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

Percentage Accurate: 99.8% → 99.8%

Time: 8.9s

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, 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. Final simplification 99.8%

   \[\leadsto x \cdot \cos y - z \cdot \sin y \]

Alternative 2: 75.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -0.12 \lor \neg \left(y \leq 0.0048\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot \left(\left(y \cdot y\right) \cdot -0.5\right) - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (- (sin y)))))
   (if (<= y -5.5e+230)
     t_0
     (if (<= y -4.1e+207)
       t_1
       (if (<= y -1.5e+166)
         t_0
         (if (<= y -1.2e+58)
           t_1
           (if (<= y -1.25e+19)
             t_0
             (if (or (<= y -0.12) (not (<= y 0.0048)))
               t_1
               (+ x (- (* x (* (* y y) -0.5)) (* y z)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * cos(y);
	double t_1 = z * -sin(y);
	double tmp;
	if (y <= -5.5e+230) {
		tmp = t_0;
	} else if (y <= -4.1e+207) {
		tmp = t_1;
	} else if (y <= -1.5e+166) {
		tmp = t_0;
	} else if (y <= -1.2e+58) {
		tmp = t_1;
	} else if (y <= -1.25e+19) {
		tmp = t_0;
	} else if ((y <= -0.12) || !(y <= 0.0048)) {
		tmp = t_1;
	} else {
		tmp = x + ((x * ((y * y) * -0.5)) - (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * cos(y)
    t_1 = z * -sin(y)
    if (y <= (-5.5d+230)) then
        tmp = t_0
    else if (y <= (-4.1d+207)) then
        tmp = t_1
    else if (y <= (-1.5d+166)) then
        tmp = t_0
    else if (y <= (-1.2d+58)) then
        tmp = t_1
    else if (y <= (-1.25d+19)) then
        tmp = t_0
    else if ((y <= (-0.12d0)) .or. (.not. (y <= 0.0048d0))) then
        tmp = t_1
    else
        tmp = x + ((x * ((y * y) * (-0.5d0))) - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.cos(y);
	double t_1 = z * -Math.sin(y);
	double tmp;
	if (y <= -5.5e+230) {
		tmp = t_0;
	} else if (y <= -4.1e+207) {
		tmp = t_1;
	} else if (y <= -1.5e+166) {
		tmp = t_0;
	} else if (y <= -1.2e+58) {
		tmp = t_1;
	} else if (y <= -1.25e+19) {
		tmp = t_0;
	} else if ((y <= -0.12) || !(y <= 0.0048)) {
		tmp = t_1;
	} else {
		tmp = x + ((x * ((y * y) * -0.5)) - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = z * -math.sin(y)
	tmp = 0
	if y <= -5.5e+230:
		tmp = t_0
	elif y <= -4.1e+207:
		tmp = t_1
	elif y <= -1.5e+166:
		tmp = t_0
	elif y <= -1.2e+58:
		tmp = t_1
	elif y <= -1.25e+19:
		tmp = t_0
	elif (y <= -0.12) or not (y <= 0.0048):
		tmp = t_1
	else:
		tmp = x + ((x * ((y * y) * -0.5)) - (y * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (y <= -5.5e+230)
		tmp = t_0;
	elseif (y <= -4.1e+207)
		tmp = t_1;
	elseif (y <= -1.5e+166)
		tmp = t_0;
	elseif (y <= -1.2e+58)
		tmp = t_1;
	elseif (y <= -1.25e+19)
		tmp = t_0;
	elseif ((y <= -0.12) || !(y <= 0.0048))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(x * Float64(Float64(y * y) * -0.5)) - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * cos(y);
	t_1 = z * -sin(y);
	tmp = 0.0;
	if (y <= -5.5e+230)
		tmp = t_0;
	elseif (y <= -4.1e+207)
		tmp = t_1;
	elseif (y <= -1.5e+166)
		tmp = t_0;
	elseif (y <= -1.2e+58)
		tmp = t_1;
	elseif (y <= -1.25e+19)
		tmp = t_0;
	elseif ((y <= -0.12) || ~((y <= 0.0048)))
		tmp = t_1;
	else
		tmp = x + ((x * ((y * y) * -0.5)) - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -5.5e+230], t$95$0, If[LessEqual[y, -4.1e+207], t$95$1, If[LessEqual[y, -1.5e+166], t$95$0, If[LessEqual[y, -1.2e+58], t$95$1, If[LessEqual[y, -1.25e+19], t$95$0, If[Or[LessEqual[y, -0.12], N[Not[LessEqual[y, 0.0048]], $MachinePrecision]], t$95$1, N[(x + N[(N[(x * N[(N[(y * y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.49999999999999979e230 or -4.1e207 < y < -1.49999999999999999e166 or -1.2e58 < y < -1.25e19

   1. Initial program 99.6%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in x around inf 78.7%

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

   if -5.49999999999999979e230 < y < -4.1e207 or -1.49999999999999999e166 < y < -1.2e58 or -1.25e19 < y < -0.12 or 0.00479999999999999958 < y

   1. Initial program 99.7%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in x around 0 72.3%

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

      1. associate-*r* 72.3%

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

      2. neg-mul-1 72.3%

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

   4. Simplified 72.3%

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

   if -0.12 < y < 0.00479999999999999958

   1. Initial program 100.0%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 99.7%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto x + \color{blue}{\left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + -1 \cdot \left(y \cdot z\right)\right)} \]

      2. mul-1-neg 99.7%

         \[\leadsto x + \left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + \color{blue}{\left(-y \cdot z\right)}\right) \]

      3. unsub-neg 99.7%

         \[\leadsto x + \color{blue}{\left(-0.5 \cdot \left(x \cdot {y}^{2}\right) - y \cdot z\right)} \]

      4. *-commutative 99.7%

         \[\leadsto x + \left(\color{blue}{\left(x \cdot {y}^{2}\right) \cdot -0.5} - y \cdot z\right) \]

      5. associate-*l* 99.7%

         \[\leadsto x + \left(\color{blue}{x \cdot \left({y}^{2} \cdot -0.5\right)} - y \cdot z\right) \]

      6. unpow2 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+58}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -0.12 \lor \neg \left(y \leq 0.0048\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot \left(\left(y \cdot y\right) \cdot -0.5\right) - y \cdot z\right)\\ \end{array} \]

Alternative 3: 85.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-152} \lor \neg \left(z \leq 2.5 \cdot 10^{-64}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-152) (not (<= z 2.5e-64)))
   (- x (* z (sin y)))
   (* x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-152) || !(z <= 2.5e-64)) {
		tmp = x - (z * sin(y));
	} 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 <= (-4.8d-152)) .or. (.not. (z <= 2.5d-64))) then
        tmp = x - (z * sin(y))
    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 <= -4.8e-152) || !(z <= 2.5e-64)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-152) or not (z <= 2.5e-64):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-152) || !(z <= 2.5e-64))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-152) || ~((z <= 2.5e-64)))
		tmp = x - (z * sin(y));
	else
		tmp = x * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-152], N[Not[LessEqual[z, 2.5e-64]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e-152 or 2.50000000000000017e-64 < z

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 90.1%

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

   if -4.8e-152 < z < 2.50000000000000017e-64

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in x around inf 90.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-152} \lor \neg \left(z \leq 2.5 \cdot 10^{-64}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]

Alternative 4: 74.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00205 \lor \neg \left(y \leq 420000\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot \left(\left(y \cdot y\right) \cdot -0.5\right) - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.00205) (not (<= y 420000.0)))
   (* x (cos y))
   (+ x (- (* x (* (* y y) -0.5)) (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00205) || !(y <= 420000.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + ((x * ((y * y) * -0.5)) - (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 <= (-0.00205d0)) .or. (.not. (y <= 420000.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + ((x * ((y * y) * (-0.5d0))) - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.00205) || !(y <= 420000.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + ((x * ((y * y) * -0.5)) - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.00205) or not (y <= 420000.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + ((x * ((y * y) * -0.5)) - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.00205) || !(y <= 420000.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(Float64(x * Float64(Float64(y * y) * -0.5)) - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.00205) || ~((y <= 420000.0)))
		tmp = x * cos(y);
	else
		tmp = x + ((x * ((y * y) * -0.5)) - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.00205], N[Not[LessEqual[y, 420000.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x * N[(N[(y * y), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00205000000000000017 or 4.2e5 < y

   1. Initial program 99.7%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in x around inf 45.7%

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

   if -0.00205000000000000017 < y < 4.2e5

   1. Initial program 100.0%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 97.1%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left(x \cdot {y}^{2}\right)\right)} \]
   3. Step-by-step derivation

      1. +-commutative 97.1%

         \[\leadsto x + \color{blue}{\left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + -1 \cdot \left(y \cdot z\right)\right)} \]

      2. mul-1-neg 97.1%

         \[\leadsto x + \left(-0.5 \cdot \left(x \cdot {y}^{2}\right) + \color{blue}{\left(-y \cdot z\right)}\right) \]

      3. unsub-neg 97.1%

         \[\leadsto x + \color{blue}{\left(-0.5 \cdot \left(x \cdot {y}^{2}\right) - y \cdot z\right)} \]

      4. *-commutative 97.1%

         \[\leadsto x + \left(\color{blue}{\left(x \cdot {y}^{2}\right) \cdot -0.5} - y \cdot z\right) \]

      5. associate-*l* 97.1%

         \[\leadsto x + \left(\color{blue}{x \cdot \left({y}^{2} \cdot -0.5\right)} - y \cdot z\right) \]

      6. unpow2 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00205 \lor \neg \left(y \leq 420000\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(x \cdot \left(\left(y \cdot y\right) \cdot -0.5\right) - y \cdot z\right)\\ \end{array} \]

Alternative 5: 40.4% accurate, 16.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-29} \lor \neg \left(x \leq -1.62 \cdot 10^{-199}\right) \land x \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.25e+18)
   x
   (if (or (<= x -1.22e-29) (and (not (<= x -1.62e-199)) (<= x 1.7e-145)))
     (* y (- z))
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.25e+18) {
		tmp = x;
	} else if ((x <= -1.22e-29) || (!(x <= -1.62e-199) && (x <= 1.7e-145))) {
		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 <= (-1.25d+18)) then
        tmp = x
    else if ((x <= (-1.22d-29)) .or. (.not. (x <= (-1.62d-199))) .and. (x <= 1.7d-145)) 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 <= -1.25e+18) {
		tmp = x;
	} else if ((x <= -1.22e-29) || (!(x <= -1.62e-199) && (x <= 1.7e-145))) {
		tmp = y * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.25e+18:
		tmp = x
	elif (x <= -1.22e-29) or (not (x <= -1.62e-199) and (x <= 1.7e-145)):
		tmp = y * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.25e+18)
		tmp = x;
	elseif ((x <= -1.22e-29) || (!(x <= -1.62e-199) && (x <= 1.7e-145)))
		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 <= -1.25e+18)
		tmp = x;
	elseif ((x <= -1.22e-29) || (~((x <= -1.62e-199)) && (x <= 1.7e-145)))
		tmp = y * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.25e+18], x, If[Or[LessEqual[x, -1.22e-29], And[N[Not[LessEqual[x, -1.62e-199]], $MachinePrecision], LessEqual[x, 1.7e-145]]], N[(y * (-z)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e18 or -1.21999999999999996e-29 < x < -1.62000000000000008e-199 or 1.6999999999999999e-145 < x

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. unsub-neg 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in x around inf 44.3%

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

   if -1.25e18 < x < -1.21999999999999996e-29 or -1.62000000000000008e-199 < x < 1.6999999999999999e-145

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in x around 0 43.1%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.22 \cdot 10^{-29} \lor \neg \left(x \leq -1.62 \cdot 10^{-199}\right) \land x \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 40.2% accurate, 16.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-196}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- z))))
   (if (<= x -1.25e+18)
     x
     (if (<= x -2.5e-29)
       t_0
       (if (<= x -6.6e-196) (+ x (* y z)) (if (<= x 1.8e-142) t_0 x))))))

C

double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (x <= -1.25e+18) {
		tmp = x;
	} else if (x <= -2.5e-29) {
		tmp = t_0;
	} else if (x <= -6.6e-196) {
		tmp = x + (y * z);
	} else if (x <= 1.8e-142) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * -z
    if (x <= (-1.25d+18)) then
        tmp = x
    else if (x <= (-2.5d-29)) then
        tmp = t_0
    else if (x <= (-6.6d-196)) then
        tmp = x + (y * z)
    else if (x <= 1.8d-142) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * -z;
	double tmp;
	if (x <= -1.25e+18) {
		tmp = x;
	} else if (x <= -2.5e-29) {
		tmp = t_0;
	} else if (x <= -6.6e-196) {
		tmp = x + (y * z);
	} else if (x <= 1.8e-142) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * -z
	tmp = 0
	if x <= -1.25e+18:
		tmp = x
	elif x <= -2.5e-29:
		tmp = t_0
	elif x <= -6.6e-196:
		tmp = x + (y * z)
	elif x <= 1.8e-142:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(-z))
	tmp = 0.0
	if (x <= -1.25e+18)
		tmp = x;
	elseif (x <= -2.5e-29)
		tmp = t_0;
	elseif (x <= -6.6e-196)
		tmp = Float64(x + Float64(y * z));
	elseif (x <= 1.8e-142)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * -z;
	tmp = 0.0;
	if (x <= -1.25e+18)
		tmp = x;
	elseif (x <= -2.5e-29)
		tmp = t_0;
	elseif (x <= -6.6e-196)
		tmp = x + (y * z);
	elseif (x <= 1.8e-142)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * (-z)), $MachinePrecision]}, If[LessEqual[x, -1.25e+18], x, If[LessEqual[x, -2.5e-29], t$95$0, If[LessEqual[x, -6.6e-196], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-142], t$95$0, x]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25e18 or 1.8e-142 < x

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 51.7%

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

      1. mul-1-neg 51.7%

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

      2. unsub-neg 51.7%

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

   4. Simplified 51.7%

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

   5. Taylor expanded in x around inf 45.7%

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

   if -1.25e18 < x < -2.49999999999999993e-29 or -6.59999999999999997e-196 < x < 1.8e-142

   1. Initial program 99.8%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 50.0%

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

      1. mul-1-neg 50.0%

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

      2. unsub-neg 50.0%

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

   4. Simplified 50.0%

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

   5. Taylor expanded in x around 0 43.1%

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

   if -2.49999999999999993e-29 < x < -6.59999999999999997e-196

   1. Initial program 99.9%

      \[x \cdot \cos y - z \cdot \sin y \]

   2. Taylor expanded in y around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. unsub-neg 50.7%

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

   4. Simplified 50.7%

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

      1. sub-neg 50.7%

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

      2. +-commutative 50.7%

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

      3. *-commutative 50.7%

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

      4. distribute-lft-neg-in 50.7%

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

      5. add-sqr-sqrt 37.8%

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

      6. sqrt-unprod 45.5%

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

      7. sqr-neg 45.5%

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

      8. sqrt-unprod 10.6%

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

      9. add-sqr-sqrt 38.3%

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

   6. Applied egg-rr 38.3%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-196}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-142}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 52.5% 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. Taylor expanded in y around 0 51.1%

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

   1. mul-1-neg 51.1%

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

   2. unsub-neg 51.1%

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

4. Simplified 51.1%

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

5. Final simplification 51.1%

   \[\leadsto x - y \cdot z \]

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. Taylor expanded in y around 0 51.1%

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

   1. mul-1-neg 51.1%

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

   2. unsub-neg 51.1%

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

4. Simplified 51.1%

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

5. Taylor expanded in x around inf 35.3%

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

6. Final simplification 35.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023290 
(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))))