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

Percentage Accurate: 99.8% → 99.8%

Time: 6.5s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 85.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-22} \lor \neg \left(x \leq 2.85 \cdot 10^{-61}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-22) (not (<= x 2.85e-61)))
   (+ z (* x (sin y)))
   (* (cos y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-22) || !(x <= 2.85e-61)) {
		tmp = z + (x * sin(y));
	} else {
		tmp = cos(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 ((x <= (-2.8d-22)) .or. (.not. (x <= 2.85d-61))) then
        tmp = z + (x * sin(y))
    else
        tmp = cos(y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-22) || !(x <= 2.85e-61)) {
		tmp = z + (x * Math.sin(y));
	} else {
		tmp = Math.cos(y) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-22) or not (x <= 2.85e-61):
		tmp = z + (x * math.sin(y))
	else:
		tmp = math.cos(y) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-22) || !(x <= 2.85e-61))
		tmp = Float64(z + Float64(x * sin(y)));
	else
		tmp = Float64(cos(y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e-22) || ~((x <= 2.85e-61)))
		tmp = z + (x * sin(y));
	else
		tmp = cos(y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-22], N[Not[LessEqual[x, 2.85e-61]], $MachinePrecision]], N[(z + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999995e-22 or 2.85000000000000003e-61 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.1%

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

   if -2.79999999999999995e-22 < x < 2.85000000000000003e-61

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 88.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-22} \lor \neg \left(x \leq 2.85 \cdot 10^{-61}\right):\\ \;\;\;\;z + x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot z\\ \end{array} \]

Alternative 4: 73.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00045 \lor \neg \left(y \leq 2.3 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00045) (not (<= y 2.3e+24))) (* x (sin y)) (+ z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00045) || !(y <= 2.3e+24)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * x);
	}
	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 <= (-0.00045d0)) .or. (.not. (y <= 2.3d+24))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00045) || !(y <= 2.3e+24)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00045) or not (y <= 2.3e+24):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00045) || !(y <= 2.3e+24))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00045) || ~((y <= 2.3e+24)))
		tmp = x * sin(y);
	else
		tmp = z + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00045], N[Not[LessEqual[y, 2.3e+24]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e-4 or 2.2999999999999999e24 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 50.6%

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

   if -4.4999999999999999e-4 < y < 2.2999999999999999e24

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.7%

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

      1. +-commutative 95.7%

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

   4. Simplified 95.7%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00045 \lor \neg \left(y \leq 2.3 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot x\\ \end{array} \]

Alternative 5: 73.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-85} \lor \neg \left(z \leq 3.9 \cdot 10^{-19}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-85) (not (<= z 3.9e-19))) (* (cos y) z) (* x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-85) || !(z <= 3.9e-19)) {
		tmp = cos(y) * z;
	} else {
		tmp = x * sin(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 <= (-5d-85)) .or. (.not. (z <= 3.9d-19))) then
        tmp = cos(y) * z
    else
        tmp = x * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-85) || !(z <= 3.9e-19)) {
		tmp = Math.cos(y) * z;
	} else {
		tmp = x * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-85) or not (z <= 3.9e-19):
		tmp = math.cos(y) * z
	else:
		tmp = x * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-85) || !(z <= 3.9e-19))
		tmp = Float64(cos(y) * z);
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-85) || ~((z <= 3.9e-19)))
		tmp = cos(y) * z;
	else
		tmp = x * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-85], N[Not[LessEqual[z, 3.9e-19]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * z), $MachinePrecision], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-85 or 3.89999999999999995e-19 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.6%

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

   if -5.0000000000000002e-85 < z < 3.89999999999999995e-19

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 69.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-85} \lor \neg \left(z \leq 3.9 \cdot 10^{-19}\right):\\ \;\;\;\;\cos y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 6: 52.3% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

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 + (y * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Taylor expanded in y around 0 49.2%

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

   1. +-commutative 49.2%

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

4. Simplified 49.2%

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

5. Final simplification 49.2%

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

Alternative 7: 39.7% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

   1. +-commutative 99.8%

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

   2. *-commutative 99.8%

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

   3. fma-def 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in y around 0 38.2%

   \[\leadsto \color{blue}{z} \]

5. Final simplification 38.2%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023306 
(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))))