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

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 7

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. Add Preprocessing

Alternative 2: 74.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.155 \lor \neg \left(y \leq 0.046\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+228)
   (* x (cos y))
   (if (or (<= y -0.155) (not (<= y 0.046)))
     (* z (sin y))
     (+ x (* y (+ z (* -0.5 (* x y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+228) {
		tmp = x * cos(y);
	} else if ((y <= -0.155) || !(y <= 0.046)) {
		tmp = z * sin(y);
	} else {
		tmp = x + (y * (z + (-0.5 * (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 <= (-2.2d+228)) then
        tmp = x * cos(y)
    else if ((y <= (-0.155d0)) .or. (.not. (y <= 0.046d0))) then
        tmp = z * sin(y)
    else
        tmp = x + (y * (z + ((-0.5d0) * (x * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+228) {
		tmp = x * Math.cos(y);
	} else if ((y <= -0.155) || !(y <= 0.046)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x + (y * (z + (-0.5 * (x * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.2e+228:
		tmp = x * math.cos(y)
	elif (y <= -0.155) or not (y <= 0.046):
		tmp = z * math.sin(y)
	else:
		tmp = x + (y * (z + (-0.5 * (x * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+228)
		tmp = Float64(x * cos(y));
	elseif ((y <= -0.155) || !(y <= 0.046))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(-0.5 * Float64(x * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.2e+228)
		tmp = x * cos(y);
	elseif ((y <= -0.155) || ~((y <= 0.046)))
		tmp = z * sin(y);
	else
		tmp = x + (y * (z + (-0.5 * (x * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+228], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -0.155], N[Not[LessEqual[y, 0.046]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(-0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2e228

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 88.6%

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

   if -2.2e228 < y < -0.154999999999999999 or 0.045999999999999999 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 58.5%

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

   if -0.154999999999999999 < y < 0.045999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.7%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+228}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.155 \lor \neg \left(y \leq 0.046\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+61} \lor \neg \left(x \leq 0.27\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e+61) (not (<= x 0.27)))
   (* x (cos y))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e+61) || !(x <= 0.27)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (z * 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 ((x <= (-1.55d+61)) .or. (.not. (x <= 0.27d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e+61) || !(x <= 0.27)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e+61) or not (x <= 0.27):
		tmp = x * math.cos(y)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e+61) || !(x <= 0.27))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55e+61) || ~((x <= 0.27)))
		tmp = x * cos(y);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e+61], N[Not[LessEqual[x, 0.27]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55e61 or 0.27000000000000002 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.0%

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

   if -1.55e61 < x < 0.27000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+61} \lor \neg \left(x \leq 0.27\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0105 \lor \neg \left(y \leq 3.1 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0105) (not (<= y 3.1e+51)))
   (* x (cos y))
   (+ x (* y (+ z (* -0.5 (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0105) || !(y <= 3.1e+51)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (-0.5 * (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 <= (-0.0105d0)) .or. (.not. (y <= 3.1d+51))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + ((-0.5d0) * (x * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0105) || !(y <= 3.1e+51)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (-0.5 * (x * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0105) or not (y <= 3.1e+51):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (-0.5 * (x * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0105) || !(y <= 3.1e+51))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(-0.5 * Float64(x * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0105) || ~((y <= 3.1e+51)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (-0.5 * (x * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0105], N[Not[LessEqual[y, 3.1e+51]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(-0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0105000000000000007 or 3.10000000000000011e51 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 51.7%

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

   if -0.0105000000000000007 < y < 3.10000000000000011e51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0105 \lor \neg \left(y \leq 3.1 \cdot 10^{+51}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.5% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+75} \lor \neg \left(z \leq 3.8 \cdot 10^{+169}\right) \land z \leq 8.7 \cdot 10^{+276}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.75e+75) (and (not (<= z 3.8e+169)) (<= z 8.7e+276)))
   (* y z)
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+75) || (!(z <= 3.8e+169) && (z <= 8.7e+276))) {
		tmp = y * z;
	} else {
		tmp = 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 ((z <= (-1.75d+75)) .or. (.not. (z <= 3.8d+169)) .and. (z <= 8.7d+276)) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+75) || (!(z <= 3.8e+169) && (z <= 8.7e+276))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.75e+75) or (not (z <= 3.8e+169) and (z <= 8.7e+276)):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.75e+75) || (!(z <= 3.8e+169) && (z <= 8.7e+276)))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.75e+75) || (~((z <= 3.8e+169)) && (z <= 8.7e+276)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.75e+75], And[N[Not[LessEqual[z, 3.8e+169]], $MachinePrecision], LessEqual[z, 8.7e+276]]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7499999999999999e75 or 3.79999999999999992e169 < z < 8.7000000000000003e276

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 50.7%

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

   4. Taylor expanded in x around 0 35.6%

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

   if -1.7499999999999999e75 < z < 3.79999999999999992e169 or 8.7000000000000003e276 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 54.3%

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

   4. Taylor expanded in x around inf 50.2%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+75} \lor \neg \left(z \leq 3.8 \cdot 10^{+169}\right) \land z \leq 8.7 \cdot 10^{+276}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% 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 53.1%

   \[\leadsto \color{blue}{x + y \cdot z} \]
4. Add Preprocessing

Alternative 7: 38.7% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 53.1%

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

4. Taylor expanded in x around inf 39.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))