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

Percentage Accurate: 99.8% → 99.8%

Time: 8.8s

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. Final simplification 99.8%

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

Alternative 2: 83.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+79} \lor \neg \left(x \leq 3.1 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e+79) (not (<= x 3.1e-94)))
   (* x (cos y))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e+79) || !(x <= 3.1e-94)) {
		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 <= (-8.5d+79)) .or. (.not. (x <= 3.1d-94))) 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 <= -8.5e+79) || !(x <= 3.1e-94)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e+79) or not (x <= 3.1e-94):
		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 <= -8.5e+79) || !(x <= 3.1e-94))
		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 <= -8.5e+79) || ~((x <= 3.1e-94)))
		tmp = x * cos(y);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e+79], N[Not[LessEqual[x, 3.1e-94]], $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 < -8.4999999999999998e79 or 3.0999999999999998e-94 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.9%

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

   if -8.4999999999999998e79 < x < 3.0999999999999998e-94

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 90.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+79} \lor \neg \left(x \leq 3.1 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.62\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5 + y \cdot \left(z \cdot -0.16666666666666666 + y \cdot \left(0.008333333333333333 \cdot \left(y \cdot z\right) + x \cdot 0.041666666666666664\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -540.0) (not (<= y 0.62)))
   (* x (cos y))
   (+
    x
    (*
     y
     (+
      z
      (*
       y
       (+
        (* x -0.5)
        (*
         y
         (+
          (* z -0.16666666666666666)
          (*
           y
           (+
            (* 0.008333333333333333 (* y z))
            (* x 0.041666666666666664))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.62)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (y * ((0.008333333333333333 * (y * z)) + (x * 0.041666666666666664)))))))));
	}
	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 <= (-540.0d0)) .or. (.not. (y <= 0.62d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * ((x * (-0.5d0)) + (y * ((z * (-0.16666666666666666d0)) + (y * ((0.008333333333333333d0 * (y * z)) + (x * 0.041666666666666664d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -540.0) || !(y <= 0.62)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (y * ((0.008333333333333333 * (y * z)) + (x * 0.041666666666666664)))))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -540.0) or not (y <= 0.62):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (y * ((0.008333333333333333 * (y * z)) + (x * 0.041666666666666664)))))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -540.0) || !(y <= 0.62))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(Float64(x * -0.5) + Float64(y * Float64(Float64(z * -0.16666666666666666) + Float64(y * Float64(Float64(0.008333333333333333 * Float64(y * z)) + Float64(x * 0.041666666666666664))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -540.0) || ~((y <= 0.62)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (y * ((0.008333333333333333 * (y * z)) + (x * 0.041666666666666664)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -540.0], N[Not[LessEqual[y, 0.62]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(y * N[(N[(z * -0.16666666666666666), $MachinePrecision] + N[(y * N[(N[(0.008333333333333333 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(x * 0.041666666666666664), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -540 or 0.619999999999999996 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 52.0%

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

   if -540 < y < 0.619999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.5%

      \[\leadsto \color{blue}{x + y \cdot \left(z + y \cdot \left(-0.5 \cdot x + y \cdot \left(-0.16666666666666666 \cdot z + y \cdot \left(0.008333333333333333 \cdot \left(y \cdot z\right) + 0.041666666666666664 \cdot x\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -540 \lor \neg \left(y \leq 0.62\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5 + y \cdot \left(z \cdot -0.16666666666666666 + y \cdot \left(0.008333333333333333 \cdot \left(y \cdot z\right) + x \cdot 0.041666666666666664\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+121} \lor \neg \left(z \leq 7 \cdot 10^{+127}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.6e+121) (not (<= z 7e+127))) (* z (sin y)) (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e+121) || !(z <= 7e+127)) {
		tmp = z * sin(y);
	} else {
		tmp = x * cos(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 <= (-8.6d+121)) .or. (.not. (z <= 7d+127))) then
        tmp = z * sin(y)
    else
        tmp = x * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.6e+121) || !(z <= 7e+127)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.6e+121) or not (z <= 7e+127):
		tmp = z * math.sin(y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.6e+121) || !(z <= 7e+127))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.6e+121) || ~((z <= 7e+127)))
		tmp = z * sin(y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.6e+121], N[Not[LessEqual[z, 7e+127]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5999999999999994e121 or 6.99999999999999956e127 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 78.9%

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

   if -8.5999999999999994e121 < z < 6.99999999999999956e127

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 77.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+121} \lor \neg \left(z \leq 7 \cdot 10^{+127}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.9% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+251} \lor \neg \left(z \leq 6.8 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+251) (not (<= z 6.8e+131))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+251) || !(z <= 6.8e+131)) {
		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 <= (-1.35d+251)) .or. (.not. (z <= 6.8d+131))) 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 <= -1.35e+251) || !(z <= 6.8e+131)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+251) or not (z <= 6.8e+131):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+251) || !(z <= 6.8e+131))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e+251) || ~((z <= 6.8e+131)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+251], N[Not[LessEqual[z, 6.8e+131]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3500000000000001e251 or 6.79999999999999972e131 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 52.8%

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

      1. +-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in y around inf 45.8%

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

   if -1.3500000000000001e251 < z < 6.79999999999999972e131

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 71.9%

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

   4. Taylor expanded in y around 0 46.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+251} \lor \neg \left(z \leq 6.8 \cdot 10^{+131}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.9% 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 53.9%

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

   1. +-commutative 53.9%

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

5. Simplified 53.9%

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

6. Final simplification 53.9%

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

Alternative 7: 38.5% 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 x around inf 61.7%

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

4. Taylor expanded in y around 0 40.5%

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

5. Final simplification 40.5%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024055 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))