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

Percentage Accurate: 99.8% → 99.8%

Time: 8.8s

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, 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. Final simplification 99.8%

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

Alternative 2: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.15e-7)
   (- x (* z (sin y)))
   (if (<= z 9.6e-88) (* x (cos y)) (fma z (- (sin y)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.15e-7) {
		tmp = x - (z * sin(y));
	} else if (z <= 9.6e-88) {
		tmp = x * cos(y);
	} else {
		tmp = fma(z, -sin(y), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.15e-7)
		tmp = Float64(x - Float64(z * sin(y)));
	elseif (z <= 9.6e-88)
		tmp = Float64(x * cos(y));
	else
		tmp = fma(z, Float64(-sin(y)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.15e-7], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-88], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z * (-N[Sin[y], $MachinePrecision]) + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1500000000000001e-7

   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 -2.1500000000000001e-7 < z < 9.5999999999999998e-88

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 90.6%

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

   if 9.5999999999999998e-88 < z

   1. Initial program 99.9%

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

      1. cancel-sign-sub-inv 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

      5. sin-neg 99.9%

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

      6. fma-define 99.9%

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

      7. sin-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 85.4%

      \[\leadsto \mathsf{fma}\left(z, -\sin y, \color{blue}{x}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-7}:\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ t_1 := x \cdot \cos y\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+138}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.062:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \mathbf{elif}\;y \leq 470000000000 \lor \neg \left(y \leq 2.5 \cdot 10^{+242}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))) (t_1 (* x (cos y))))
   (if (<= y -2.55e+138)
     t_0
     (if (<= y -1.95e+30)
       t_1
       (if (<= y -0.18)
         t_0
         (if (<= y 0.062)
           (+
            x
            (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* y z)))) z)))
           (if (or (<= y 470000000000.0) (not (<= y 2.5e+242))) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double t_1 = x * cos(y);
	double tmp;
	if (y <= -2.55e+138) {
		tmp = t_0;
	} else if (y <= -1.95e+30) {
		tmp = t_1;
	} else if (y <= -0.18) {
		tmp = t_0;
	} else if (y <= 0.062) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	} else if ((y <= 470000000000.0) || !(y <= 2.5e+242)) {
		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 = sin(y) * -z
    t_1 = x * cos(y)
    if (y <= (-2.55d+138)) then
        tmp = t_0
    else if (y <= (-1.95d+30)) then
        tmp = t_1
    else if (y <= (-0.18d0)) then
        tmp = t_0
    else if (y <= 0.062d0) then
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (y * z)))) - z))
    else if ((y <= 470000000000.0d0) .or. (.not. (y <= 2.5d+242))) 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 = Math.sin(y) * -z;
	double t_1 = x * Math.cos(y);
	double tmp;
	if (y <= -2.55e+138) {
		tmp = t_0;
	} else if (y <= -1.95e+30) {
		tmp = t_1;
	} else if (y <= -0.18) {
		tmp = t_0;
	} else if (y <= 0.062) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	} else if ((y <= 470000000000.0) || !(y <= 2.5e+242)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	t_1 = x * math.cos(y)
	tmp = 0
	if y <= -2.55e+138:
		tmp = t_0
	elif y <= -1.95e+30:
		tmp = t_1
	elif y <= -0.18:
		tmp = t_0
	elif y <= 0.062:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z))
	elif (y <= 470000000000.0) or not (y <= 2.5e+242):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	t_1 = Float64(x * cos(y))
	tmp = 0.0
	if (y <= -2.55e+138)
		tmp = t_0;
	elseif (y <= -1.95e+30)
		tmp = t_1;
	elseif (y <= -0.18)
		tmp = t_0;
	elseif (y <= 0.062)
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(y * z)))) - z)));
	elseif ((y <= 470000000000.0) || !(y <= 2.5e+242))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	t_1 = x * cos(y);
	tmp = 0.0;
	if (y <= -2.55e+138)
		tmp = t_0;
	elseif (y <= -1.95e+30)
		tmp = t_1;
	elseif (y <= -0.18)
		tmp = t_0;
	elseif (y <= 0.062)
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	elseif ((y <= 470000000000.0) || ~((y <= 2.5e+242)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+138], t$95$0, If[LessEqual[y, -1.95e+30], t$95$1, If[LessEqual[y, -0.18], t$95$0, If[LessEqual[y, 0.062], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 470000000000.0], N[Not[LessEqual[y, 2.5e+242]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5499999999999999e138 or -1.95000000000000005e30 < y < -0.17999999999999999 or 0.062 < y < 4.7e11 or 2.5000000000000002e242 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. neg-mul-1 76.0%

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

      2. *-commutative 76.0%

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

      3. distribute-rgt-neg-in 76.0%

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

   5. Simplified 76.0%

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

   if -2.5499999999999999e138 < y < -1.95000000000000005e30 or 4.7e11 < y < 2.5000000000000002e242

   1. Initial program 99.5%

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

   3. Taylor expanded in x around inf 66.6%

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

   if -0.17999999999999999 < y < 0.062

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+138}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.18:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.062:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \mathbf{elif}\;y \leq 470000000000 \lor \neg \left(y \leq 2.5 \cdot 10^{+242}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-7} \lor \neg \left(z \leq 9.6 \cdot 10^{-88}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e-7) (not (<= z 9.6e-88)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-7) || !(z <= 9.6e-88)) {
		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 <= (-3.5d-7)) .or. (.not. (z <= 9.6d-88))) 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 <= -3.5e-7) || !(z <= 9.6e-88)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e-7) or not (z <= 9.6e-88):
		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 <= -3.5e-7) || !(z <= 9.6e-88))
		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 <= -3.5e-7) || ~((z <= 9.6e-88)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-7], N[Not[LessEqual[z, 9.6e-88]], $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 < -3.49999999999999984e-7 or 9.5999999999999998e-88 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 86.7%

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

   if -3.49999999999999984e-7 < z < 9.5999999999999998e-88

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 90.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-7} \lor \neg \left(z \leq 9.6 \cdot 10^{-88}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.33 \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.33) (not (<= y 0.00078)))
   (* x (cos y))
   (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* y z)))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.33) || !(y <= 0.00078)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - 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 <= (-0.33d0)) .or. (.not. (y <= 0.00078d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (y * z)))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.33) || !(y <= 0.00078)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.33) or not (y <= 0.00078):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.33) || !(y <= 0.00078))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(y * z)))) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.33) || ~((y <= 0.00078)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.33], N[Not[LessEqual[y, 0.00078]], $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[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.330000000000000016 or 7.79999999999999986e-4 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 51.8%

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

   if -0.330000000000000016 < y < 7.79999999999999986e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.5%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.33 \lor \neg \left(y \leq 0.00078\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 42.2% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e-120) x (if (<= x 5.2e-188) (* y (- z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-120) {
		tmp = x;
	} else if (x <= 5.2e-188) {
		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 (x <= (-2.8d-120)) then
        tmp = x
    else if (x <= 5.2d-188) 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 (x <= -2.8e-120) {
		tmp = x;
	} else if (x <= 5.2e-188) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e-120:
		tmp = x
	elif x <= 5.2e-188:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e-120)
		tmp = x;
	elseif (x <= 5.2e-188)
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.8e-120)
		tmp = x;
	elseif (x <= 5.2e-188)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e-120], x, If[LessEqual[x, 5.2e-188], N[(y * (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999994e-120 or 5.2000000000000001e-188 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 76.6%

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

   4. Taylor expanded in y around 0 48.2%

      \[\leadsto \color{blue}{x} \]

   if -2.79999999999999994e-120 < x < 5.2000000000000001e-188

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.8%

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

      1. neg-mul-1 80.8%

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

      2. *-commutative 80.8%

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

      3. distribute-rgt-neg-in 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in y around 0 40.9%

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

      1. mul-1-neg 40.9%

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

      2. distribute-rgt-neg-in 40.9%

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

   8. Simplified 40.9%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-188}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.1% 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 53.3%

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

   1. mul-1-neg 53.3%

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

   2. unsub-neg 53.3%

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

5. Simplified 53.3%

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

6. Final simplification 53.3%

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

Alternative 8: 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. Taylor expanded in x around inf 63.2%

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

4. Taylor expanded in y around 0 41.2%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 41.2%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(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))))