Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 9.4s

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. Final simplification 99.8%

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

Alternative 2: 85.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16} \lor \neg \left(z \leq 4.1 \cdot 10^{-27}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-16) (not (<= z 4.1e-27)))
   (+ x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-16) || !(z <= 4.1e-27)) {
		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 <= (-2.4d-16)) .or. (.not. (z <= 4.1d-27))) 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 <= -2.4e-16) || !(z <= 4.1e-27)) {
		tmp = x + (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-16) or not (z <= 4.1e-27):
		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 <= -2.4e-16) || !(z <= 4.1e-27))
		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 <= -2.4e-16) || ~((z <= 4.1e-27)))
		tmp = x + (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e-16], N[Not[LessEqual[z, 4.1e-27]], $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 < -2.40000000000000005e-16 or 4.0999999999999999e-27 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 89.0%

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

   if -2.40000000000000005e-16 < z < 4.0999999999999999e-27

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 87.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16} \lor \neg \left(z \leq 4.1 \cdot 10^{-27}\right):\\ \;\;\;\;x + z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+33} \lor \neg \left(y \leq 14\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e+33) (not (<= y 14.0)))
   (* x (cos y))
   (+ x (* y (+ z (* -0.5 (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+33) || !(y <= 14.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (-0.5 * (x * 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 ((y <= (-4.3d+33)) .or. (.not. (y <= 14.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + ((-0.5d0) * (x * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e+33) || !(y <= 14.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (-0.5 * (x * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e+33) or not (y <= 14.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (-0.5 * (x * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e+33) || !(y <= 14.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(-0.5 * Float64(x * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.3e+33) || ~((y <= 14.0)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (-0.5 * (x * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e+33], N[Not[LessEqual[y, 14.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(-0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.30000000000000028e33 or 14 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 48.8%

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

   if -4.30000000000000028e33 < y < 14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.3%

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

      1. *-commutative 96.3%

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

   5. Simplified 96.3%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+33} \lor \neg \left(y \leq 14\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+211} \lor \neg \left(z \leq 5.4 \cdot 10^{+125}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.2e+211) (not (<= z 5.4e+125))) (* z (sin y)) (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.2e+211) || !(z <= 5.4e+125)) {
		tmp = 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 <= (-1.2d+211)) .or. (.not. (z <= 5.4d+125))) then
        tmp = 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 <= -1.2e+211) || !(z <= 5.4e+125)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.2e+211) or not (z <= 5.4e+125):
		tmp = z * math.sin(y)
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.2e+211) || !(z <= 5.4e+125))
		tmp = 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 <= -1.2e+211) || ~((z <= 5.4e+125)))
		tmp = z * sin(y);
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.2e+211], N[Not[LessEqual[z, 5.4e+125]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000009e211 or 5.3999999999999997e125 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 82.3%

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

   if -1.20000000000000009e211 < z < 5.3999999999999997e125

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 74.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+211} \lor \neg \left(z \leq 5.4 \cdot 10^{+125}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.2% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e-224) x (if (<= x 1.55e-97) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e-224) {
		tmp = x;
	} else if (x <= 1.55e-97) {
		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 <= (-1.25d-224)) then
        tmp = x
    else if (x <= 1.55d-97) 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 <= -1.25e-224) {
		tmp = x;
	} else if (x <= 1.55e-97) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e-224:
		tmp = x
	elif x <= 1.55e-97:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e-224)
		tmp = x;
	elseif (x <= 1.55e-97)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.25e-224)
		tmp = x;
	elseif (x <= 1.55e-97)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e-224], x, If[LessEqual[x, 1.55e-97], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e-224 or 1.55000000000000001e-97 < x

   1. Initial program 99.8%

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

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \cos y + z \cdot \sin y} \cdot \sqrt[3]{x \cdot \cos y + z \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \cos y + z \cdot \sin y}} \]

      2. pow3 97.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \cos y + z \cdot \sin y}\right)}^{3}} \]

      3. +-commutative 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot \sin y + x \cdot \cos y}}\right)}^{3} \]

      4. fma-define 97.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}}\right)}^{3} \]

   4. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}\right)}^{3}} \]

   5. Taylor expanded in z around 0 71.3%

      \[\leadsto \color{blue}{x \cdot \cos y} \]
   6. Step-by-step derivation

      1. *-commutative 71.3%

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

   7. Simplified 71.3%

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

   8. Taylor expanded in y around 0 44.3%

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

   if -1.25e-224 < x < 1.55000000000000001e-97

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 50.1%

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

      1. +-commutative 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in y around inf 38.0%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-224}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% 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 49.2%

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

   1. +-commutative 49.2%

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

5. Simplified 49.2%

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

6. Final simplification 49.2%

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

Alternative 7: 39.0% 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. Step-by-step derivation

   1. add-cube-cbrt 97.8%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \cos y + z \cdot \sin y} \cdot \sqrt[3]{x \cdot \cos y + z \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \cos y + z \cdot \sin y}} \]

   2. pow3 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \cos y + z \cdot \sin y}\right)}^{3}} \]

   3. +-commutative 97.8%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{z \cdot \sin y + x \cdot \cos y}}\right)}^{3} \]

   4. fma-define 97.8%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}}\right)}^{3} \]

4. Applied egg-rr 97.8%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, \sin y, x \cdot \cos y\right)}\right)}^{3}} \]

5. Taylor expanded in z around 0 58.9%

   \[\leadsto \color{blue}{x \cdot \cos y} \]
6. Step-by-step derivation

   1. *-commutative 58.9%

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

7. Simplified 58.9%

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

8. Taylor expanded in y around 0 37.4%

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

9. Final simplification 37.4%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))