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

Percentage Accurate: 99.8% → 99.8%

Time: 7.6s

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x \cdot \cos y - z \cdot \sin y \]

2. Final simplification 99.8%

   \[\leadsto \cos y \cdot x - z \cdot \sin y \]

Alternative 3: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.0068:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+20}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= y -2.95e-5)
     t_0
     (if (<= y 0.0068) (- x (* y z)) (if (<= y 3.6e+20) (* (cos y) x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (y <= -2.95e-5) {
		tmp = t_0;
	} else if (y <= 0.0068) {
		tmp = x - (y * z);
	} else if (y <= 3.6e+20) {
		tmp = cos(y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -sin(y)
    if (y <= (-2.95d-5)) then
        tmp = t_0
    else if (y <= 0.0068d0) then
        tmp = x - (y * z)
    else if (y <= 3.6d+20) then
        tmp = cos(y) * x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -Math.sin(y);
	double tmp;
	if (y <= -2.95e-5) {
		tmp = t_0;
	} else if (y <= 0.0068) {
		tmp = x - (y * z);
	} else if (y <= 3.6e+20) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	tmp = 0
	if y <= -2.95e-5:
		tmp = t_0
	elif y <= 0.0068:
		tmp = x - (y * z)
	elif y <= 3.6e+20:
		tmp = math.cos(y) * x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (y <= -2.95e-5)
		tmp = t_0;
	elseif (y <= 0.0068)
		tmp = Float64(x - Float64(y * z));
	elseif (y <= 3.6e+20)
		tmp = Float64(cos(y) * x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	tmp = 0.0;
	if (y <= -2.95e-5)
		tmp = t_0;
	elseif (y <= 0.0068)
		tmp = x - (y * z);
	elseif (y <= 3.6e+20)
		tmp = cos(y) * x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -2.95e-5], t$95$0, If[LessEqual[y, 0.0068], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+20], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9499999999999999e-5 or 3.6e20 < y

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in x around 0 60.3%

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

      1. associate-*r* 60.3%

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

      2. neg-mul-1 60.3%

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

   4. Simplified 60.3%

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

   if -2.9499999999999999e-5 < y < 0.00679999999999999962

   1. Initial program 100.0%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   if 0.00679999999999999962 < y < 3.6e20

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. fma-neg 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around inf 100.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 0.0068:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+20}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]

Alternative 4: 85.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-32} \lor \neg \left(z \leq 2.1 \cdot 10^{-129}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e-32) (not (<= z 2.1e-129)))
   (- x (* z (sin y)))
   (* (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-32) || !(z <= 2.1e-129)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = cos(y) * 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 <= (-4.6d-32)) .or. (.not. (z <= 2.1d-129))) then
        tmp = x - (z * sin(y))
    else
        tmp = cos(y) * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-32) || !(z <= 2.1e-129)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e-32) or not (z <= 2.1e-129):
		tmp = x - (z * math.sin(y))
	else:
		tmp = math.cos(y) * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.6e-32) || !(z <= 2.1e-129))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.6e-32) || ~((z <= 2.1e-129)))
		tmp = x - (z * sin(y));
	else
		tmp = cos(y) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e-32], N[Not[LessEqual[z, 2.1e-129]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6000000000000001e-32 or 2.1e-129 < z

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 89.7%

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

   if -4.6000000000000001e-32 < z < 2.1e-129

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. fma-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around inf 91.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-32} \lor \neg \left(z \leq 2.1 \cdot 10^{-129}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \]

Alternative 5: 75.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.09 \lor \neg \left(y \leq 0.0011\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.09) (not (<= y 0.0011))) (* (cos y) x) (- x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.09) || !(y <= 0.0011)) {
		tmp = cos(y) * x;
	} else {
		tmp = x - (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 <= (-0.09d0)) .or. (.not. (y <= 0.0011d0))) then
        tmp = cos(y) * x
    else
        tmp = x - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.09) || !(y <= 0.0011)) {
		tmp = Math.cos(y) * x;
	} else {
		tmp = x - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.09) or not (y <= 0.0011):
		tmp = math.cos(y) * x
	else:
		tmp = x - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.09) || !(y <= 0.0011))
		tmp = Float64(cos(y) * x);
	else
		tmp = Float64(x - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.09) || ~((y <= 0.0011)))
		tmp = cos(y) * x;
	else
		tmp = x - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.09], N[Not[LessEqual[y, 0.0011]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.089999999999999997 or 0.00110000000000000007 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. fma-neg 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 44.5%

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

   if -0.089999999999999997 < y < 0.00110000000000000007

   1. Initial program 100.0%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 99.3%

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

      1. +-commutative 99.3%

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

      2. mul-1-neg 99.3%

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

      3. unsub-neg 99.3%

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

   4. Simplified 99.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.09 \lor \neg \left(y \leq 0.0011\right):\\ \;\;\;\;\cos y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot z\\ \end{array} \]

Alternative 6: 52.8% 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. Taylor expanded in y around 0 56.7%

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

   1. +-commutative 56.7%

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

   2. mul-1-neg 56.7%

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

   3. unsub-neg 56.7%

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

4. Simplified 56.7%

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

5. Final simplification 56.7%

   \[\leadsto x - y \cdot z \]

Alternative 7: 40.2% 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. Step-by-step derivation

   1. *-commutative 99.8%

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

   2. fma-neg 99.8%

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

   3. distribute-rgt-neg-in 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in y around 0 44.6%

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

5. Final simplification 44.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(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))))