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

Percentage Accurate: 99.8% → 99.8%

Time: 9.2s

Alternatives: 9

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: 79.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(1 + \frac{z}{\frac{x}{\sin y}}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+196}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e-94)
   (* x (+ 1.0 (/ z (/ x (sin y)))))
   (if (<= z 2.5e-65)
     (* x (cos y))
     (if (<= z 9.2e+196) (* x (+ 1.0 (* z (/ (sin y) x)))) (* z (sin y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e-94) {
		tmp = x * (1.0 + (z / (x / sin(y))));
	} else if (z <= 2.5e-65) {
		tmp = x * cos(y);
	} else if (z <= 9.2e+196) {
		tmp = x * (1.0 + (z * (sin(y) / x)));
	} else {
		tmp = 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 (z <= (-1.5d-94)) then
        tmp = x * (1.0d0 + (z / (x / sin(y))))
    else if (z <= 2.5d-65) then
        tmp = x * cos(y)
    else if (z <= 9.2d+196) then
        tmp = x * (1.0d0 + (z * (sin(y) / x)))
    else
        tmp = z * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e-94) {
		tmp = x * (1.0 + (z / (x / Math.sin(y))));
	} else if (z <= 2.5e-65) {
		tmp = x * Math.cos(y);
	} else if (z <= 9.2e+196) {
		tmp = x * (1.0 + (z * (Math.sin(y) / x)));
	} else {
		tmp = z * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e-94:
		tmp = x * (1.0 + (z / (x / math.sin(y))))
	elif z <= 2.5e-65:
		tmp = x * math.cos(y)
	elif z <= 9.2e+196:
		tmp = x * (1.0 + (z * (math.sin(y) / x)))
	else:
		tmp = z * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e-94)
		tmp = Float64(x * Float64(1.0 + Float64(z / Float64(x / sin(y)))));
	elseif (z <= 2.5e-65)
		tmp = Float64(x * cos(y));
	elseif (z <= 9.2e+196)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(sin(y) / x))));
	else
		tmp = Float64(z * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e-94)
		tmp = x * (1.0 + (z / (x / sin(y))));
	elseif (z <= 2.5e-65)
		tmp = x * cos(y);
	elseif (z <= 9.2e+196)
		tmp = x * (1.0 + (z * (sin(y) / x)));
	else
		tmp = z * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e-94], N[(x * N[(1.0 + N[(z / N[(x / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-65], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+196], N[(x * N[(1.0 + N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.5000000000000001e-94

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 92.1%

      \[\leadsto \color{blue}{x \cdot \left(\cos y + \frac{z \cdot \sin y}{x}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 92.0%

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

   5. Simplified 92.0%

      \[\leadsto \color{blue}{x \cdot \left(\cos y + z \cdot \frac{\sin y}{x}\right)} \]
   6. Step-by-step derivation

      1. clear-num 91.9%

         \[\leadsto x \cdot \left(\cos y + z \cdot \color{blue}{\frac{1}{\frac{x}{\sin y}}}\right) \]

      2. un-div-inv 92.0%

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

   7. Applied egg-rr 92.0%

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

   8. Taylor expanded in y around 0 81.5%

      \[\leadsto x \cdot \left(\color{blue}{1} + \frac{z}{\frac{x}{\sin y}}\right) \]

   if -1.5000000000000001e-94 < z < 2.49999999999999991e-65

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 96.6%

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

   if 2.49999999999999991e-65 < z < 9.19999999999999922e196

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{x \cdot \left(\cos y + \frac{z \cdot \sin y}{x}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in y around 0 83.0%

      \[\leadsto x \cdot \left(\color{blue}{1} + z \cdot \frac{\sin y}{x}\right) \]

   if 9.19999999999999922e196 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.8%

      \[\leadsto \color{blue}{z \cdot \sin y} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 79.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot \frac{\sin y}{x}\right)\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{-95}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+195}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (/ (sin y) x))))))
   (if (<= z -2.75e-95)
     t_0
     (if (<= z 2.45e-65)
       (* x (cos y))
       (if (<= z 1.2e+195) t_0 (* z (sin y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (sin(y) / x)));
	double tmp;
	if (z <= -2.75e-95) {
		tmp = t_0;
	} else if (z <= 2.45e-65) {
		tmp = x * cos(y);
	} else if (z <= 1.2e+195) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 + (z * (sin(y) / x)))
    if (z <= (-2.75d-95)) then
        tmp = t_0
    else if (z <= 2.45d-65) then
        tmp = x * cos(y)
    else if (z <= 1.2d+195) then
        tmp = t_0
    else
        tmp = z * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (Math.sin(y) / x)));
	double tmp;
	if (z <= -2.75e-95) {
		tmp = t_0;
	} else if (z <= 2.45e-65) {
		tmp = x * Math.cos(y);
	} else if (z <= 1.2e+195) {
		tmp = t_0;
	} else {
		tmp = z * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * (math.sin(y) / x)))
	tmp = 0
	if z <= -2.75e-95:
		tmp = t_0
	elif z <= 2.45e-65:
		tmp = x * math.cos(y)
	elif z <= 1.2e+195:
		tmp = t_0
	else:
		tmp = z * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * Float64(sin(y) / x))))
	tmp = 0.0
	if (z <= -2.75e-95)
		tmp = t_0;
	elseif (z <= 2.45e-65)
		tmp = Float64(x * cos(y));
	elseif (z <= 1.2e+195)
		tmp = t_0;
	else
		tmp = Float64(z * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * (sin(y) / x)));
	tmp = 0.0;
	if (z <= -2.75e-95)
		tmp = t_0;
	elseif (z <= 2.45e-65)
		tmp = x * cos(y);
	elseif (z <= 1.2e+195)
		tmp = t_0;
	else
		tmp = z * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e-95], t$95$0, If[LessEqual[z, 2.45e-65], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+195], t$95$0, N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.75000000000000001e-95 or 2.44999999999999982e-65 < z < 1.2000000000000001e195

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 93.9%

      \[\leadsto \color{blue}{x \cdot \left(\cos y + \frac{z \cdot \sin y}{x}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in y around 0 82.0%

      \[\leadsto x \cdot \left(\color{blue}{1} + z \cdot \frac{\sin y}{x}\right) \]

   if -2.75000000000000001e-95 < z < 2.44999999999999982e-65

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 96.6%

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

   if 1.2000000000000001e195 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.8%

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

Alternative 4: 85.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-95} \lor \neg \left(z \leq 1.8 \cdot 10^{-71}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e-95) (not (<= z 1.8e-71)))
   (+ x (* z (* x (/ (sin y) x))))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e-95) || !(z <= 1.8e-71)) {
		tmp = x + (z * (x * (sin(y) / x)));
	} 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 <= (-3.1d-95)) .or. (.not. (z <= 1.8d-71))) then
        tmp = x + (z * (x * (sin(y) / x)))
    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 <= -3.1e-95) || !(z <= 1.8e-71)) {
		tmp = x + (z * (x * (Math.sin(y) / x)));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e-95) or not (z <= 1.8e-71):
		tmp = x + (z * (x * (math.sin(y) / x)))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e-95) || !(z <= 1.8e-71))
		tmp = Float64(x + Float64(z * Float64(x * Float64(sin(y) / x))));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.1e-95) || ~((z <= 1.8e-71)))
		tmp = x + (z * (x * (sin(y) / x)));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e-95], N[Not[LessEqual[z, 1.8e-71]], $MachinePrecision]], N[(x + N[(z * N[(x * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999992e-95 or 1.8e-71 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 90.2%

      \[\leadsto \color{blue}{x \cdot \left(\cos y + \frac{z \cdot \sin y}{x}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

      \[\leadsto \color{blue}{x \cdot \left(\cos y + z \cdot \frac{\sin y}{x}\right)} \]
   6. Step-by-step derivation

      1. +-commutative 90.1%

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

      2. distribute-lft-in 90.1%

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

      3. *-commutative 90.1%

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

      4. associate-*l* 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around 0 89.5%

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

   if -3.09999999999999992e-95 < z < 1.8e-71

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 96.6%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-95} \lor \neg \left(z \leq 1.8 \cdot 10^{-71}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -115:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 24:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (<= y -3.3e+118)
     t_0
     (if (<= y -115.0)
       (* x (cos y))
       (if (<= y 24.0) (+ x (* y (+ z (* y (* x -0.5))))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if (y <= -3.3e+118) {
		tmp = t_0;
	} else if (y <= -115.0) {
		tmp = x * cos(y);
	} else if (y <= 24.0) {
		tmp = x + (y * (z + (y * (x * -0.5))));
	} 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 = z * sin(y)
    if (y <= (-3.3d+118)) then
        tmp = t_0
    else if (y <= (-115.0d0)) then
        tmp = x * cos(y)
    else if (y <= 24.0d0) then
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if (y <= -3.3e+118) {
		tmp = t_0;
	} else if (y <= -115.0) {
		tmp = x * Math.cos(y);
	} else if (y <= 24.0) {
		tmp = x + (y * (z + (y * (x * -0.5))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if y <= -3.3e+118:
		tmp = t_0
	elif y <= -115.0:
		tmp = x * math.cos(y)
	elif y <= 24.0:
		tmp = x + (y * (z + (y * (x * -0.5))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if (y <= -3.3e+118)
		tmp = t_0;
	elseif (y <= -115.0)
		tmp = Float64(x * cos(y));
	elseif (y <= 24.0)
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if (y <= -3.3e+118)
		tmp = t_0;
	elseif (y <= -115.0)
		tmp = x * cos(y);
	elseif (y <= 24.0)
		tmp = x + (y * (z + (y * (x * -0.5))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+118], t$95$0, If[LessEqual[y, -115.0], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 24.0], N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3e118 or 24 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 59.8%

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

   if -3.3e118 < y < -115

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 62.5%

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

   if -115 < y < 24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

      \[\leadsto \color{blue}{x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 98.7%

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

      2. *-commutative 98.7%

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

   5. Simplified 98.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq -115:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq 24:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -115 \lor \neg \left(y \leq 1.06 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -115.0) (not (<= y 1.06e-5)))
   (* x (cos y))
   (+ x (* y (+ z (* y (* x -0.5)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -115.0) || !(y <= 1.06e-5)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	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 <= (-115.0d0)) .or. (.not. (y <= 1.06d-5))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * (x * (-0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -115.0) || !(y <= 1.06e-5)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * (x * -0.5))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -115.0) or not (y <= 1.06e-5):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * (x * -0.5))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -115.0) || !(y <= 1.06e-5))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(x * -0.5)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -115.0) || ~((y <= 1.06e-5)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * (x * -0.5))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -115.0], N[Not[LessEqual[y, 1.06e-5]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -115 or 1.06e-5 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 47.7%

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

   if -115 < y < 1.06e-5

   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%

      \[\leadsto \color{blue}{x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 99.3%

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

      2. *-commutative 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -115 \lor \neg \left(y \leq 1.06 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+184} \lor \neg \left(z \leq 7.8 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e+184) (not (<= z 7.8e-24))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e+184) || !(z <= 7.8e-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 <= (-2.7d+184)) .or. (.not. (z <= 7.8d-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 <= -2.7e+184) || !(z <= 7.8e-24)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e+184) or not (z <= 7.8e-24):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e+184) || !(z <= 7.8e-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 <= -2.7e+184) || ~((z <= 7.8e-24)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e+184], N[Not[LessEqual[z, 7.8e-24]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e184 or 7.8e-24 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 74.0%

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

   4. Taylor expanded in y around 0 34.8%

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

   if -2.6999999999999999e184 < z < 7.8e-24

   1. Initial program 99.8%

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

      1. log1p-expm1-u 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 53.3%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+184} \lor \neg \left(z \leq 7.8 \cdot 10^{-24}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 56.1%

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

Alternative 9: 38.9% 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. log1p-expm1-u 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in y around 0 40.5%

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

Reproduce

herbie shell --seed 2024133 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))