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

Percentage Accurate: 99.8% → 99.8%

Time: 10.1s

Alternatives: 9

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. cancel-sign-sub-inv 99.8%

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

   2. +-commutative 99.8%

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

   3. distribute-lft-neg-out 99.8%

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

   4. distribute-rgt-neg-in 99.8%

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

   5. sin-neg 99.8%

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

   6. fma-define 99.8%

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

   7. sin-neg 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, -\sin y, x \cdot \cos y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 86.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-27} \lor \neg \left(z \leq 2.2 \cdot 10^{-97}\right):\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.62e-27) (not (<= z 2.2e-97)))
   (fma z (- (sin y)) x)
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.62e-27) || !(z <= 2.2e-97)) {
		tmp = fma(z, -sin(y), x);
	} else {
		tmp = x * cos(y);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.62e-27) || !(z <= 2.2e-97))
		tmp = fma(z, Float64(-sin(y)), x);
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.62e-27], N[Not[LessEqual[z, 2.2e-97]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision]) + x), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.61999999999999993e-27 or 2.1999999999999999e-97 < z

   1. Initial program 99.7%

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

      1. cancel-sign-sub-inv 99.7%

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

      2. +-commutative 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. sin-neg 99.7%

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

      6. fma-define 99.8%

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

      7. sin-neg 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 86.4%

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

   if -1.61999999999999993e-27 < z < 2.1999999999999999e-97

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-27} \lor \neg \left(z \leq 2.2 \cdot 10^{-97}\right):\\ \;\;\;\;\mathsf{fma}\left(z, -\sin y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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. Add Preprocessing

Alternative 4: 78.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+156}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-27} \lor \neg \left(z \leq 6 \cdot 10^{-98}\right):\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.48e+156)
   (* (sin y) (- z))
   (if (or (<= z -1.5e-27) (not (<= z 6e-98)))
     (* x (- 1.0 (* z (/ (sin y) x))))
     (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.48e+156) {
		tmp = sin(y) * -z;
	} else if ((z <= -1.5e-27) || !(z <= 6e-98)) {
		tmp = x * (1.0 - (z * (sin(y) / x)));
	} 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 <= (-1.48d+156)) then
        tmp = sin(y) * -z
    else if ((z <= (-1.5d-27)) .or. (.not. (z <= 6d-98))) then
        tmp = x * (1.0d0 - (z * (sin(y) / x)))
    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 <= -1.48e+156) {
		tmp = Math.sin(y) * -z;
	} else if ((z <= -1.5e-27) || !(z <= 6e-98)) {
		tmp = x * (1.0 - (z * (Math.sin(y) / x)));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.48e+156:
		tmp = math.sin(y) * -z
	elif (z <= -1.5e-27) or not (z <= 6e-98):
		tmp = x * (1.0 - (z * (math.sin(y) / x)))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.48e+156)
		tmp = Float64(sin(y) * Float64(-z));
	elseif ((z <= -1.5e-27) || !(z <= 6e-98))
		tmp = Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x))));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.48e+156)
		tmp = sin(y) * -z;
	elseif ((z <= -1.5e-27) || ~((z <= 6e-98)))
		tmp = x * (1.0 - (z * (sin(y) / x)));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.48e+156], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], If[Or[LessEqual[z, -1.5e-27], N[Not[LessEqual[z, 6e-98]], $MachinePrecision]], N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4799999999999999e156

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 90.4%

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

      1. neg-mul-1 90.4%

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

      2. *-commutative 90.4%

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

      3. distribute-rgt-neg-in 90.4%

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

   5. Simplified 90.4%

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

   if -1.4799999999999999e156 < z < -1.5000000000000001e-27 or 6e-98 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. *-commutative 94.1%

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

      4. associate-/l* 89.2%

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

   5. Simplified 89.2%

      \[\leadsto \color{blue}{x \cdot \left(\cos y - \sin y \cdot \frac{z}{x}\right)} \]
   6. Step-by-step derivation

      1. clear-num 89.1%

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

      2. un-div-inv 89.2%

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

   7. Applied egg-rr 89.2%

      \[\leadsto x \cdot \left(\cos y - \color{blue}{\frac{\sin y}{\frac{x}{z}}}\right) \]
   8. Step-by-step derivation

      1. associate-/r/ 94.0%

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

   9. Applied egg-rr 94.0%

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

   10. Taylor expanded in y around 0 77.6%

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

   if -1.5000000000000001e-27 < z < 6e-98

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{+156}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-27} \lor \neg \left(z \leq 6 \cdot 10^{-98}\right):\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2500 \lor \neg \left(y \leq 0.72\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2500.0) (not (<= y 0.72)))
   (* x (cos y))
   (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* z y)))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2500.0) || !(y <= 0.72)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * 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 ((y <= (-2500.0d0)) .or. (.not. (y <= 0.72d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (z * y)))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2500.0) || !(y <= 0.72)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2500.0) or not (y <= 0.72):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2500.0) || !(y <= 0.72))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(z * y)))) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2500.0) || ~((y <= 0.72)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2500.0], N[Not[LessEqual[y, 0.72]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2500 or 0.71999999999999997 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 58.4%

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

   if -2500 < y < 0.71999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(-0.5 \cdot x + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2500 \lor \neg \left(y \leq 0.72\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.185:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.72:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.185)
   (* (sin y) (- z))
   (if (<= y 0.72)
     (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* z y)))) z)))
     (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.185) {
		tmp = sin(y) * -z;
	} else if (y <= 0.72) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	} 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 (y <= (-0.185d0)) then
        tmp = sin(y) * -z
    else if (y <= 0.72d0) then
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (z * y)))) - z))
    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 (y <= -0.185) {
		tmp = Math.sin(y) * -z;
	} else if (y <= 0.72) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.185:
		tmp = math.sin(y) * -z
	elif y <= 0.72:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.185)
		tmp = Float64(sin(y) * Float64(-z));
	elseif (y <= 0.72)
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(z * y)))) - z)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.185)
		tmp = sin(y) * -z;
	elseif (y <= 0.72)
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (z * y)))) - z));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.185], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 0.72], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.185

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 57.7%

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

      1. neg-mul-1 57.7%

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

      2. *-commutative 57.7%

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

      3. distribute-rgt-neg-in 57.7%

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

   5. Simplified 57.7%

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

   if -0.185 < y < 0.71999999999999997

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{x + y \cdot \left(y \cdot \left(-0.5 \cdot x + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)} \]

   if 0.71999999999999997 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 67.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.185:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 0.72:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 41.6% accurate, 23.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -1.1e+156) (* z (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+156) {
		tmp = z * -y;
	} 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 (z <= (-1.1d+156)) then
        tmp = z * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+156) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+156:
		tmp = z * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+156)
		tmp = Float64(z * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+156)
		tmp = z * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+156], N[(z * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.10000000000000002e156

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 49.5%

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

      1. mul-1-neg 49.5%

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

      2. unsub-neg 49.5%

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

      3. *-commutative 49.5%

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

   5. Simplified 49.5%

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

   6. Taylor expanded in x around 0 43.3%

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

      1. mul-1-neg 43.3%

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

      2. *-commutative 43.3%

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

   8. Applied egg-rr 43.3%

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

   if -1.10000000000000002e156 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 42.2%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+156}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.3% accurate, 41.4× 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 49.7%

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

   1. mul-1-neg 49.7%

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

   2. unsub-neg 49.7%

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

   3. *-commutative 49.7%

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

5. Simplified 49.7%

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

Alternative 9: 39.7% 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. Taylor expanded in y around 0 38.1%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024129 
(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))))