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

Percentage Accurate: 99.8% → 99.8%

Time: 8.3s

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: 81.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+33} \lor \neg \left(x \leq 9.6 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e+33) (not (<= x 9.6e-15)))
   (+ (* x (cos y)) (* y z))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e+33) || !(x <= 9.6e-15)) {
		tmp = (x * cos(y)) + (y * z);
	} 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 <= (-3.8d+33)) .or. (.not. (x <= 9.6d-15))) then
        tmp = (x * cos(y)) + (y * z)
    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 <= -3.8e+33) || !(x <= 9.6e-15)) {
		tmp = (x * Math.cos(y)) + (y * z);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e+33) or not (x <= 9.6e-15):
		tmp = (x * math.cos(y)) + (y * z)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e+33) || !(x <= 9.6e-15))
		tmp = Float64(Float64(x * cos(y)) + Float64(y * z));
	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 <= -3.8e+33) || ~((x <= 9.6e-15)))
		tmp = (x * cos(y)) + (y * z);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e+33], N[Not[LessEqual[x, 9.6e-15]], $MachinePrecision]], N[(N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000002e33 or 9.5999999999999998e-15 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 79.4%

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

   if -3.80000000000000002e33 < x < 9.5999999999999998e-15

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+33} \lor \neg \left(x \leq 9.6 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \cos y + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -68000000000 \lor \neg \left(y \leq 7.6 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -68000000000.0) (not (<= y 7.6e-5)))
   (* z (sin y))
   (+ x (* y (+ z (* -0.5 (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -68000000000.0) || !(y <= 7.6e-5)) {
		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 <= (-68000000000.0d0)) .or. (.not. (y <= 7.6d-5))) 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 <= -68000000000.0) || !(y <= 7.6e-5)) {
		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 <= -68000000000.0) or not (y <= 7.6e-5):
		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 <= -68000000000.0) || !(y <= 7.6e-5))
		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 <= -68000000000.0) || ~((y <= 7.6e-5)))
		tmp = z * sin(y);
	else
		tmp = x + (y * (z + (-0.5 * (x * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -68000000000.0], N[Not[LessEqual[y, 7.6e-5]], $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 2 regimes

2. if y < -6.8e10 or 7.6000000000000004e-5 < y

   1. Initial program 99.6%

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

      1. expm1-log1p-u 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around 0 48.0%

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

   if -6.8e10 < y < 7.6000000000000004e-5

   1. Initial program 100.0%

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

      1. expm1-log1p-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 97.7%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -68000000000 \lor \neg \left(y \leq 7.6 \cdot 10^{-5}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + 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. Taylor expanded in y around 0 74.3%

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

Alternative 5: 33.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -38000000000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -38000000000000.0) (not (<= z 4.2e+58))) (* y z) (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -38000000000000.0) || !(z <= 4.2e+58)) {
		tmp = y * z;
	} else {
		tmp = 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 ((z <= (-38000000000000.0d0)) .or. (.not. (z <= 4.2d+58))) then
        tmp = y * z
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -38000000000000.0) || !(z <= 4.2e+58)) {
		tmp = y * z;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -38000000000000.0) or not (z <= 4.2e+58):
		tmp = y * z
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -38000000000000.0) || !(z <= 4.2e+58))
		tmp = Float64(y * z);
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -38000000000000.0) || ~((z <= 4.2e+58)))
		tmp = y * z;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -38000000000000.0], N[Not[LessEqual[z, 4.2e+58]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e13 or 4.20000000000000024e58 < z

   1. Initial program 99.8%

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

      1. expm1-log1p-u 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 68.7%

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

   6. Taylor expanded in y around 0 34.9%

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

   if -3.8e13 < z < 4.20000000000000024e58

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 64.8%

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

   4. Taylor expanded in y around 0 48.9%

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

   5. Taylor expanded in y around inf 39.1%

      \[\leadsto \color{blue}{y \cdot \left(z + \frac{x}{y}\right)} \]

   6. Taylor expanded in z around 0 34.8%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000000000000 \lor \neg \left(z \leq 4.2 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.8% 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 74.3%

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

4. Taylor expanded in y around 0 50.8%

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

5. Final simplification 50.8%

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

Alternative 7: 17.2% 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. Step-by-step derivation

   1. expm1-log1p-u 99.7%

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

4. Applied egg-rr 99.7%

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

5. Taylor expanded in x around 0 42.0%

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

6. Taylor expanded in y around 0 19.5%

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

7. Final simplification 19.5%

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))