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

Percentage Accurate: 99.8% → 99.8%

Time: 10.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

Alternative 2: 75.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+109}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -66000000 \lor \neg \left(z \leq 2.9 \cdot 10^{-173}\right):\\ \;\;\;\;x \cdot \left(1 - \sin y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e+109)
   (* (sin y) (- z))
   (if (or (<= z -66000000.0) (not (<= z 2.9e-173)))
     (* x (- 1.0 (* (sin y) (/ z x))))
     (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+109) {
		tmp = sin(y) * -z;
	} else if ((z <= -66000000.0) || !(z <= 2.9e-173)) {
		tmp = x * (1.0 - (sin(y) * (z / 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 <= (-1.85d+109)) then
        tmp = sin(y) * -z
    else if ((z <= (-66000000.0d0)) .or. (.not. (z <= 2.9d-173))) then
        tmp = x * (1.0d0 - (sin(y) * (z / 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 <= -1.85e+109) {
		tmp = Math.sin(y) * -z;
	} else if ((z <= -66000000.0) || !(z <= 2.9e-173)) {
		tmp = x * (1.0 - (Math.sin(y) * (z / x)));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e+109:
		tmp = math.sin(y) * -z
	elif (z <= -66000000.0) or not (z <= 2.9e-173):
		tmp = x * (1.0 - (math.sin(y) * (z / x)))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e+109)
		tmp = Float64(sin(y) * Float64(-z));
	elseif ((z <= -66000000.0) || !(z <= 2.9e-173))
		tmp = Float64(x * Float64(1.0 - Float64(sin(y) * Float64(z / x))));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.85e+109)
		tmp = sin(y) * -z;
	elseif ((z <= -66000000.0) || ~((z <= 2.9e-173)))
		tmp = x * (1.0 - (sin(y) * (z / x)));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e+109], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], If[Or[LessEqual[z, -66000000.0], N[Not[LessEqual[z, 2.9e-173]], $MachinePrecision]], N[(x * N[(1.0 - N[(N[Sin[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8500000000000001e109

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. *-commutative 69.0%

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

      3. distribute-rgt-neg-in 69.0%

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

   5. Simplified 69.0%

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

   if -1.8500000000000001e109 < z < -6.6e7 or 2.8999999999999998e-173 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

      3. *-commutative 92.5%

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

      4. associate-/l* 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in y around 0 77.9%

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

   if -6.6e7 < z < 2.8999999999999998e-173

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 93.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+109}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -66000000 \lor \neg \left(z \leq 2.9 \cdot 10^{-173}\right):\\ \;\;\;\;x \cdot \left(1 - \sin y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -6 \cdot 10^{+193}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0185:\\ \;\;\;\;x + y \cdot \left(z + \left(z \cdot -2 + y \cdot \left(x \cdot -0.5 + y \cdot \left(z \cdot -0.16666666666666666 + z \cdot 0.3333333333333333\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* (sin y) (- z))))
   (if (<= y -6e+193)
     t_0
     (if (<= y -0.05)
       t_1
       (if (<= y 0.0185)
         (+
          x
          (*
           y
           (+
            z
            (+
             (* z -2.0)
             (*
              y
              (+
               (* x -0.5)
               (*
                y
                (+ (* z -0.16666666666666666) (* z 0.3333333333333333)))))))))
         (if (<= y 2.45e+252) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = sin(y) * -z;
	double tmp;
	if (y <= -6e+193) {
		tmp = t_0;
	} else if (y <= -0.05) {
		tmp = t_1;
	} else if (y <= 0.0185) {
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))));
	} else if (y <= 2.45e+252) {
		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 = x * cos(y)
    t_1 = sin(y) * -z
    if (y <= (-6d+193)) then
        tmp = t_0
    else if (y <= (-0.05d0)) then
        tmp = t_1
    else if (y <= 0.0185d0) then
        tmp = x + (y * (z + ((z * (-2.0d0)) + (y * ((x * (-0.5d0)) + (y * ((z * (-0.16666666666666666d0)) + (z * 0.3333333333333333d0))))))))
    else if (y <= 2.45d+252) 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 = x * Math.cos(y);
	double t_1 = Math.sin(y) * -z;
	double tmp;
	if (y <= -6e+193) {
		tmp = t_0;
	} else if (y <= -0.05) {
		tmp = t_1;
	} else if (y <= 0.0185) {
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))));
	} else if (y <= 2.45e+252) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = math.sin(y) * -z
	tmp = 0
	if y <= -6e+193:
		tmp = t_0
	elif y <= -0.05:
		tmp = t_1
	elif y <= 0.0185:
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))))
	elif y <= 2.45e+252:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (y <= -6e+193)
		tmp = t_0;
	elseif (y <= -0.05)
		tmp = t_1;
	elseif (y <= 0.0185)
		tmp = Float64(x + Float64(y * Float64(z + Float64(Float64(z * -2.0) + Float64(y * Float64(Float64(x * -0.5) + Float64(y * Float64(Float64(z * -0.16666666666666666) + Float64(z * 0.3333333333333333)))))))));
	elseif (y <= 2.45e+252)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	t_1 = sin(y) * -z;
	tmp = 0.0;
	if (y <= -6e+193)
		tmp = t_0;
	elseif (y <= -0.05)
		tmp = t_1;
	elseif (y <= 0.0185)
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))));
	elseif (y <= 2.45e+252)
		tmp = t_1;
	else
		tmp = t_0;
	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[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[y, -6e+193], t$95$0, If[LessEqual[y, -0.05], t$95$1, If[LessEqual[y, 0.0185], N[(x + N[(y * N[(z + N[(N[(z * -2.0), $MachinePrecision] + N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(y * N[(N[(z * -0.16666666666666666), $MachinePrecision] + N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e+252], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e193 or 2.4499999999999999e252 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 68.1%

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

   if -6e193 < y < -0.050000000000000003 or 0.0184999999999999991 < y < 2.4499999999999999e252

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. *-commutative 58.5%

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

      3. distribute-rgt-neg-in 58.5%

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

   5. Simplified 58.5%

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

   if -0.050000000000000003 < y < 0.0184999999999999991

   1. Initial program 100.0%

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

      1. prod-diff 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-+l+ 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 99.7%

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

      7. *-commutative 99.7%

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

      8. fma-undefine 100.0%

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

      9. distribute-lft-neg-in 100.0%

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

      10. *-commutative 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. fma-define 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{x + y \cdot \left(z + \left(-2 \cdot z + y \cdot \left(-0.5 \cdot x + y \cdot \left(-0.16666666666666666 \cdot z + 0.3333333333333333 \cdot z\right)\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.05:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.0185:\\ \;\;\;\;x + y \cdot \left(z + \left(z \cdot -2 + y \cdot \left(x \cdot -0.5 + y \cdot \left(z \cdot -0.16666666666666666 + z \cdot 0.3333333333333333\right)\right)\right)\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+252}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0066 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + \left(z \cdot -2 + y \cdot \left(x \cdot -0.5 + y \cdot \left(z \cdot -0.16666666666666666 + z \cdot 0.3333333333333333\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0066) (not (<= y 0.035)))
   (* x (cos y))
   (+
    x
    (*
     y
     (+
      z
      (+
       (* z -2.0)
       (*
        y
        (+
         (* x -0.5)
         (* y (+ (* z -0.16666666666666666) (* z 0.3333333333333333)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0066) || !(y <= 0.035)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))));
	}
	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 <= (-0.0066d0)) .or. (.not. (y <= 0.035d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + ((z * (-2.0d0)) + (y * ((x * (-0.5d0)) + (y * ((z * (-0.16666666666666666d0)) + (z * 0.3333333333333333d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0066) || !(y <= 0.035)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0066) or not (y <= 0.035):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0066) || !(y <= 0.035))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(Float64(z * -2.0) + Float64(y * Float64(Float64(x * -0.5) + Float64(y * Float64(Float64(z * -0.16666666666666666) + Float64(z * 0.3333333333333333)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0066) || ~((y <= 0.035)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + ((z * -2.0) + (y * ((x * -0.5) + (y * ((z * -0.16666666666666666) + (z * 0.3333333333333333))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0066], N[Not[LessEqual[y, 0.035]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(N[(z * -2.0), $MachinePrecision] + N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(y * N[(N[(z * -0.16666666666666666), $MachinePrecision] + N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0066 or 0.035000000000000003 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 49.7%

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

   if -0.0066 < y < 0.035000000000000003

   1. Initial program 100.0%

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

      1. prod-diff 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-define 100.0%

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

      4. associate-+l+ 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 99.7%

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

      7. *-commutative 99.7%

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

      8. fma-undefine 100.0%

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

      9. distribute-lft-neg-in 100.0%

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

      10. *-commutative 100.0%

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

      11. distribute-rgt-neg-in 100.0%

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

      12. fma-define 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{x + y \cdot \left(z + \left(-2 \cdot z + y \cdot \left(-0.5 \cdot x + y \cdot \left(-0.16666666666666666 \cdot z + 0.3333333333333333 \cdot z\right)\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0066 \lor \neg \left(y \leq 0.035\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + \left(z \cdot -2 + y \cdot \left(x \cdot -0.5 + y \cdot \left(z \cdot -0.16666666666666666 + z \cdot 0.3333333333333333\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.8% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.25 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-100}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.25e-25) x (if (<= x 2.9e-100) (* y (- z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.25e-25) {
		tmp = x;
	} else if (x <= 2.9e-100) {
		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 <= (-3.25d-25)) then
        tmp = x
    else if (x <= 2.9d-100) 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 <= -3.25e-25) {
		tmp = x;
	} else if (x <= 2.9e-100) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.25e-25:
		tmp = x
	elif x <= 2.9e-100:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.25e-25)
		tmp = x;
	elseif (x <= 2.9e-100)
		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 <= -3.25e-25)
		tmp = x;
	elseif (x <= 2.9e-100)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.25e-25], x, If[LessEqual[x, 2.9e-100], N[(y * (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.25e-25 or 2.89999999999999975e-100 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. unsub-neg 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in x around inf 46.6%

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

   if -3.25e-25 < x < 2.89999999999999975e-100

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 50.4%

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

      1. mul-1-neg 50.4%

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

      2. unsub-neg 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in x around 0 34.7%

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

      1. neg-mul-1 34.7%

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

      2. distribute-rgt-neg-in 34.7%

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

   8. Simplified 34.7%

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

Alternative 6: 51.5% 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 51.1%

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

   1. mul-1-neg 51.1%

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

   2. unsub-neg 51.1%

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

5. Simplified 51.1%

   \[\leadsto \color{blue}{x - y \cdot z} \]
6. Add Preprocessing

Alternative 7: 38.0% 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 51.1%

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

   1. mul-1-neg 51.1%

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

   2. unsub-neg 51.1%

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

5. Simplified 51.1%

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

6. Taylor expanded in x around inf 36.7%

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

Reproduce

herbie shell --seed 2024137 
(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))))