Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Percentage Accurate: 99.8% → 99.8%

Time: 9.8s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \sin y, z \cdot \cos y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x (sin y) (* z (cos y))))

C

double code(double x, double y, double z) {
	return fma(x, sin(y), (z * cos(y)));
}

Julia

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

Wolfram

code[x_, y_, z_] := N[(x * N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

   1. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 3: 79.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ t_1 := z \cdot \left(1 + \frac{x}{\frac{z}{\sin y}}\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-177}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))) (t_1 (* z (+ 1.0 (/ x (/ z (sin y)))))))
   (if (<= z -6e-13)
     t_0
     (if (<= z -5.8e-146)
       t_1
       (if (<= z 4.5e-177) (* x (sin y)) (if (<= z 6e+45) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double t_1 = z * (1.0 + (x / (z / sin(y))));
	double tmp;
	if (z <= -6e-13) {
		tmp = t_0;
	} else if (z <= -5.8e-146) {
		tmp = t_1;
	} else if (z <= 4.5e-177) {
		tmp = x * sin(y);
	} else if (z <= 6e+45) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * cos(y)
    t_1 = z * (1.0d0 + (x / (z / sin(y))))
    if (z <= (-6d-13)) then
        tmp = t_0
    else if (z <= (-5.8d-146)) then
        tmp = t_1
    else if (z <= 4.5d-177) then
        tmp = x * sin(y)
    else if (z <= 6d+45) then
        tmp = t_1
    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.cos(y);
	double t_1 = z * (1.0 + (x / (z / Math.sin(y))));
	double tmp;
	if (z <= -6e-13) {
		tmp = t_0;
	} else if (z <= -5.8e-146) {
		tmp = t_1;
	} else if (z <= 4.5e-177) {
		tmp = x * Math.sin(y);
	} else if (z <= 6e+45) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	t_1 = z * (1.0 + (x / (z / math.sin(y))))
	tmp = 0
	if z <= -6e-13:
		tmp = t_0
	elif z <= -5.8e-146:
		tmp = t_1
	elif z <= 4.5e-177:
		tmp = x * math.sin(y)
	elif z <= 6e+45:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	t_1 = Float64(z * Float64(1.0 + Float64(x / Float64(z / sin(y)))))
	tmp = 0.0
	if (z <= -6e-13)
		tmp = t_0;
	elseif (z <= -5.8e-146)
		tmp = t_1;
	elseif (z <= 4.5e-177)
		tmp = Float64(x * sin(y));
	elseif (z <= 6e+45)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	t_1 = z * (1.0 + (x / (z / sin(y))));
	tmp = 0.0;
	if (z <= -6e-13)
		tmp = t_0;
	elseif (z <= -5.8e-146)
		tmp = t_1;
	elseif (z <= 4.5e-177)
		tmp = x * sin(y);
	elseif (z <= 6e+45)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(1.0 + N[(x / N[(z / N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e-13], t$95$0, If[LessEqual[z, -5.8e-146], t$95$1, If[LessEqual[z, 4.5e-177], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+45], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.99999999999999968e-13 or 6.00000000000000021e45 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.4%

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

   if -5.99999999999999968e-13 < z < -5.80000000000000022e-146 or 4.5000000000000003e-177 < z < 6.00000000000000021e45

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 96.9%

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

      1. associate-/l* 96.7%

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

   5. Simplified 96.7%

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

      1. clear-num 96.7%

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

      2. un-div-inv 96.8%

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

   7. Applied egg-rr 96.8%

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

   8. Taylor expanded in y around 0 82.3%

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

   if -5.80000000000000022e-146 < z < 4.5000000000000003e-177

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 86.0%

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

Alternative 4: 75.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-146}:\\ \;\;\;\;z \cdot \left(1 + x \cdot \frac{\sin y}{z}\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -6.2e-13)
     t_0
     (if (<= z -5.8e-146)
       (* z (+ 1.0 (* x (/ (sin y) z))))
       (if (<= z 4e-114) (* x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -6.2e-13) {
		tmp = t_0;
	} else if (z <= -5.8e-146) {
		tmp = z * (1.0 + (x * (sin(y) / z)));
	} else if (z <= 4e-114) {
		tmp = x * sin(y);
	} 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 * cos(y)
    if (z <= (-6.2d-13)) then
        tmp = t_0
    else if (z <= (-5.8d-146)) then
        tmp = z * (1.0d0 + (x * (sin(y) / z)))
    else if (z <= 4d-114) then
        tmp = x * sin(y)
    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.cos(y);
	double tmp;
	if (z <= -6.2e-13) {
		tmp = t_0;
	} else if (z <= -5.8e-146) {
		tmp = z * (1.0 + (x * (Math.sin(y) / z)));
	} else if (z <= 4e-114) {
		tmp = x * Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -6.2e-13:
		tmp = t_0
	elif z <= -5.8e-146:
		tmp = z * (1.0 + (x * (math.sin(y) / z)))
	elif z <= 4e-114:
		tmp = x * math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -6.2e-13)
		tmp = t_0;
	elseif (z <= -5.8e-146)
		tmp = Float64(z * Float64(1.0 + Float64(x * Float64(sin(y) / z))));
	elseif (z <= 4e-114)
		tmp = Float64(x * sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -6.2e-13)
		tmp = t_0;
	elseif (z <= -5.8e-146)
		tmp = z * (1.0 + (x * (sin(y) / z)));
	elseif (z <= 4e-114)
		tmp = x * sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-13], t$95$0, If[LessEqual[z, -5.8e-146], N[(z * N[(1.0 + N[(x * N[(N[Sin[y], $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-114], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999998e-13 or 4.0000000000000002e-114 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.7%

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

   if -6.1999999999999998e-13 < z < -5.80000000000000022e-146

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 93.2%

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

      1. associate-/l* 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in y around 0 85.0%

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

   if -5.80000000000000022e-146 < z < 4.0000000000000002e-114

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 83.2%

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

Alternative 5: 73.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-45} \lor \neg \left(z \leq 1.7 \cdot 10^{-115}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.6e-45) (not (<= z 1.7e-115))) (* z (cos y)) (* x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e-45) || !(z <= 1.7e-115)) {
		tmp = z * cos(y);
	} else {
		tmp = x * 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 <= (-1.6d-45)) .or. (.not. (z <= 1.7d-115))) then
        tmp = z * cos(y)
    else
        tmp = x * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.6e-45) || !(z <= 1.7e-115)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.6e-45) or not (z <= 1.7e-115):
		tmp = z * math.cos(y)
	else:
		tmp = x * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.6e-45) || !(z <= 1.7e-115))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.6e-45) || ~((z <= 1.7e-115)))
		tmp = z * cos(y);
	else
		tmp = x * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.6e-45], N[Not[LessEqual[z, 1.7e-115]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000004e-45 or 1.6999999999999999e-115 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 82.3%

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

   if -1.60000000000000004e-45 < z < 1.6999999999999999e-115

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 78.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-45} \lor \neg \left(z \leq 1.7 \cdot 10^{-115}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00162 \lor \neg \left(y \leq 750\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00162) (not (<= y 750.0)))
   (* x (sin y))
   (+ z (* y (+ x (* -0.5 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00162) || !(y <= 750.0)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (-0.5 * (y * z))));
	}
	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 <= (-0.00162d0)) .or. (.not. (y <= 750.0d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + ((-0.5d0) * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00162) || !(y <= 750.0)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (-0.5 * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00162) or not (y <= 750.0):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (-0.5 * (y * z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00162) || !(y <= 750.0))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(-0.5 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00162) || ~((y <= 750.0)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (-0.5 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00162], N[Not[LessEqual[y, 750.0]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0016199999999999999 or 750 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 50.3%

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

   if -0.0016199999999999999 < y < 750

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

      1. *-commutative 98.6%

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

   5. Simplified 98.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00162 \lor \neg \left(y \leq 750\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.9% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 51.1%

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

   1. *-commutative 51.1%

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

5. Simplified 51.1%

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

6. Final simplification 51.1%

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

Alternative 8: 38.6% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 51.1%

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

   1. *-commutative 51.1%

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

5. Simplified 51.1%

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

6. Taylor expanded in z around inf 36.2%

   \[\leadsto \color{blue}{z} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))