Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 7.7s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 73.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -0.0021:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+210} \lor \neg \left(y \leq 2.75 \cdot 10^{+287}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= y -0.0021)
     t_0
     (if (<= y 1.32e+20)
       (+ x (* y z))
       (if (or (<= y 2.05e+210) (not (<= y 2.75e+287))) (* z (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (y <= -0.0021) {
		tmp = t_0;
	} else if (y <= 1.32e+20) {
		tmp = x + (y * z);
	} else if ((y <= 2.05e+210) || !(y <= 2.75e+287)) {
		tmp = z * sin(y);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * cos(y)
    if (y <= (-0.0021d0)) then
        tmp = t_0
    else if (y <= 1.32d+20) then
        tmp = x + (y * z)
    else if ((y <= 2.05d+210) .or. (.not. (y <= 2.75d+287))) then
        tmp = z * sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.cos(y);
	double tmp;
	if (y <= -0.0021) {
		tmp = t_0;
	} else if (y <= 1.32e+20) {
		tmp = x + (y * z);
	} else if ((y <= 2.05e+210) || !(y <= 2.75e+287)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	tmp = 0
	if y <= -0.0021:
		tmp = t_0
	elif y <= 1.32e+20:
		tmp = x + (y * z)
	elif (y <= 2.05e+210) or not (y <= 2.75e+287):
		tmp = z * math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -0.0021)
		tmp = t_0;
	elseif (y <= 1.32e+20)
		tmp = Float64(x + Float64(y * z));
	elseif ((y <= 2.05e+210) || !(y <= 2.75e+287))
		tmp = Float64(z * sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	tmp = 0.0;
	if (y <= -0.0021)
		tmp = t_0;
	elseif (y <= 1.32e+20)
		tmp = x + (y * z);
	elseif ((y <= 2.05e+210) || ~((y <= 2.75e+287)))
		tmp = z * sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0021], t$95$0, If[LessEqual[y, 1.32e+20], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.05e+210], N[Not[LessEqual[y, 2.75e+287]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00209999999999999987 or 2.05e210 < y < 2.75e287

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 66.6%

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

   if -0.00209999999999999987 < y < 1.32e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.8%

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

      1. +-commutative 97.8%

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

   5. Simplified 97.8%

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

   if 1.32e20 < y < 2.05e210 or 2.75e287 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 62.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0021:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+20}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+210} \lor \neg \left(y \leq 2.75 \cdot 10^{+287}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ \mathbf{if}\;y \leq -0.0003:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+211} \lor \neg \left(y \leq 2.65 \cdot 10^{+287}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))))
   (if (<= y -0.0003)
     t_0
     (if (<= y 1.32e+20)
       (fma y z x)
       (if (or (<= y 1.85e+211) (not (<= y 2.65e+287))) (* z (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double tmp;
	if (y <= -0.0003) {
		tmp = t_0;
	} else if (y <= 1.32e+20) {
		tmp = fma(y, z, x);
	} else if ((y <= 1.85e+211) || !(y <= 2.65e+287)) {
		tmp = z * sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -0.0003)
		tmp = t_0;
	elseif (y <= 1.32e+20)
		tmp = fma(y, z, x);
	elseif ((y <= 1.85e+211) || !(y <= 2.65e+287))
		tmp = Float64(z * sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0003], t$95$0, If[LessEqual[y, 1.32e+20], N[(y * z + x), $MachinePrecision], If[Or[LessEqual[y, 1.85e+211], N[Not[LessEqual[y, 2.65e+287]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999974e-4 or 1.85000000000000005e211 < y < 2.6499999999999998e287

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 66.6%

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

   if -2.99999999999999974e-4 < y < 1.32e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.8%

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

      1. +-commutative 97.8%

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

      2. fma-def 97.8%

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

   5. Simplified 97.8%

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

   if 1.32e20 < y < 1.85000000000000005e211 or 2.6499999999999998e287 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 62.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0003:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(y, z, x\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+211} \lor \neg \left(y \leq 2.65 \cdot 10^{+287}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00012 \lor \neg \left(y \leq 6.4 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00012) (not (<= y 6.4e-35))) (* x (cos y)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00012) || !(y <= 6.4e-35)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (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 ((y <= (-0.00012d0)) .or. (.not. (y <= 6.4d-35))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00012) || !(y <= 6.4e-35)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00012) or not (y <= 6.4e-35):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00012) || !(y <= 6.4e-35))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00012) || ~((y <= 6.4e-35)))
		tmp = x * cos(y);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00012], N[Not[LessEqual[y, 6.4e-35]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.20000000000000003e-4 or 6.3999999999999996e-35 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 57.9%

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

   if -1.20000000000000003e-4 < y < 6.3999999999999996e-35

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00012 \lor \neg \left(y \leq 6.4 \cdot 10^{-35}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.4% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 59.9%

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

   1. +-commutative 59.9%

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

5. Simplified 59.9%

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

6. Final simplification 59.9%

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

Alternative 6: 17.4% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in x around 0 36.3%

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

4. Taylor expanded in y around 0 19.4%

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

5. Final simplification 19.4%

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

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))