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

Percentage Accurate: 99.8% → 99.8%

Time: 9.6s

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: 85.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-8} \lor \neg \left(z \leq 1400000000000\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.2e-8) (not (<= z 1400000000000.0)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.2e-8) || !(z <= 1400000000000.0)) {
		tmp = x + (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 <= (-8.2d-8)) .or. (.not. (z <= 1400000000000.0d0))) then
        tmp = x + (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 <= -8.2e-8) || !(z <= 1400000000000.0)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.2e-8) or not (z <= 1400000000000.0):
		tmp = x + (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.2e-8) || !(z <= 1400000000000.0))
		tmp = Float64(x + 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 <= -8.2e-8) || ~((z <= 1400000000000.0)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.2e-8], N[Not[LessEqual[z, 1400000000000.0]], $MachinePrecision]], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.20000000000000063e-8 or 1.4e12 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 91.2%

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

   if -8.20000000000000063e-8 < z < 1.4e12

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-8} \lor \neg \left(z \leq 1400000000000\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 8.5 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.1e-6) (not (<= z 8.5e+14))) (* z (sin y)) (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.1e-6) || !(z <= 8.5e+14)) {
		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 <= (-5.1d-6)) .or. (.not. (z <= 8.5d+14))) 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 <= -5.1e-6) || !(z <= 8.5e+14)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.1e-6) or not (z <= 8.5e+14):
		tmp = z * math.sin(y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.1e-6) || !(z <= 8.5e+14))
		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 <= -5.1e-6) || ~((z <= 8.5e+14)))
		tmp = z * sin(y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.1e-6], N[Not[LessEqual[z, 8.5e+14]], $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 < -5.1000000000000003e-6 or 8.5e14 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 73.2%

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

   if -5.1000000000000003e-6 < z < 8.5e14

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 8.5 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{-7} \lor \neg \left(y \leq 235\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(z \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.45e-7) (not (<= y 235.0)))
   (* x (cos y))
   (+ x (* y (+ z (* y (* z (* y -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.45e-7) || !(y <= 235.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * (z * (y * -0.16666666666666666)))));
	}
	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 <= (-3.45d-7)) .or. (.not. (y <= 235.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * (z * (y * (-0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.45e-7) || !(y <= 235.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * (z * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.45e-7) or not (y <= 235.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * (z * (y * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.45e-7) || !(y <= 235.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(z * Float64(y * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.45e-7) || ~((y <= 235.0)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * (z * (y * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.45e-7], N[Not[LessEqual[y, 235.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(z * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4499999999999998e-7 or 235 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 54.5%

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

   if -3.4499999999999998e-7 < y < 235

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

      \[\leadsto \color{blue}{x + y \cdot \left(z + y \cdot \left(-0.5 \cdot x + -0.16666666666666666 \cdot \left(y \cdot z\right)\right)\right)} \]

   4. Taylor expanded in x around 0 99.3%

      \[\leadsto x + y \cdot \left(z + y \cdot \color{blue}{\left(-0.16666666666666666 \cdot \left(y \cdot z\right)\right)}\right) \]
   5. Step-by-step derivation

      1. *-commutative 99.3%

         \[\leadsto x + y \cdot \left(z + y \cdot \color{blue}{\left(\left(y \cdot z\right) \cdot -0.16666666666666666\right)}\right) \]

      2. *-commutative 99.3%

         \[\leadsto x + y \cdot \left(z + y \cdot \left(\color{blue}{\left(z \cdot y\right)} \cdot -0.16666666666666666\right)\right) \]

      3. associate-*r* 99.3%

         \[\leadsto x + y \cdot \left(z + y \cdot \color{blue}{\left(z \cdot \left(y \cdot -0.16666666666666666\right)\right)}\right) \]

   6. Simplified 99.3%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{-7} \lor \neg \left(y \leq 235\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(z \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.3% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+100} \lor \neg \left(z \leq 5.5 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+100) (not (<= z 5.5e+24))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+100) || !(z <= 5.5e+24)) {
		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 <= (-1.3d+100)) .or. (.not. (z <= 5.5d+24))) 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 <= -1.3e+100) || !(z <= 5.5e+24)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+100) or not (z <= 5.5e+24):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e+100) || !(z <= 5.5e+24))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e+100) || ~((z <= 5.5e+24)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+100], N[Not[LessEqual[z, 5.5e+24]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e100 or 5.5000000000000002e24 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 52.8%

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

   4. Taylor expanded in y around inf 44.5%

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

   5. Taylor expanded in z around inf 38.6%

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

   if -1.3000000000000001e100 < z < 5.5000000000000002e24

   1. Initial program 99.7%

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

      1. expm1-log1p-u 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0 45.9%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+100} \lor \neg \left(z \leq 5.5 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% 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 50.7%

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

Alternative 7: 39.1% 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. Step-by-step derivation

   1. expm1-log1p-u 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in y around 0 34.8%

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

Reproduce

herbie shell --seed 2024135 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))