Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Final simplification 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \cos y \]

Alternative 3: 73.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-282}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+35}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.15e+138)
     t_0
     (if (<= z -1.25e-190)
       (+ z x)
       (if (<= z 8.2e-282) (+ y (+ z x)) (if (<= z 8e+35) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.15e+138) {
		tmp = t_0;
	} else if (z <= -1.25e-190) {
		tmp = z + x;
	} else if (z <= 8.2e-282) {
		tmp = y + (z + x);
	} else if (z <= 8e+35) {
		tmp = z + x;
	} 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) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.15d+138)) then
        tmp = t_0
    else if (z <= (-1.25d-190)) then
        tmp = z + x
    else if (z <= 8.2d-282) then
        tmp = y + (z + x)
    else if (z <= 8d+35) then
        tmp = z + x
    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.cos(y);
	double tmp;
	if (z <= -1.15e+138) {
		tmp = t_0;
	} else if (z <= -1.25e-190) {
		tmp = z + x;
	} else if (z <= 8.2e-282) {
		tmp = y + (z + x);
	} else if (z <= 8e+35) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.15e+138:
		tmp = t_0
	elif z <= -1.25e-190:
		tmp = z + x
	elif z <= 8.2e-282:
		tmp = y + (z + x)
	elif z <= 8e+35:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.15e+138)
		tmp = t_0;
	elseif (z <= -1.25e-190)
		tmp = Float64(z + x);
	elseif (z <= 8.2e-282)
		tmp = Float64(y + Float64(z + x));
	elseif (z <= 8e+35)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.15e+138)
		tmp = t_0;
	elseif (z <= -1.25e-190)
		tmp = z + x;
	elseif (z <= 8.2e-282)
		tmp = y + (z + x);
	elseif (z <= 8e+35)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+138], t$95$0, If[LessEqual[z, -1.25e-190], N[(z + x), $MachinePrecision], If[LessEqual[z, 8.2e-282], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+35], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000004e138 or 7.9999999999999997e35 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.1%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 99.1%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 99.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 99.1%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 87.9%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 87.9%

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

      2. *-commutative 87.9%

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

      3. *-lft-identity 87.9%

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

   6. Simplified 87.9%

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

   if -1.15000000000000004e138 < z < -1.25000000000000009e-190 or 8.19999999999999954e-282 < z < 7.9999999999999997e35

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 73.1%

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

   if -1.25000000000000009e-190 < z < 8.19999999999999954e-282

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 75.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-190}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-282}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+35}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 84.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.85e+138)
     t_0
     (if (<= z -1.4e-23) (+ z x) (if (<= z 2e+34) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.85e+138) {
		tmp = t_0;
	} else if (z <= -1.4e-23) {
		tmp = z + x;
	} else if (z <= 2e+34) {
		tmp = x + sin(y);
	} 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) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.85d+138)) then
        tmp = t_0
    else if (z <= (-1.4d-23)) then
        tmp = z + x
    else if (z <= 2d+34) then
        tmp = x + sin(y)
    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.cos(y);
	double tmp;
	if (z <= -1.85e+138) {
		tmp = t_0;
	} else if (z <= -1.4e-23) {
		tmp = z + x;
	} else if (z <= 2e+34) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.85e+138:
		tmp = t_0
	elif z <= -1.4e-23:
		tmp = z + x
	elif z <= 2e+34:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.85e+138)
		tmp = t_0;
	elseif (z <= -1.4e-23)
		tmp = Float64(z + x);
	elseif (z <= 2e+34)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.85e+138)
		tmp = t_0;
	elseif (z <= -1.4e-23)
		tmp = z + x;
	elseif (z <= 2e+34)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+138], t$95$0, If[LessEqual[z, -1.4e-23], N[(z + x), $MachinePrecision], If[LessEqual[z, 2e+34], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8499999999999999e138 or 1.99999999999999989e34 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.1%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 99.1%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 99.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 99.1%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 87.9%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 87.9%

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

      2. *-commutative 87.9%

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

      3. *-lft-identity 87.9%

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

   6. Simplified 87.9%

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

   if -1.8499999999999999e138 < z < -1.3999999999999999e-23

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 73.4%

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

   if -1.3999999999999999e-23 < z < 1.99999999999999989e34

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 99.9%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 99.9%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 99.9%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in z around 0 89.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+34}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 94.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-23} \lor \neg \left(z \leq 2.2 \cdot 10^{-133}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e-23) (not (<= z 2.2e-133)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-23) || !(z <= 2.2e-133)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + 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 ((z <= (-1.5d-23)) .or. (.not. (z <= 2.2d-133))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-23) || !(z <= 2.2e-133)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e-23) or not (z <= 2.2e-133):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e-23) || !(z <= 2.2e-133))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e-23) || ~((z <= 2.2e-133)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e-23], N[Not[LessEqual[z, 2.2e-133]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000001e-23 or 2.2000000000000001e-133 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 95.9%

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

   if -1.50000000000000001e-23 < z < 2.2000000000000001e-133

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 100.0%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 100.0%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in z around 0 92.9%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-23} \lor \neg \left(z \leq 2.2 \cdot 10^{-133}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 99.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22 \lor \neg \left(z \leq 3.1\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -22.0) (not (<= z 3.1)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22.0) || !(z <= 3.1)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + 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 ((z <= (-22.0d0)) .or. (.not. (z <= 3.1d0))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22.0) || !(z <= 3.1)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -22.0) or not (z <= 3.1):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -22.0) || !(z <= 3.1))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -22.0) || ~((z <= 3.1)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -22.0], N[Not[LessEqual[z, 3.1]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -22 or 3.10000000000000009 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 97.9%

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

   if -22 < z < 3.10000000000000009

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 99.3%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22 \lor \neg \left(z \leq 3.1\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 70.9% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 3.2:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+27) (+ z x) (if (<= y 3.2) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+27) {
		tmp = z + x;
	} else if (y <= 3.2) {
		tmp = y + (z + x);
	} else {
		tmp = z + 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 (y <= (-6.5d+27)) then
        tmp = z + x
    else if (y <= 3.2d0) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+27) {
		tmp = z + x;
	} else if (y <= 3.2) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+27:
		tmp = z + x
	elif y <= 3.2:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+27)
		tmp = Float64(z + x);
	elseif (y <= 3.2)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+27)
		tmp = z + x;
	elseif (y <= 3.2)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+27], N[(z + x), $MachinePrecision], If[LessEqual[y, 3.2], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000005e27 or 3.2000000000000002 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 40.5%

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

   if -6.5000000000000005e27 < y < 3.2000000000000002

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 95.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 3.2:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 59.1% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 580000000000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7e+27) x (if (<= x 580000000000.0) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7e+27) {
		tmp = x;
	} else if (x <= 580000000000.0) {
		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 (x <= (-7d+27)) then
        tmp = x
    else if (x <= 580000000000.0d0) 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 (x <= -7e+27) {
		tmp = x;
	} else if (x <= 580000000000.0) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7e+27:
		tmp = x
	elif x <= 580000000000.0:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7e+27)
		tmp = x;
	elseif (x <= 580000000000.0)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7e+27)
		tmp = x;
	elseif (x <= 580000000000.0)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7e+27], x, If[LessEqual[x, 580000000000.0], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000004e27 or 5.8e11 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. add-cube-cbrt 99.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in x around inf 73.0%

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

   if -7.0000000000000004e27 < x < 5.8e11

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around 0 88.6%

      \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]
   3. Step-by-step derivation

      1. *-commutative 88.6%

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

      2. fma-def 88.6%

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

   4. Simplified 88.6%

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

   5. Taylor expanded in y around 0 41.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 580000000000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.6% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.85e-44) (+ z x) (if (<= y 0.00032) (+ z y) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.85e-44) {
		tmp = z + x;
	} else if (y <= 0.00032) {
		tmp = z + y;
	} else {
		tmp = z + 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 (y <= 1.85d-44) then
        tmp = z + x
    else if (y <= 0.00032d0) then
        tmp = z + y
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.85e-44) {
		tmp = z + x;
	} else if (y <= 0.00032) {
		tmp = z + y;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.85e-44:
		tmp = z + x
	elif y <= 0.00032:
		tmp = z + y
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.85e-44)
		tmp = Float64(z + x);
	elseif (y <= 0.00032)
		tmp = Float64(z + y);
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.85e-44)
		tmp = z + x;
	elseif (y <= 0.00032)
		tmp = z + y;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.85e-44], N[(z + x), $MachinePrecision], If[LessEqual[y, 0.00032], N[(z + y), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 1.85e-44 or 3.20000000000000026e-4 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 66.5%

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

   if 1.85e-44 < y < 3.20000000000000026e-4

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{z \cdot \cos y + \sin y} \]
   3. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. fma-def 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 93.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{-44}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 0.00032:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 10: 51.7% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+137}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.95e+137) z (if (<= z 4.6e+83) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+137) {
		tmp = z;
	} else if (z <= 4.6e+83) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-1.95d+137)) then
        tmp = z
    else if (z <= 4.6d+83) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+137) {
		tmp = z;
	} else if (z <= 4.6e+83) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.95e+137:
		tmp = z
	elif z <= 4.6e+83:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.95e+137)
		tmp = z;
	elseif (z <= 4.6e+83)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.95e+137)
		tmp = z;
	elseif (z <= 4.6e+83)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.95e+137], z, If[LessEqual[z, 4.6e+83], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000015e137 or 4.5999999999999999e83 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.2%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 99.2%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 99.2%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 88.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 88.8%

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

      2. *-commutative 88.8%

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

      3. *-lft-identity 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in y around 0 49.8%

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

   if -1.95000000000000015e137 < z < 4.5999999999999999e83

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. add-cube-cbrt 99.8%

         \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

      3. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

      4. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

      5. pow2 99.8%

         \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

   4. Taylor expanded in x around inf 56.9%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+137}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 11: 42.6% 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 99.9%

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

   1. +-commutative 99.9%

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

   2. add-cube-cbrt 99.6%

      \[\leadsto z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} + \left(x + \sin y\right) \]

   3. associate-*r* 99.6%

      \[\leadsto \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} + \left(x + \sin y\right) \]

   4. fma-def 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right), \sqrt[3]{\cos y}, x + \sin y\right)} \]

   5. pow2 99.6%

      \[\leadsto \mathsf{fma}\left(z \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y}, x + \sin y\right) \]

3. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot {\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y}, x + \sin y\right)} \]

4. Taylor expanded in x around inf 40.5%

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

5. Final simplification 40.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))