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

Percentage Accurate: 99.8% → 99.8%

Time: 8.5s

Alternatives: 8

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. cancel-sign-sub-inv 99.8%

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

   2. +-commutative 99.8%

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

   3. distribute-lft-neg-out 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. sin-neg 99.8%

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

   6. fma-define 99.8%

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

   7. sin-neg 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 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 3: 74.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -0.13:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.098:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+114} \lor \neg \left(y \leq 4.5 \cdot 10^{+246}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (- (sin y)))))
   (if (<= y -2.2e+158)
     t_0
     (if (<= y -0.13)
       t_1
       (if (<= y 0.098)
         (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* z y)))) z)))
         (if (or (<= y 2.25e+114) (not (<= y 4.5e+246))) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = z * -sin(y);
	double tmp;
	if (y <= -2.2e+158) {
		tmp = t_0;
	} else if (y <= -0.13) {
		tmp = t_1;
	} else if (y <= 0.098) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	} else if ((y <= 2.25e+114) || !(y <= 4.5e+246)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = x * cos(y)
    t_1 = z * -sin(y)
    if (y <= (-2.2d+158)) then
        tmp = t_0
    else if (y <= (-0.13d0)) then
        tmp = t_1
    else if (y <= 0.098d0) then
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (z * y)))) - z))
    else if ((y <= 2.25d+114) .or. (.not. (y <= 4.5d+246))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.cos(y);
	double t_1 = z * -Math.sin(y);
	double tmp;
	if (y <= -2.2e+158) {
		tmp = t_0;
	} else if (y <= -0.13) {
		tmp = t_1;
	} else if (y <= 0.098) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	} else if ((y <= 2.25e+114) || !(y <= 4.5e+246)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = z * -math.sin(y)
	tmp = 0
	if y <= -2.2e+158:
		tmp = t_0
	elif y <= -0.13:
		tmp = t_1
	elif y <= 0.098:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z))
	elif (y <= 2.25e+114) or not (y <= 4.5e+246):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (y <= -2.2e+158)
		tmp = t_0;
	elseif (y <= -0.13)
		tmp = t_1;
	elseif (y <= 0.098)
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(z * y)))) - z)));
	elseif ((y <= 2.25e+114) || !(y <= 4.5e+246))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	t_1 = z * -sin(y);
	tmp = 0.0;
	if (y <= -2.2e+158)
		tmp = t_0;
	elseif (y <= -0.13)
		tmp = t_1;
	elseif (y <= 0.098)
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	elseif ((y <= 2.25e+114) || ~((y <= 4.5e+246)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -2.2e+158], t$95$0, If[LessEqual[y, -0.13], t$95$1, If[LessEqual[y, 0.098], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.25e+114], N[Not[LessEqual[y, 4.5e+246]], $MachinePrecision]], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2000000000000001e158 or 0.098000000000000004 < y < 2.25e114 or 4.5e246 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 64.9%

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

   if -2.2000000000000001e158 < y < -0.13 or 2.25e114 < y < 4.5e246

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 64.4%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \sin y\right)} \]
   4. Step-by-step derivation

      1. neg-mul-1 64.4%

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

      2. distribute-rgt-neg-in 64.4%

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

   5. Simplified 64.4%

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

   if -0.13 < y < 0.098000000000000004

   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%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.13:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 0.098:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+114} \lor \neg \left(y \leq 4.5 \cdot 10^{+246}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-137} \lor \neg \left(z \leq 4.8 \cdot 10^{-46}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e-137) (not (<= z 4.8e-46)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-137) || !(z <= 4.8e-46)) {
		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 <= (-1.8d-137)) .or. (.not. (z <= 4.8d-46))) 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 <= -1.8e-137) || !(z <= 4.8e-46)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e-137) or not (z <= 4.8e-46):
		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 <= -1.8e-137) || !(z <= 4.8e-46))
		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 <= -1.8e-137) || ~((z <= 4.8e-46)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e-137], N[Not[LessEqual[z, 4.8e-46]], $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 < -1.80000000000000003e-137 or 4.80000000000000027e-46 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 87.8%

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

   if -1.80000000000000003e-137 < z < 4.80000000000000027e-46

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 86.9%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-137} \lor \neg \left(z \leq 4.8 \cdot 10^{-46}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3700000 \lor \neg \left(y \leq 0.066\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3700000.0) (not (<= y 0.066)))
   (* x (cos y))
   (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* z y)))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3700000.0) || !(y <= 0.066)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * 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 <= (-3700000.0d0)) .or. (.not. (y <= 0.066d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (z * y)))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3700000.0) || !(y <= 0.066)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3700000.0) or not (y <= 0.066):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3700000.0) || !(y <= 0.066))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(z * y)))) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3700000.0) || ~((y <= 0.066)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3700000.0], N[Not[LessEqual[y, 0.066]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e6 or 0.066000000000000003 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 52.4%

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

   if -3.7e6 < y < 0.066000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3700000 \lor \neg \left(y \leq 0.066\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.5% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+211} \lor \neg \left(z \leq 3.8 \cdot 10^{+158}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e+211) (not (<= z 3.8e+158))) (* z (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+211) || !(z <= 3.8e+158)) {
		tmp = z * -y;
	} 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 <= (-1.4d+211)) .or. (.not. (z <= 3.8d+158))) then
        tmp = z * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e+211) || !(z <= 3.8e+158)) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e+211) or not (z <= 3.8e+158):
		tmp = z * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e+211) || !(z <= 3.8e+158))
		tmp = Float64(z * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e+211) || ~((z <= 3.8e+158)))
		tmp = z * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e+211], N[Not[LessEqual[z, 3.8e+158]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e211 or 3.7999999999999998e158 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 53.2%

      \[\leadsto \color{blue}{x + -1 \cdot \left(y \cdot z\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 53.2%

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

      2. unsub-neg 53.2%

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

   5. Simplified 53.2%

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

   6. Taylor expanded in x around 0 43.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 43.8%

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

      2. distribute-lft-neg-in 43.8%

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

   8. Simplified 43.8%

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

   if -1.4e211 < z < 3.7999999999999998e158

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 47.7%

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

      1. sub-neg 47.7%

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

      2. +-commutative 47.7%

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

      3. neg-mul-1 47.7%

         \[\leadsto x + y \cdot \left(\color{blue}{-1 \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right) \]

      4. neg-mul-1 47.7%

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

      5. +-commutative 47.7%

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

      6. sub-neg 47.7%

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

      7. associate-*r* 47.7%

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

      8. *-commutative 47.7%

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

   5. Simplified 47.7%

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

   6. Taylor expanded in y around 0 37.2%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+211} \lor \neg \left(z \leq 3.8 \cdot 10^{+158}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.5% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x - N[(z * y), $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 49.9%

   \[\leadsto \color{blue}{x + -1 \cdot \left(y \cdot z\right)} \]
4. Step-by-step derivation

   1. mul-1-neg 49.9%

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

   2. unsub-neg 49.9%

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

5. Simplified 49.9%

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

6. Final simplification 49.9%

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

Alternative 8: 38.2% 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 y around 0 48.8%

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

   1. sub-neg 48.8%

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

   2. +-commutative 48.8%

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

   3. neg-mul-1 48.8%

      \[\leadsto x + y \cdot \left(\color{blue}{-1 \cdot z} + -0.5 \cdot \left(x \cdot y\right)\right) \]

   4. neg-mul-1 48.8%

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

   5. +-commutative 48.8%

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

   6. sub-neg 48.8%

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

   7. associate-*r* 48.8%

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

   8. *-commutative 48.8%

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

5. Simplified 48.8%

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

6. Taylor expanded in y around 0 31.6%

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

Reproduce

herbie shell --seed 2024088 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))