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

Percentage Accurate: 99.8% → 99.8%

Time: 6.8s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x * N[Cos[y], $MachinePrecision] + 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. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 3: 85.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+78} \lor \neg \left(x \leq 8 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+78) (not (<= x 8e-22)))
   (* x (cos y))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+78) || !(x <= 8e-22)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (z * sin(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 ((x <= (-1.9d+78)) .or. (.not. (x <= 8d-22))) then
        tmp = x * cos(y)
    else
        tmp = x + (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+78) || !(x <= 8e-22)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+78) or not (x <= 8e-22):
		tmp = x * math.cos(y)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+78) || !(x <= 8e-22))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e+78) || ~((x <= 8e-22)))
		tmp = x * cos(y);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+78], N[Not[LessEqual[x, 8e-22]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e78 or 8.0000000000000004e-22 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.6%

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

      3. associate-*l* 99.6%

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

      4. fma-def 99.6%

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

      5. pow2 99.6%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \sin y, x \cdot \cos y\right) \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \sin y, x \cdot \cos y\right)} \]

   4. Taylor expanded in z around 0 84.0%

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

   if -1.9e78 < x < 8.0000000000000004e-22

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 89.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+78} \lor \neg \left(x \leq 8 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]

Alternative 4: 74.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0215 \lor \neg \left(y \leq 0.0152\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + -0.5 \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0215) (not (<= y 0.0152)))
   (* z (sin y))
   (+ (* y z) (+ x (* -0.5 (* y (* x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0215) || !(y <= 0.0152)) {
		tmp = z * sin(y);
	} else {
		tmp = (y * z) + (x + (-0.5 * (y * (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 <= (-0.0215d0)) .or. (.not. (y <= 0.0152d0))) then
        tmp = z * sin(y)
    else
        tmp = (y * z) + (x + ((-0.5d0) * (y * (x * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0215) || !(y <= 0.0152)) {
		tmp = z * Math.sin(y);
	} else {
		tmp = (y * z) + (x + (-0.5 * (y * (x * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0215) or not (y <= 0.0152):
		tmp = z * math.sin(y)
	else:
		tmp = (y * z) + (x + (-0.5 * (y * (x * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0215) || !(y <= 0.0152))
		tmp = Float64(z * sin(y));
	else
		tmp = Float64(Float64(y * z) + Float64(x + Float64(-0.5 * Float64(y * Float64(x * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0215) || ~((y <= 0.0152)))
		tmp = z * sin(y);
	else
		tmp = (y * z) + (x + (-0.5 * (y * (x * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0215], N[Not[LessEqual[y, 0.0152]], $MachinePrecision]], N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] + N[(x + N[(-0.5 * N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.021499999999999998 or 0.0152 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 58.1%

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

   if -0.021499999999999998 < y < 0.0152

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.7%

      \[\leadsto \color{blue}{y \cdot z + \left(-0.5 \cdot \left({y}^{2} \cdot x\right) + x\right)} \]
   3. Step-by-step derivation

      1. expm1-log1p-u 97.2%

         \[\leadsto y \cdot z + \left(-0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({y}^{2} \cdot x\right)\right)} + x\right) \]

      2. expm1-udef 97.0%

         \[\leadsto y \cdot z + \left(-0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({y}^{2} \cdot x\right)} - 1\right)} + x\right) \]

      3. unpow2 97.0%

         \[\leadsto y \cdot z + \left(-0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot y\right)} \cdot x\right)} - 1\right) + x\right) \]

      4. associate-*l* 97.0%

         \[\leadsto y \cdot z + \left(-0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{y \cdot \left(y \cdot x\right)}\right)} - 1\right) + x\right) \]

   4. Applied egg-rr 97.0%

      \[\leadsto y \cdot z + \left(-0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \left(y \cdot x\right)\right)} - 1\right)} + x\right) \]
   5. Step-by-step derivation

      1. expm1-def 97.2%

         \[\leadsto y \cdot z + \left(-0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(y \cdot x\right)\right)\right)} + x\right) \]

      2. expm1-log1p 99.7%

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

   6. Simplified 99.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0215 \lor \neg \left(y \leq 0.0152\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + -0.5 \cdot \left(y \cdot \left(x \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 5: 41.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-168}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.2e-101) x (if (<= x 6.6e-168) (* y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e-101) {
		tmp = x;
	} else if (x <= 6.6e-168) {
		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 <= (-2.2d-101)) then
        tmp = x
    else if (x <= 6.6d-168) 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 <= -2.2e-101) {
		tmp = x;
	} else if (x <= 6.6e-168) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.2e-101:
		tmp = x
	elif x <= 6.6e-168:
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.2e-101)
		tmp = x;
	elseif (x <= 6.6e-168)
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.2e-101)
		tmp = x;
	elseif (x <= 6.6e-168)
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.2e-101], x, If[LessEqual[x, 6.6e-168], N[(y * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1999999999999999e-101 or 6.6000000000000003e-168 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.4%

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

      3. associate-*l* 99.4%

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

      4. fma-def 99.4%

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

      5. pow2 99.4%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \sin y, x \cdot \cos y\right) \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \sin y, x \cdot \cos y\right)} \]

   4. Taylor expanded in y around 0 43.4%

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

   if -2.1999999999999999e-101 < x < 6.6000000000000003e-168

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 44.5%

      \[\leadsto \color{blue}{y \cdot z + \left(-0.5 \cdot \left({y}^{2} \cdot x\right) + x\right)} \]

   3. Taylor expanded in z around inf 31.8%

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

      1. *-commutative 31.8%

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

   5. Simplified 31.8%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-101}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-168}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 51.6% 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 48.3%

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

3. Final simplification 48.3%

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

Alternative 7: 38.5% 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%

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

   2. add-cube-cbrt 99.0%

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

   3. associate-*l* 99.0%

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

   4. fma-def 99.0%

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

   5. pow2 99.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z}\right)}^{2}}, \sqrt[3]{z} \cdot \sin y, x \cdot \cos y\right) \]

3. Applied egg-rr 99.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z}\right)}^{2}, \sqrt[3]{z} \cdot \sin y, x \cdot \cos y\right)} \]

4. Taylor expanded in y around 0 33.9%

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

5. Final simplification 33.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023215 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))