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

Percentage Accurate: 99.8% → 99.8%

Time: 7.7s

Alternatives: 7

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 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 74.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \sin y\\ \mathbf{if}\;y \leq -3600000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 31000:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+146} \lor \neg \left(y \leq 1.08 \cdot 10^{+186}\right) \land y \leq 1.35 \cdot 10^{+230}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (sin y))))
   (if (<= y -3600000000.0)
     t_0
     (if (<= y 31000.0)
       (+ z (* x y))
       (if (or (<= y 2.75e+146) (and (not (<= y 1.08e+186)) (<= y 1.35e+230)))
         t_0
         (* z (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * sin(y);
	double tmp;
	if (y <= -3600000000.0) {
		tmp = t_0;
	} else if (y <= 31000.0) {
		tmp = z + (x * y);
	} else if ((y <= 2.75e+146) || (!(y <= 1.08e+186) && (y <= 1.35e+230))) {
		tmp = t_0;
	} else {
		tmp = z * 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) :: t_0
    real(8) :: tmp
    t_0 = x * sin(y)
    if (y <= (-3600000000.0d0)) then
        tmp = t_0
    else if (y <= 31000.0d0) then
        tmp = z + (x * y)
    else if ((y <= 2.75d+146) .or. (.not. (y <= 1.08d+186)) .and. (y <= 1.35d+230)) then
        tmp = t_0
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.sin(y);
	double tmp;
	if (y <= -3600000000.0) {
		tmp = t_0;
	} else if (y <= 31000.0) {
		tmp = z + (x * y);
	} else if ((y <= 2.75e+146) || (!(y <= 1.08e+186) && (y <= 1.35e+230))) {
		tmp = t_0;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.sin(y)
	tmp = 0
	if y <= -3600000000.0:
		tmp = t_0
	elif y <= 31000.0:
		tmp = z + (x * y)
	elif (y <= 2.75e+146) or (not (y <= 1.08e+186) and (y <= 1.35e+230)):
		tmp = t_0
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * sin(y))
	tmp = 0.0
	if (y <= -3600000000.0)
		tmp = t_0;
	elseif (y <= 31000.0)
		tmp = Float64(z + Float64(x * y));
	elseif ((y <= 2.75e+146) || (!(y <= 1.08e+186) && (y <= 1.35e+230)))
		tmp = t_0;
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * sin(y);
	tmp = 0.0;
	if (y <= -3600000000.0)
		tmp = t_0;
	elseif (y <= 31000.0)
		tmp = z + (x * y);
	elseif ((y <= 2.75e+146) || (~((y <= 1.08e+186)) && (y <= 1.35e+230)))
		tmp = t_0;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3600000000.0], t$95$0, If[LessEqual[y, 31000.0], N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.75e+146], And[N[Not[LessEqual[y, 1.08e+186]], $MachinePrecision], LessEqual[y, 1.35e+230]]], t$95$0, N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e9 or 31000 < y < 2.7500000000000002e146 or 1.08000000000000003e186 < y < 1.35000000000000002e230

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 62.7%

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

   if -3.6e9 < y < 31000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.5%

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

      1. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   if 2.7500000000000002e146 < y < 1.08000000000000003e186 or 1.35000000000000002e230 < y

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 69.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3600000000:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{elif}\;y \leq 31000:\\ \;\;\;\;z + x \cdot y\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+146} \lor \neg \left(y \leq 1.08 \cdot 10^{+186}\right) \land y \leq 1.35 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+191} \lor \neg \left(z \leq 0.455\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+191) (not (<= z 0.455)))
   (* z (cos y))
   (+ (* x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+191) || !(z <= 0.455)) {
		tmp = z * cos(y);
	} else {
		tmp = (x * sin(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 ((z <= (-1.3d+191)) .or. (.not. (z <= 0.455d0))) then
        tmp = z * cos(y)
    else
        tmp = (x * sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+191) || !(z <= 0.455)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (x * Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+191) or not (z <= 0.455):
		tmp = z * math.cos(y)
	else:
		tmp = (x * math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e+191) || !(z <= 0.455))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(x * sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e+191) || ~((z <= 0.455)))
		tmp = z * cos(y);
	else
		tmp = (x * sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+191], N[Not[LessEqual[z, 0.455]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e191 or 0.455000000000000016 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.2%

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

   if -1.3e191 < z < 0.455000000000000016

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+191} \lor \neg \left(z \leq 0.455\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \sin y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3600000000 \lor \neg \left(y \leq 31000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3600000000.0) (not (<= y 31000.0)))
   (* x (sin y))
   (+ z (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3600000000.0) || !(y <= 31000.0)) {
		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 <= (-3600000000.0d0)) .or. (.not. (y <= 31000.0d0))) 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 <= -3600000000.0) || !(y <= 31000.0)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3600000000.0) or not (y <= 31000.0):
		tmp = x * math.sin(y)
	else:
		tmp = z + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3600000000.0) || !(y <= 31000.0))
		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 <= -3600000000.0) || ~((y <= 31000.0)))
		tmp = x * sin(y);
	else
		tmp = z + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3600000000.0], N[Not[LessEqual[y, 31000.0]], $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 < -3.6e9 or 31000 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 56.0%

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

   if -3.6e9 < y < 31000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.5%

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

      1. +-commutative 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3600000000 \lor \neg \left(y \leq 31000\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 40.1% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+142}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 1.5e+142) z (* x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e+142) {
		tmp = z;
	} else {
		tmp = 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 (x <= 1.5d+142) then
        tmp = z
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.5e+142) {
		tmp = z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.5e+142:
		tmp = z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.5e+142)
		tmp = z;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.5e+142)
		tmp = z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.5e+142], z, N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.49999999999999987e142

   1. Initial program 99.8%

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

      1. add-cube-cbrt 99.1%

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

      2. pow3 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in y around 0 76.2%

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

   6. Taylor expanded in x around 0 45.6%

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

   if 1.49999999999999987e142 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.0%

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

   4. Taylor expanded in y around 0 37.6%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+142}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.5% 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 99.8%

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

3. Taylor expanded in y around 0 52.4%

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

   1. +-commutative 52.4%

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

5. Simplified 52.4%

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

6. Final simplification 52.4%

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

Alternative 7: 39.0% 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 99.8%

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

   1. add-cube-cbrt 99.0%

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

   2. pow3 99.0%

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

4. Applied egg-rr 99.0%

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

5. Taylor expanded in y around 0 78.8%

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

6. Taylor expanded in x around 0 40.5%

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

7. Final simplification 40.5%

   \[\leadsto z \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024039 
(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))))