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

Percentage Accurate: 99.8% → 99.8%

Time: 35.1s

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, 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 2: 79.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ t_1 := x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+223}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))) (t_1 (* x (- 1.0 (* z (/ (sin y) x))))))
   (if (<= z -1.8e+223)
     t_0
     (if (<= z -4.8e-36)
       t_1
       (if (<= z 7e-68) (* x (cos y)) (if (<= z 2e+164) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double t_1 = x * (1.0 - (z * (sin(y) / x)));
	double tmp;
	if (z <= -1.8e+223) {
		tmp = t_0;
	} else if (z <= -4.8e-36) {
		tmp = t_1;
	} else if (z <= 7e-68) {
		tmp = x * cos(y);
	} else if (z <= 2e+164) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * -sin(y)
    t_1 = x * (1.0d0 - (z * (sin(y) / x)))
    if (z <= (-1.8d+223)) then
        tmp = t_0
    else if (z <= (-4.8d-36)) then
        tmp = t_1
    else if (z <= 7d-68) then
        tmp = x * cos(y)
    else if (z <= 2d+164) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -Math.sin(y);
	double t_1 = x * (1.0 - (z * (Math.sin(y) / x)));
	double tmp;
	if (z <= -1.8e+223) {
		tmp = t_0;
	} else if (z <= -4.8e-36) {
		tmp = t_1;
	} else if (z <= 7e-68) {
		tmp = x * Math.cos(y);
	} else if (z <= 2e+164) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	t_1 = x * (1.0 - (z * (math.sin(y) / x)))
	tmp = 0
	if z <= -1.8e+223:
		tmp = t_0
	elif z <= -4.8e-36:
		tmp = t_1
	elif z <= 7e-68:
		tmp = x * math.cos(y)
	elif z <= 2e+164:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	t_1 = Float64(x * Float64(1.0 - Float64(z * Float64(sin(y) / x))))
	tmp = 0.0
	if (z <= -1.8e+223)
		tmp = t_0;
	elseif (z <= -4.8e-36)
		tmp = t_1;
	elseif (z <= 7e-68)
		tmp = Float64(x * cos(y));
	elseif (z <= 2e+164)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	t_1 = x * (1.0 - (z * (sin(y) / x)));
	tmp = 0.0;
	if (z <= -1.8e+223)
		tmp = t_0;
	elseif (z <= -4.8e-36)
		tmp = t_1;
	elseif (z <= 7e-68)
		tmp = x * cos(y);
	elseif (z <= 2e+164)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 - N[(z * N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+223], t$95$0, If[LessEqual[z, -4.8e-36], t$95$1, If[LessEqual[z, 7e-68], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+164], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999996e223 or 2e164 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 90.7%

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

      1. neg-mul-1 90.7%

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

      2. distribute-lft-neg-in 90.7%

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

   5. Simplified 90.7%

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

   if -1.79999999999999996e223 < z < -4.8e-36 or 7.00000000000000026e-68 < z < 2e164

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. unsub-neg 91.5%

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

      3. associate-/l* 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in y around 0 78.2%

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

   if -4.8e-36 < z < 7.00000000000000026e-68

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 93.5%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \frac{\sin y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.072 \lor \neg \left(y \leq 750\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.072) (not (<= y 750.0)))
   (* x (cos y))
   (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* y z)))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.072) || !(y <= 750.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - 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 <= (-0.072d0)) .or. (.not. (y <= 750.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (y * z)))) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.072) || !(y <= 750.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.072) or not (y <= 750.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.072) || !(y <= 750.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(y * z)))) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.072) || ~((y <= 750.0)))
		tmp = x * cos(y);
	else
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.072], N[Not[LessEqual[y, 750.0]], $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[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0719999999999999946 or 750 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 50.5%

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

   if -0.0719999999999999946 < y < 750

   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 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.072 \lor \neg \left(y \leq 750\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 750:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+14)
   (* z (- (sin y)))
   (if (<= y 750.0)
     (+ x (* y (- (* y (+ (* x -0.5) (* 0.16666666666666666 (* y z)))) z)))
     (* x (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+14) {
		tmp = z * -sin(y);
	} else if (y <= 750.0) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - 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 <= (-2.7d+14)) then
        tmp = z * -sin(y)
    else if (y <= 750.0d0) then
        tmp = x + (y * ((y * ((x * (-0.5d0)) + (0.16666666666666666d0 * (y * z)))) - 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 <= -2.7e+14) {
		tmp = z * -Math.sin(y);
	} else if (y <= 750.0) {
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+14:
		tmp = z * -math.sin(y)
	elif y <= 750.0:
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+14)
		tmp = Float64(z * Float64(-sin(y)));
	elseif (y <= 750.0)
		tmp = Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(x * -0.5) + Float64(0.16666666666666666 * Float64(y * z)))) - z)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+14)
		tmp = z * -sin(y);
	elseif (y <= 750.0)
		tmp = x + (y * ((y * ((x * -0.5) + (0.16666666666666666 * (y * z)))) - z));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+14], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 750.0], N[(x + N[(y * N[(N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(0.16666666666666666 * N[(y * z), $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 < -2.7e14

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 62.6%

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

      1. neg-mul-1 62.6%

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

      2. distribute-lft-neg-in 62.6%

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

   5. Simplified 62.6%

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

   if -2.7e14 < y < 750

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.9%

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

   if 750 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 56.7%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+14}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq 750:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(y \cdot z\right)\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.7% accurate, 14.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.4e-200) x (if (<= x 7.2e-158) (* y (- z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e-200) {
		tmp = x;
	} else if (x <= 7.2e-158) {
		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 <= (-4.4d-200)) then
        tmp = x
    else if (x <= 7.2d-158) 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 <= -4.4e-200) {
		tmp = x;
	} else if (x <= 7.2e-158) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e-200:
		tmp = x
	elif x <= 7.2e-158:
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e-200)
		tmp = x;
	elseif (x <= 7.2e-158)
		tmp = Float64(y * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e-200)
		tmp = x;
	elseif (x <= 7.2e-158)
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e-200], x, If[LessEqual[x, 7.2e-158], N[(y * (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.40000000000000027e-200 or 7.19999999999999982e-158 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 96.1%

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

      1. mul-1-neg 96.1%

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

      2. unsub-neg 96.1%

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

      3. associate-/l* 96.0%

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

   5. Simplified 96.0%

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

   6. Taylor expanded in y around 0 47.5%

      \[\leadsto x \cdot \color{blue}{\left(1 + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \frac{y \cdot z}{x} - 0.5\right) - \frac{z}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. clear-num 47.5%

         \[\leadsto x \cdot \left(1 + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \color{blue}{\frac{1}{\frac{x}{y \cdot z}}} - 0.5\right) - \frac{z}{x}\right)\right) \]

      2. un-div-inv 47.5%

         \[\leadsto x \cdot \left(1 + y \cdot \left(y \cdot \left(\color{blue}{\frac{0.16666666666666666}{\frac{x}{y \cdot z}}} - 0.5\right) - \frac{z}{x}\right)\right) \]

   8. Applied egg-rr 47.5%

      \[\leadsto x \cdot \left(1 + y \cdot \left(y \cdot \left(\color{blue}{\frac{0.16666666666666666}{\frac{x}{y \cdot z}}} - 0.5\right) - \frac{z}{x}\right)\right) \]

   9. Taylor expanded in y around 0 45.0%

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

   if -4.40000000000000027e-200 < x < 7.19999999999999982e-158

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 51.3%

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

      1. mul-1-neg 51.3%

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

      2. unsub-neg 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in x around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-rgt-neg-out 40.6%

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

   8. Simplified 40.6%

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

Alternative 6: 52.0% 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. Add Preprocessing

3. Taylor expanded in y around 0 50.8%

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

   1. mul-1-neg 50.8%

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

   2. unsub-neg 50.8%

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

5. Simplified 50.8%

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

Alternative 7: 38.9% 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 x around inf 88.9%

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

   1. mul-1-neg 88.9%

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

   2. unsub-neg 88.9%

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

   3. associate-/l* 88.8%

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

5. Simplified 88.8%

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

6. Taylor expanded in y around 0 42.7%

   \[\leadsto x \cdot \color{blue}{\left(1 + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \frac{y \cdot z}{x} - 0.5\right) - \frac{z}{x}\right)\right)} \]
7. Step-by-step derivation

   1. clear-num 42.7%

      \[\leadsto x \cdot \left(1 + y \cdot \left(y \cdot \left(0.16666666666666666 \cdot \color{blue}{\frac{1}{\frac{x}{y \cdot z}}} - 0.5\right) - \frac{z}{x}\right)\right) \]

   2. un-div-inv 42.7%

      \[\leadsto x \cdot \left(1 + y \cdot \left(y \cdot \left(\color{blue}{\frac{0.16666666666666666}{\frac{x}{y \cdot z}}} - 0.5\right) - \frac{z}{x}\right)\right) \]

8. Applied egg-rr 42.7%

   \[\leadsto x \cdot \left(1 + y \cdot \left(y \cdot \left(\color{blue}{\frac{0.16666666666666666}{\frac{x}{y \cdot z}}} - 0.5\right) - \frac{z}{x}\right)\right) \]

9. Taylor expanded in y around 0 37.8%

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

Reproduce

herbie shell --seed 2024116 
(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))))