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

Percentage Accurate: 99.8% → 99.8%

Time: 9.6s

Alternatives: 6

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 85.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot x\\ \mathbf{if}\;x \leq -4.9 \cdot 10^{+117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;1 \cdot x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) x)))
   (if (<= x -4.9e+117)
     t_0
     (if (<= x 1.5e+21) (- (* 1.0 x) (* (sin y) z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * x;
	double tmp;
	if (x <= -4.9e+117) {
		tmp = t_0;
	} else if (x <= 1.5e+21) {
		tmp = (1.0 * x) - (sin(y) * z);
	} 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 = cos(y) * x
    if (x <= (-4.9d+117)) then
        tmp = t_0
    else if (x <= 1.5d+21) then
        tmp = (1.0d0 * x) - (sin(y) * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.cos(y) * x;
	double tmp;
	if (x <= -4.9e+117) {
		tmp = t_0;
	} else if (x <= 1.5e+21) {
		tmp = (1.0 * x) - (Math.sin(y) * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.cos(y) * x
	tmp = 0
	if x <= -4.9e+117:
		tmp = t_0
	elif x <= 1.5e+21:
		tmp = (1.0 * x) - (math.sin(y) * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * x)
	tmp = 0.0
	if (x <= -4.9e+117)
		tmp = t_0;
	elseif (x <= 1.5e+21)
		tmp = Float64(Float64(1.0 * x) - Float64(sin(y) * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = cos(y) * x;
	tmp = 0.0;
	if (x <= -4.9e+117)
		tmp = t_0;
	elseif (x <= 1.5e+21)
		tmp = (1.0 * x) - (sin(y) * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -4.9e+117], t$95$0, If[LessEqual[x, 1.5e+21], N[(N[(1.0 * x), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9000000000000001e117 or 1.5e21 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 90.7

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

   5. Applied rewrites 90.7%

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

   if -4.9000000000000001e117 < x < 1.5e21

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

      \[\leadsto x \cdot \color{blue}{1} - z \cdot \sin y \]
   4. Step-by-step derivation

   5. Applied rewrites 85.0%

      \[\leadsto x \cdot \color{blue}{1} - z \cdot \sin y \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+117}:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+21}:\\ \;\;\;\;1 \cdot x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.45:\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{elif}\;y \leq 90000:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot \left(y \cdot x\right) - z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.45)
   (* (- z) (sin y))
   (if (<= y 90000.0) (fma (- (* -0.5 (* y x)) z) y x) (* (cos y) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.45) {
		tmp = -z * sin(y);
	} else if (y <= 90000.0) {
		tmp = fma(((-0.5 * (y * x)) - z), y, x);
	} else {
		tmp = cos(y) * x;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.45)
		tmp = Float64(Float64(-z) * sin(y));
	elseif (y <= 90000.0)
		tmp = fma(Float64(Float64(-0.5 * Float64(y * x)) - z), y, x);
	else
		tmp = Float64(cos(y) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.45], N[((-z) * N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 90000.0], N[(N[(N[(-0.5 * N[(y * x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] * y + x), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.450000000000000011

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. distribute-lft-neg-in N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-sin.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -0.450000000000000011 < y < 9e4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot \left(x \cdot y\right) - z, y, x\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot \left(x \cdot y\right) - z}, y, x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot y\right) \cdot \frac{-1}{2}} - z, y, x\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot y\right) \cdot \frac{-1}{2}} - z, y, x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{-1}{2} - z, y, x\right) \]

      8. lower-*.f64 98.8

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

   5. Applied rewrites 98.8%

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

   if 9e4 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 61.3

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

   5. Applied rewrites 61.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.45:\\ \;\;\;\;\left(-z\right) \cdot \sin y\\ \mathbf{elif}\;y \leq 90000:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot \left(y \cdot x\right) - z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos y \cdot x\\ \mathbf{if}\;y \leq -0.038:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 90000:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot \left(y \cdot x\right) - z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (cos y) x)))
   (if (<= y -0.038)
     t_0
     (if (<= y 90000.0) (fma (- (* -0.5 (* y x)) z) y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = cos(y) * x;
	double tmp;
	if (y <= -0.038) {
		tmp = t_0;
	} else if (y <= 90000.0) {
		tmp = fma(((-0.5 * (y * x)) - z), y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(cos(y) * x)
	tmp = 0.0
	if (y <= -0.038)
		tmp = t_0;
	elseif (y <= 90000.0)
		tmp = fma(Float64(Float64(-0.5 * Float64(y * x)) - z), y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Cos[y], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[y, -0.038], t$95$0, If[LessEqual[y, 90000.0], N[(N[(N[(-0.5 * N[(y * x), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] * y + x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0379999999999999991 or 9e4 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-cos.f64 49.4

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

   5. Applied rewrites 49.4%

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

   if -0.0379999999999999991 < y < 9e4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{2} \cdot \left(x \cdot y\right) - z, y, x\right)} \]

      4. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{-1}{2} \cdot \left(x \cdot y\right) - z}, y, x\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot y\right) \cdot \frac{-1}{2}} - z, y, x\right) \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(x \cdot y\right) \cdot \frac{-1}{2}} - z, y, x\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{-1}{2} - z, y, x\right) \]

      8. lower-*.f64 99.3

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

   5. Applied rewrites 99.3%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.038:\\ \;\;\;\;\cos y \cdot x\\ \mathbf{elif}\;y \leq 90000:\\ \;\;\;\;\mathsf{fma}\left(-0.5 \cdot \left(y \cdot x\right) - z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 23.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. mul-1-neg N/A

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

   2. unsub-neg N/A

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

   3. lower--.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 55.2

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

5. Applied rewrites 55.2%

   \[\leadsto \color{blue}{x - z \cdot y} \]
6. Add Preprocessing

Alternative 6: 17.0% accurate, 26.8× speedup

Math

\[\begin{array}{l} \\ \left(-y\right) \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   1. mul-1-neg N/A

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

   2. unsub-neg N/A

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

   3. lower--.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 55.2

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

5. Applied rewrites 55.2%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 14.0%

   \[\leadsto \left(-y\right) \cdot \color{blue}{z} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024249 
(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))))