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

Percentage Accurate: 99.8% → 99.8%

Time: 10.1s

Alternatives: 8

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. Final simplification 99.8%

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

Alternative 2: 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. Final simplification 99.8%

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

Alternative 3: 84.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-46} \lor \neg \left(x \leq 2.6 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(\frac{1}{z} - \frac{\sin y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.45e-46) (not (<= x 2.6e-19)))
   (* x (cos y))
   (* z (* x (- (/ 1.0 z) (/ (sin y) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e-46) || !(x <= 2.6e-19)) {
		tmp = x * cos(y);
	} else {
		tmp = z * (x * ((1.0 / z) - (sin(y) / 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 <= (-1.45d-46)) .or. (.not. (x <= 2.6d-19))) then
        tmp = x * cos(y)
    else
        tmp = z * (x * ((1.0d0 / z) - (sin(y) / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.45e-46) || !(x <= 2.6e-19)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = z * (x * ((1.0 / z) - (Math.sin(y) / x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.45e-46) or not (x <= 2.6e-19):
		tmp = x * math.cos(y)
	else:
		tmp = z * (x * ((1.0 / z) - (math.sin(y) / x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.45e-46) || !(x <= 2.6e-19))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(z * Float64(x * Float64(Float64(1.0 / z) - Float64(sin(y) / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.45e-46) || ~((x <= 2.6e-19)))
		tmp = x * cos(y);
	else
		tmp = z * (x * ((1.0 / z) - (sin(y) / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.45e-46], N[Not[LessEqual[x, 2.6e-19]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45000000000000002e-46 or 2.60000000000000013e-19 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 88.6%

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

   if -1.45000000000000002e-46 < x < 2.60000000000000013e-19

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 99.6%

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

      1. +-commutative 99.6%

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

      2. mul-1-neg 99.6%

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

      3. unsub-neg 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around 0 87.7%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-46} \lor \neg \left(x \leq 2.6 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(\frac{1}{z} - \frac{\sin y}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq -0.215 \lor \neg \left(y \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.4e+187)
   (* z (- (sin y)))
   (if (or (<= y -0.215) (not (<= y 1.85e-6)))
     (* 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 <= -5.4e+187) {
		tmp = z * -sin(y);
	} else if ((y <= -0.215) || !(y <= 1.85e-6)) {
		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 <= (-5.4d+187)) then
        tmp = z * -sin(y)
    else if ((y <= (-0.215d0)) .or. (.not. (y <= 1.85d-6))) 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 <= -5.4e+187) {
		tmp = z * -Math.sin(y);
	} else if ((y <= -0.215) || !(y <= 1.85e-6)) {
		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 <= -5.4e+187:
		tmp = z * -math.sin(y)
	elif (y <= -0.215) or not (y <= 1.85e-6):
		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 <= -5.4e+187)
		tmp = Float64(z * Float64(-sin(y)));
	elseif ((y <= -0.215) || !(y <= 1.85e-6))
		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 <= -5.4e+187)
		tmp = z * -sin(y);
	elseif ((y <= -0.215) || ~((y <= 1.85e-6)))
		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[LessEqual[y, -5.4e+187], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], If[Or[LessEqual[y, -0.215], N[Not[LessEqual[y, 1.85e-6]], $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 3 regimes

2. if y < -5.40000000000000016e187

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 66.4%

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

      1. neg-mul-1 66.4%

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

      2. distribute-rgt-neg-in 66.4%

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

   5. Simplified 66.4%

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

   if -5.40000000000000016e187 < y < -0.214999999999999997 or 1.8500000000000001e-6 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 72.8%

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

   if -0.214999999999999997 < y < 1.8500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq -0.215 \lor \neg \left(y \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.23 \lor \neg \left(y \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.23) (not (<= y 1.85e-6)))
   (* 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 <= -0.23) || !(y <= 1.85e-6)) {
		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 <= (-0.23d0)) .or. (.not. (y <= 1.85d-6))) 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 <= -0.23) || !(y <= 1.85e-6)) {
		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 <= -0.23) or not (y <= 1.85e-6):
		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 <= -0.23) || !(y <= 1.85e-6))
		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 <= -0.23) || ~((y <= 1.85e-6)))
		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, -0.23], N[Not[LessEqual[y, 1.85e-6]], $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 < -0.23000000000000001 or 1.8500000000000001e-6 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 65.3%

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

   if -0.23000000000000001 < y < 1.8500000000000001e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.23 \lor \neg \left(y \leq 1.85 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(y \cdot \left(x \cdot -0.5 + 0.16666666666666666 \cdot \left(z \cdot y\right)\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.6% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+214} \lor \neg \left(z \leq 6.6 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e+214) (not (<= z 6.6e+113))) (* z (- y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e+214) || !(z <= 6.6e+113)) {
		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 <= (-1.35d+214)) .or. (.not. (z <= 6.6d+113))) 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 <= -1.35e+214) || !(z <= 6.6e+113)) {
		tmp = z * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e+214) or not (z <= 6.6e+113):
		tmp = z * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e+214) || !(z <= 6.6e+113))
		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 <= -1.35e+214) || ~((z <= 6.6e+113)))
		tmp = z * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e+214], N[Not[LessEqual[z, 6.6e+113]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.35000000000000005e214 or 6.6000000000000006e113 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in x around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. distribute-rgt-neg-out 52.0%

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

   8. Simplified 52.0%

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

   if -1.35000000000000005e214 < z < 6.6000000000000006e113

   1. Initial program 99.8%

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

      1. flip-- 59.3%

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

      2. div-inv 59.2%

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

   4. Applied egg-rr 43.4%

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

   5. Taylor expanded in y around 0 43.1%

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

   6. Taylor expanded in y around 0 46.4%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+214} \lor \neg \left(z \leq 6.6 \cdot 10^{+113}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% 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 54.1%

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

   1. mul-1-neg 54.1%

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

   2. unsub-neg 54.1%

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

5. Simplified 54.1%

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

6. Final simplification 54.1%

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

Alternative 8: 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. Step-by-step derivation

   1. flip-- 58.2%

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

   2. div-inv 58.0%

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

4. Applied egg-rr 37.6%

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

5. Taylor expanded in y around 0 37.9%

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

6. Taylor expanded in y around 0 40.7%

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

7. Final simplification 40.7%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024060 
(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))))