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

Percentage Accurate: 99.8% → 99.8%

Time: 6.8s

Alternatives: 7

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-155} \lor \neg \left(x \leq 3.5 \cdot 10^{+32}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e-155) (not (<= x 3.5e+32)))
   (+ z (* x (sin y)))
   (+ (* z (cos y)) (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e-155) || !(x <= 3.5e+32)) {
		tmp = z + (x * sin(y));
	} 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 ((x <= (-2.3d-155)) .or. (.not. (x <= 3.5d+32))) then
        tmp = z + (x * sin(y))
    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 ((x <= -2.3e-155) || !(x <= 3.5e+32)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = (z * Math.cos(y)) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.3e-155) or not (x <= 3.5e+32):
		tmp = z + (x * math.sin(y))
	else:
		tmp = (z * math.cos(y)) + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e-155) || !(x <= 3.5e+32))
		tmp = Float64(z + Float64(x * sin(y)));
	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 ((x <= -2.3e-155) || ~((x <= 3.5e+32)))
		tmp = z + (x * sin(y));
	else
		tmp = (z * cos(y)) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e-155], N[Not[LessEqual[x, 3.5e+32]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000005e-155 or 3.5000000000000001e32 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 87.8%

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

   if -2.30000000000000005e-155 < x < 3.5000000000000001e32

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-155} \lor \neg \left(x \leq 3.5 \cdot 10^{+32}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y + x \cdot y\\ \end{array} \]

Alternative 4: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0018 \lor \neg \left(y \leq 1.35 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(1 + \left(y \cdot y\right) \cdot -0.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0018) (not (<= y 1.35e-6)))
   (* x (sin y))
   (+ (* x y) (* z (+ 1.0 (* (* y y) -0.5))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0018) || !(y <= 1.35e-6)) {
		tmp = x * sin(y);
	} else {
		tmp = (x * y) + (z * (1.0 + ((y * y) * -0.5)));
	}
	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 <= (-0.0018d0)) .or. (.not. (y <= 1.35d-6))) then
        tmp = x * sin(y)
    else
        tmp = (x * y) + (z * (1.0d0 + ((y * y) * (-0.5d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0018) || !(y <= 1.35e-6)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = (x * y) + (z * (1.0 + ((y * y) * -0.5)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0018) or not (y <= 1.35e-6):
		tmp = x * math.sin(y)
	else:
		tmp = (x * y) + (z * (1.0 + ((y * y) * -0.5)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0018) || !(y <= 1.35e-6))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(Float64(x * y) + Float64(z * Float64(1.0 + Float64(Float64(y * y) * -0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0018) || ~((y <= 1.35e-6)))
		tmp = x * sin(y);
	else
		tmp = (x * y) + (z * (1.0 + ((y * y) * -0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0018], N[Not[LessEqual[y, 1.35e-6]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 + N[(N[(y * y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0018 or 1.34999999999999999e-6 < y

   1. Initial program 99.6%

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

      1. expm1-log1p-u 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in y around 0 16.5%

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

      1. *-commutative 16.5%

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

      2. unpow2 16.5%

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

   6. Simplified 16.5%

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

   7. Taylor expanded in x around inf 49.9%

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

   if -0.0018 < y < 1.34999999999999999e-6

   1. Initial program 100.0%

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

      1. expm1-log1p-u 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0018 \lor \neg \left(y \leq 1.35 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + z \cdot \left(1 + \left(y \cdot y\right) \cdot -0.5\right)\\ \end{array} \]

Alternative 5: 77.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 76.6%

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

3. Final simplification 76.6%

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

Alternative 6: 52.1% 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 7: 17.0% 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 15.4%

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

4. Final simplification 15.4%

   \[\leadsto x \cdot y \]

Reproduce

herbie shell --seed 2023213 
(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))))