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

Percentage Accurate: 99.8% → 99.8%

Time: 11.4s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 2: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -360000000000 \lor \neg \left(y \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -360000000000.0) (not (<= y 8e-7)))
   (* x (sin y))
   (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -360000000000.0) || !(y <= 8e-7)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (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 <= (-360000000000.0d0)) .or. (.not. (y <= 8d-7))) then
        tmp = x * sin(y)
    else
        tmp = z + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -360000000000.0) || !(y <= 8e-7)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -360000000000.0) or not (y <= 8e-7):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -360000000000.0) || !(y <= 8e-7))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -360000000000.0) || ~((y <= 8e-7)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -360000000000.0], N[Not[LessEqual[y, 8e-7]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e11 or 7.9999999999999996e-7 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 49.9%

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

   if -3.6e11 < y < 7.9999999999999996e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.4%

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

      1. +-commutative 99.4%

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

   4. Simplified 99.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -360000000000 \lor \neg \left(y \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]

Alternative 3: 74.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0014:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y + \left(z + \left(y \cdot y\right) \cdot \left(z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.0014)
   (* z (cos y))
   (if (<= y 8e-7) (+ (* x y) (+ z (* (* y y) (* z -0.5)))) (* x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0014) {
		tmp = z * cos(y);
	} else if (y <= 8e-7) {
		tmp = (x * y) + (z + ((y * y) * (z * -0.5)));
	} else {
		tmp = x * 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 (y <= (-0.0014d0)) then
        tmp = z * cos(y)
    else if (y <= 8d-7) then
        tmp = (x * y) + (z + ((y * y) * (z * (-0.5d0))))
    else
        tmp = x * sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.0014) {
		tmp = z * Math.cos(y);
	} else if (y <= 8e-7) {
		tmp = (x * y) + (z + ((y * y) * (z * -0.5)));
	} else {
		tmp = x * Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.0014:
		tmp = z * math.cos(y)
	elif y <= 8e-7:
		tmp = (x * y) + (z + ((y * y) * (z * -0.5)))
	else:
		tmp = x * math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.0014)
		tmp = Float64(z * cos(y));
	elseif (y <= 8e-7)
		tmp = Float64(Float64(x * y) + Float64(z + Float64(Float64(y * y) * Float64(z * -0.5))));
	else
		tmp = Float64(x * sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.0014)
		tmp = z * cos(y);
	elseif (y <= 8e-7)
		tmp = (x * y) + (z + ((y * y) * (z * -0.5)));
	else
		tmp = x * sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.0014], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-7], N[(N[(x * y), $MachinePrecision] + N[(z + N[(N[(y * y), $MachinePrecision] * N[(z * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00139999999999999999

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 62.6%

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

   if -0.00139999999999999999 < y < 7.9999999999999996e-7

   1. Initial program 100.0%

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

      1. add-cube-cbrt 98.6%

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

      2. pow3 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in y around 0 98.6%

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

   5. Taylor expanded in y around 0 100.0%

      \[\leadsto x \cdot y + \color{blue}{\left({1}^{0.3333333333333333} \cdot z + {y}^{2} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot z\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 100.0%

         \[\leadsto x \cdot y + \left(\color{blue}{1} \cdot z + {y}^{2} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot z\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot z\right)\right)\right) \]

      2. *-lft-identity 100.0%

         \[\leadsto x \cdot y + \left(\color{blue}{z} + {y}^{2} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot z\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot z\right)\right)\right) \]

      3. unpow2 100.0%

         \[\leadsto x \cdot y + \left(z + \color{blue}{\left(y \cdot y\right)} \cdot \left(-0.3333333333333333 \cdot \left({1}^{0.3333333333333333} \cdot z\right) + -0.16666666666666666 \cdot \left({1}^{0.3333333333333333} \cdot z\right)\right)\right) \]

      4. distribute-rgt-out 100.0%

         \[\leadsto x \cdot y + \left(z + \left(y \cdot y\right) \cdot \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot z\right) \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)}\right) \]

      5. pow-base-1 100.0%

         \[\leadsto x \cdot y + \left(z + \left(y \cdot y\right) \cdot \left(\left(\color{blue}{1} \cdot z\right) \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)\right) \]

      6. *-lft-identity 100.0%

         \[\leadsto x \cdot y + \left(z + \left(y \cdot y\right) \cdot \left(\color{blue}{z} \cdot \left(-0.3333333333333333 + -0.16666666666666666\right)\right)\right) \]

      7. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   if 7.9999999999999996e-7 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 56.5%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0014:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-7}:\\ \;\;\;\;x \cdot y + \left(z + \left(y \cdot y\right) \cdot \left(z \cdot -0.5\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y\\ \end{array} \]

Alternative 4: 42.2% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-157}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e-157) z (if (<= z 1.1e-194) (* x y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-157) {
		tmp = z;
	} else if (z <= 1.1e-194) {
		tmp = x * y;
	} else {
		tmp = 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 (z <= (-4.8d-157)) then
        tmp = z
    else if (z <= 1.1d-194) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e-157) {
		tmp = z;
	} else if (z <= 1.1e-194) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.8e-157:
		tmp = z
	elif z <= 1.1e-194:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e-157)
		tmp = z;
	elseif (z <= 1.1e-194)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.8e-157)
		tmp = z;
	elseif (z <= 1.1e-194)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e-157], z, If[LessEqual[z, 1.1e-194], N[(x * y), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-157 or 1.1000000000000001e-194 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

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

      2. pow3 98.4%

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

   3. Applied egg-rr 98.4%

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

   4. Taylor expanded in y around 0 72.9%

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

   5. Taylor expanded in y around 0 52.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot z} \]
   6. Step-by-step derivation

      1. pow-base-1 52.4%

         \[\leadsto \color{blue}{1} \cdot z \]

      2. *-lft-identity 52.4%

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

   7. Simplified 52.4%

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

   if -4.8e-157 < z < 1.1000000000000001e-194

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around 0 54.6%

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

   5. Taylor expanded in x around inf 38.9%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-157}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-194}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 5: 52.3% accurate, 41.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z):
	return z + (x * y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 57.0%

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

   1. +-commutative 57.0%

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

4. Simplified 57.0%

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

5. Final simplification 57.0%

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

Alternative 6: 39.2% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return 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 = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 98.7%

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

   2. pow3 98.7%

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

3. Applied egg-rr 98.7%

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

4. Taylor expanded in y around 0 68.9%

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

5. Taylor expanded in y around 0 44.5%

   \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot z} \]
6. Step-by-step derivation

   1. pow-base-1 44.5%

      \[\leadsto \color{blue}{1} \cdot z \]

   2. *-lft-identity 44.5%

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

7. Simplified 44.5%

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

8. Final simplification 44.5%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023287 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))