Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3

Percentage Accurate: 99.8% → 99.8%

Time: 9.6s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. fma-define 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 3: 74.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \cos y\\ t_1 := z \cdot \sin y\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+277}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1800000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+114} \lor \neg \left(y \leq 1.1 \cdot 10^{+247}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (cos y))) (t_1 (* z (sin y))))
   (if (<= y -3.4e+277)
     t_0
     (if (<= y -1800000000000.0)
       t_1
       (if (<= y 5.3e-5)
         (+ x (* y (+ z (* -0.5 (* x y)))))
         (if (or (<= y 1.02e+114) (not (<= y 1.1e+247))) t_1 t_0))))))

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 <= -3.4e+277) {
		tmp = t_0;
	} else if (y <= -1800000000000.0) {
		tmp = t_1;
	} else if (y <= 5.3e-5) {
		tmp = x + (y * (z + (-0.5 * (x * y))));
	} else if ((y <= 1.02e+114) || !(y <= 1.1e+247)) {
		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 = x * cos(y)
    t_1 = z * sin(y)
    if (y <= (-3.4d+277)) then
        tmp = t_0
    else if (y <= (-1800000000000.0d0)) then
        tmp = t_1
    else if (y <= 5.3d-5) then
        tmp = x + (y * (z + ((-0.5d0) * (x * y))))
    else if ((y <= 1.02d+114) .or. (.not. (y <= 1.1d+247))) 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 = x * Math.cos(y);
	double t_1 = z * Math.sin(y);
	double tmp;
	if (y <= -3.4e+277) {
		tmp = t_0;
	} else if (y <= -1800000000000.0) {
		tmp = t_1;
	} else if (y <= 5.3e-5) {
		tmp = x + (y * (z + (-0.5 * (x * y))));
	} else if ((y <= 1.02e+114) || !(y <= 1.1e+247)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.cos(y)
	t_1 = z * math.sin(y)
	tmp = 0
	if y <= -3.4e+277:
		tmp = t_0
	elif y <= -1800000000000.0:
		tmp = t_1
	elif y <= 5.3e-5:
		tmp = x + (y * (z + (-0.5 * (x * y))))
	elif (y <= 1.02e+114) or not (y <= 1.1e+247):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * cos(y))
	t_1 = Float64(z * sin(y))
	tmp = 0.0
	if (y <= -3.4e+277)
		tmp = t_0;
	elseif (y <= -1800000000000.0)
		tmp = t_1;
	elseif (y <= 5.3e-5)
		tmp = Float64(x + Float64(y * Float64(z + Float64(-0.5 * Float64(x * y)))));
	elseif ((y <= 1.02e+114) || !(y <= 1.1e+247))
		tmp = t_1;
	else
		tmp = t_0;
	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 <= -3.4e+277)
		tmp = t_0;
	elseif (y <= -1800000000000.0)
		tmp = t_1;
	elseif (y <= 5.3e-5)
		tmp = x + (y * (z + (-0.5 * (x * y))));
	elseif ((y <= 1.02e+114) || ~((y <= 1.1e+247)))
		tmp = t_1;
	else
		tmp = t_0;
	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, -3.4e+277], t$95$0, If[LessEqual[y, -1800000000000.0], t$95$1, If[LessEqual[y, 5.3e-5], N[(x + N[(y * N[(z + N[(-0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.02e+114], N[Not[LessEqual[y, 1.1e+247]], $MachinePrecision]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4000000000000001e277 or 1.01999999999999999e114 < y < 1.10000000000000006e247

   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 -3.4000000000000001e277 < y < -1.8e12 or 5.3000000000000001e-5 < y < 1.01999999999999999e114 or 1.10000000000000006e247 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 65.9%

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

   if -1.8e12 < y < 5.3000000000000001e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+277}:\\ \;\;\;\;x \cdot \cos y\\ \mathbf{elif}\;y \leq -1800000000000:\\ \;\;\;\;z \cdot \sin y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-5}:\\ \;\;\;\;x + y \cdot \left(z + -0.5 \cdot \left(x \cdot y\right)\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+114} \lor \neg \left(y \leq 1.1 \cdot 10^{+247}\right):\\ \;\;\;\;z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+113} \lor \neg \left(x \leq 10^{+133}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.08e+113) (not (<= x 1e+133)))
   (* x (cos y))
   (+ x (* z (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.08e+113) || !(x <= 1e+133)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (z * sin(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 ((x <= (-1.08d+113)) .or. (.not. (x <= 1d+133))) then
        tmp = x * cos(y)
    else
        tmp = x + (z * sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.08e+113) || !(x <= 1e+133)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (z * Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.08e+113) or not (x <= 1e+133):
		tmp = x * math.cos(y)
	else:
		tmp = x + (z * math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.08e+113) || !(x <= 1e+133))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(z * sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.08e+113) || ~((x <= 1e+133)))
		tmp = x * cos(y);
	else
		tmp = x + (z * sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.08e+113], N[Not[LessEqual[x, 1e+133]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.08e113 or 1e133 < x

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 89.4%

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

   if -1.08e113 < x < 1e133

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 88.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+113} \lor \neg \left(x \leq 10^{+133}\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.048 \lor \neg \left(y \leq 16\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5 + -0.16666666666666666 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.048) (not (<= y 16.0)))
   (* x (cos y))
   (+ x (* y (+ z (* y (+ (* x -0.5) (* -0.16666666666666666 (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.048) || !(y <= 16.0)) {
		tmp = x * cos(y);
	} else {
		tmp = x + (y * (z + (y * ((x * -0.5) + (-0.16666666666666666 * (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 <= (-0.048d0)) .or. (.not. (y <= 16.0d0))) then
        tmp = x * cos(y)
    else
        tmp = x + (y * (z + (y * ((x * (-0.5d0)) + ((-0.16666666666666666d0) * (y * z))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.048) || !(y <= 16.0)) {
		tmp = x * Math.cos(y);
	} else {
		tmp = x + (y * (z + (y * ((x * -0.5) + (-0.16666666666666666 * (y * z))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.048) or not (y <= 16.0):
		tmp = x * math.cos(y)
	else:
		tmp = x + (y * (z + (y * ((x * -0.5) + (-0.16666666666666666 * (y * z))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.048) || !(y <= 16.0))
		tmp = Float64(x * cos(y));
	else
		tmp = Float64(x + Float64(y * Float64(z + Float64(y * Float64(Float64(x * -0.5) + Float64(-0.16666666666666666 * Float64(y * z)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.048) || ~((y <= 16.0)))
		tmp = x * cos(y);
	else
		tmp = x + (y * (z + (y * ((x * -0.5) + (-0.16666666666666666 * (y * z))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.048], N[Not[LessEqual[y, 16.0]], $MachinePrecision]], N[(x * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z + N[(y * N[(N[(x * -0.5), $MachinePrecision] + N[(-0.16666666666666666 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.048000000000000001 or 16 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 46.4%

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

   if -0.048000000000000001 < y < 16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.048 \lor \neg \left(y \leq 16\right):\\ \;\;\;\;x \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z + y \cdot \left(x \cdot -0.5 + -0.16666666666666666 \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 41.4% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+177} \lor \neg \left(z \leq 8 \cdot 10^{+234}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e+177) (not (<= z 8e+234))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e+177) || !(z <= 8e+234)) {
		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 ((z <= (-3.5d+177)) .or. (.not. (z <= 8d+234))) 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 ((z <= -3.5e+177) || !(z <= 8e+234)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e+177) or not (z <= 8e+234):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e+177) || !(z <= 8e+234))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e+177) || ~((z <= 8e+234)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e+177], N[Not[LessEqual[z, 8e+234]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999991e177 or 8.00000000000000014e234 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 47.5%

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

   4. Taylor expanded in x around 0 34.5%

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

   if -3.49999999999999991e177 < z < 8.00000000000000014e234

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 95.9%

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

      1. associate-/l* 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in y around 0 50.4%

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

   7. Taylor expanded in y around 0 47.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+177} \lor \neg \left(z \leq 8 \cdot 10^{+234}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% 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 51.5%

   \[\leadsto \color{blue}{x + y \cdot z} \]
4. Add Preprocessing

Alternative 8: 38.8% 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 92.1%

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

   1. associate-/l* 92.0%

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

5. Simplified 92.0%

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

6. Taylor expanded in y around 0 46.3%

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

7. Taylor expanded in y around 0 40.3%

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

Reproduce

herbie shell --seed 2024131 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))