0 51.1%

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

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+137} \lor \neg \left(x \leq 9.6 \cdot 10^{+112}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.0% 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. Add Preprocessing

3. Taylor expanded in y around 0 83.8%

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

4. Taylor expanded in y around 0 53.2%

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

5. Final simplification 53.2%

   \[\leadsto z + x \cdot y \]
6. Add Preprocessing

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. Add Preprocessing

3. Taylor expanded in y around 0 83.8%

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

4. Taylor expanded in y around 0 53.2%

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

5. Taylor expanded in x around inf 16.9%

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

   1. *-commutative 16.9%

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

7. Simplified 16.9%

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

8. Final simplification 16.9%

   \[\leadsto x \cdot y \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024060 
(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))))