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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(z * N[Cos[y], $MachinePrecision]), $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. Final simplification 99.9%

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

Alternative 2: 68.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-18}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-154}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-214}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+180}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4.8e+113)
     t_0
     (if (<= z -3.15e-18)
       (+ x z)
       (if (<= z -1.75e-154)
         (sin y)
         (if (<= z 5.5e-214)
           (+ y (+ x z))
           (if (<= z 8.8e+180) (+ x z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4.8e+113) {
		tmp = t_0;
	} else if (z <= -3.15e-18) {
		tmp = x + z;
	} else if (z <= -1.75e-154) {
		tmp = sin(y);
	} else if (z <= 5.5e-214) {
		tmp = y + (x + z);
	} else if (z <= 8.8e+180) {
		tmp = x + z;
	} 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 <= (-4.8d+113)) then
        tmp = t_0
    else if (z <= (-3.15d-18)) then
        tmp = x + z
    else if (z <= (-1.75d-154)) then
        tmp = sin(y)
    else if (z <= 5.5d-214) then
        tmp = y + (x + z)
    else if (z <= 8.8d+180) then
        tmp = x + z
    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 <= -4.8e+113) {
		tmp = t_0;
	} else if (z <= -3.15e-18) {
		tmp = x + z;
	} else if (z <= -1.75e-154) {
		tmp = Math.sin(y);
	} else if (z <= 5.5e-214) {
		tmp = y + (x + z);
	} else if (z <= 8.8e+180) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -4.8e+113:
		tmp = t_0
	elif z <= -3.15e-18:
		tmp = x + z
	elif z <= -1.75e-154:
		tmp = math.sin(y)
	elif z <= 5.5e-214:
		tmp = y + (x + z)
	elif z <= 8.8e+180:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -4.8e+113)
		tmp = t_0;
	elseif (z <= -3.15e-18)
		tmp = Float64(x + z);
	elseif (z <= -1.75e-154)
		tmp = sin(y);
	elseif (z <= 5.5e-214)
		tmp = Float64(y + Float64(x + z));
	elseif (z <= 8.8e+180)
		tmp = Float64(x + z);
	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 <= -4.8e+113)
		tmp = t_0;
	elseif (z <= -3.15e-18)
		tmp = x + z;
	elseif (z <= -1.75e-154)
		tmp = sin(y);
	elseif (z <= 5.5e-214)
		tmp = y + (x + z);
	elseif (z <= 8.8e+180)
		tmp = x + z;
	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, -4.8e+113], t$95$0, If[LessEqual[z, -3.15e-18], N[(x + z), $MachinePrecision], If[LessEqual[z, -1.75e-154], N[Sin[y], $MachinePrecision], If[LessEqual[z, 5.5e-214], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e+180], N[(x + z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.79999999999999966e113 or 8.7999999999999997e180 < 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 92.1%

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

      1. pow-base-1 92.1%

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

      2. *-commutative 92.1%

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

      3. *-lft-identity 92.1%

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

   6. Simplified 92.1%

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

   if -4.79999999999999966e113 < z < -3.1500000000000002e-18 or 5.50000000000000024e-214 < z < 8.7999999999999997e180

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.1%

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

   if -3.1500000000000002e-18 < z < -1.75e-154

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 71.6%

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

   3. Taylor expanded in z around 0 60.9%

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

   if -1.75e-154 < z < 5.50000000000000024e-214

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{y + \left(z + x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-18}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-154}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-214}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+180}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 3: 77.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y + z\\ \mathbf{if}\;x \leq -2500:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-262}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (sin y) z)))
   (if (<= x -2500.0)
     (+ x z)
     (if (<= x 3.1e-262)
       t_0
       (if (<= x 3.3e-227) (* z (cos y)) (if (<= x 3.5e-9) t_0 (+ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) + z;
	double tmp;
	if (x <= -2500.0) {
		tmp = x + z;
	} else if (x <= 3.1e-262) {
		tmp = t_0;
	} else if (x <= 3.3e-227) {
		tmp = z * cos(y);
	} else if (x <= 3.5e-9) {
		tmp = t_0;
	} else {
		tmp = x + 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) :: tmp
    t_0 = sin(y) + z
    if (x <= (-2500.0d0)) then
        tmp = x + z
    else if (x <= 3.1d-262) then
        tmp = t_0
    else if (x <= 3.3d-227) then
        tmp = z * cos(y)
    else if (x <= 3.5d-9) then
        tmp = t_0
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) + z;
	double tmp;
	if (x <= -2500.0) {
		tmp = x + z;
	} else if (x <= 3.1e-262) {
		tmp = t_0;
	} else if (x <= 3.3e-227) {
		tmp = z * Math.cos(y);
	} else if (x <= 3.5e-9) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) + z
	tmp = 0
	if x <= -2500.0:
		tmp = x + z
	elif x <= 3.1e-262:
		tmp = t_0
	elif x <= 3.3e-227:
		tmp = z * math.cos(y)
	elif x <= 3.5e-9:
		tmp = t_0
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) + z)
	tmp = 0.0
	if (x <= -2500.0)
		tmp = Float64(x + z);
	elseif (x <= 3.1e-262)
		tmp = t_0;
	elseif (x <= 3.3e-227)
		tmp = Float64(z * cos(y));
	elseif (x <= 3.5e-9)
		tmp = t_0;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) + z;
	tmp = 0.0;
	if (x <= -2500.0)
		tmp = x + z;
	elseif (x <= 3.1e-262)
		tmp = t_0;
	elseif (x <= 3.3e-227)
		tmp = z * cos(y);
	elseif (x <= 3.5e-9)
		tmp = t_0;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision]}, If[LessEqual[x, -2500.0], N[(x + z), $MachinePrecision], If[LessEqual[x, 3.1e-262], t$95$0, If[LessEqual[x, 3.3e-227], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e-9], t$95$0, N[(x + z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2500 or 3.4999999999999999e-9 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 85.8%

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

   if -2500 < x < 3.0999999999999998e-262 or 3.2999999999999999e-227 < x < 3.4999999999999999e-9

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.4%

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

   3. Taylor expanded in y around 0 78.7%

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

   if 3.0999999999999998e-262 < x < 3.2999999999999999e-227

   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 98.9%

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

      3. associate-*r* 98.7%

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

      4. fma-def 98.7%

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

      5. pow2 98.7%

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

   3. Applied egg-rr 98.7%

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

   4. Taylor expanded in z around inf 91.5%

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

      1. pow-base-1 91.5%

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

      2. *-commutative 91.5%

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

      3. *-lft-identity 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2500:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-262}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\sin y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+181}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.05e+103)
     t_0
     (if (<= z -2.1e-17)
       (+ x z)
       (if (<= z 1.25e-59) (+ x (sin y)) (if (<= z 1.38e+181) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.05e+103) {
		tmp = t_0;
	} else if (z <= -2.1e-17) {
		tmp = x + z;
	} else if (z <= 1.25e-59) {
		tmp = x + sin(y);
	} else if (z <= 1.38e+181) {
		tmp = x + z;
	} 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 <= (-1.05d+103)) then
        tmp = t_0
    else if (z <= (-2.1d-17)) then
        tmp = x + z
    else if (z <= 1.25d-59) then
        tmp = x + sin(y)
    else if (z <= 1.38d+181) then
        tmp = x + z
    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 <= -1.05e+103) {
		tmp = t_0;
	} else if (z <= -2.1e-17) {
		tmp = x + z;
	} else if (z <= 1.25e-59) {
		tmp = x + Math.sin(y);
	} else if (z <= 1.38e+181) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.05e+103:
		tmp = t_0
	elif z <= -2.1e-17:
		tmp = x + z
	elif z <= 1.25e-59:
		tmp = x + math.sin(y)
	elif z <= 1.38e+181:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.05e+103)
		tmp = t_0;
	elseif (z <= -2.1e-17)
		tmp = Float64(x + z);
	elseif (z <= 1.25e-59)
		tmp = Float64(x + sin(y));
	elseif (z <= 1.38e+181)
		tmp = Float64(x + z);
	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 <= -1.05e+103)
		tmp = t_0;
	elseif (z <= -2.1e-17)
		tmp = x + z;
	elseif (z <= 1.25e-59)
		tmp = x + sin(y);
	elseif (z <= 1.38e+181)
		tmp = x + z;
	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, -1.05e+103], t$95$0, If[LessEqual[z, -2.1e-17], N[(x + z), $MachinePrecision], If[LessEqual[z, 1.25e-59], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e+181], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0500000000000001e103 or 1.3799999999999999e181 < 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 92.1%

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

      1. pow-base-1 92.1%

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

      2. *-commutative 92.1%

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

      3. *-lft-identity 92.1%

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

   6. Simplified 92.1%

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

   if -1.0500000000000001e103 < z < -2.09999999999999992e-17 or 1.25e-59 < z < 1.3799999999999999e181

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.8%

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

   if -2.09999999999999992e-17 < z < 1.25e-59

   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 94.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-59}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+181}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 95.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-18} \lor \neg \left(z \leq 8.5 \cdot 10^{-60}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e-18) (not (<= z 8.5e-60)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-18) || !(z <= 8.5e-60)) {
		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 <= (-4.1d-18)) .or. (.not. (z <= 8.5d-60))) 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 <= -4.1e-18) || !(z <= 8.5e-60)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.1e-18) or not (z <= 8.5e-60):
		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 <= -4.1e-18) || !(z <= 8.5e-60))
		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 <= -4.1e-18) || ~((z <= 8.5e-60)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.1e-18], N[Not[LessEqual[z, 8.5e-60]], $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 < -4.0999999999999998e-18 or 8.50000000000000044e-60 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 98.4%

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

   if -4.0999999999999998e-18 < z < 8.50000000000000044e-60

   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 94.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-18} \lor \neg \left(z \leq 8.5 \cdot 10^{-60}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 98.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -700000000000 \lor \neg \left(z \leq 3.2 \cdot 10^{-32}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -700000000000.0) (not (<= z 3.2e-32)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -700000000000.0) || !(z <= 3.2e-32)) {
		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 <= (-700000000000.0d0)) .or. (.not. (z <= 3.2d-32))) 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 <= -700000000000.0) || !(z <= 3.2e-32)) {
		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 <= -700000000000.0) or not (z <= 3.2e-32):
		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 <= -700000000000.0) || !(z <= 3.2e-32))
		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 <= -700000000000.0) || ~((z <= 3.2e-32)))
		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, -700000000000.0], N[Not[LessEqual[z, 3.2e-32]], $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 < -7e11 or 3.2000000000000002e-32 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 99.7%

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

   if -7e11 < z < 3.2000000000000002e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -700000000000 \lor \neg \left(z \leq 3.2 \cdot 10^{-32}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 70.2% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+62}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -90000.0) (+ x z) (if (<= y 3.4e+62) (+ y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -90000.0) {
		tmp = x + z;
	} else if (y <= 3.4e+62) {
		tmp = y + (x + z);
	} else {
		tmp = x + 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 <= (-90000.0d0)) then
        tmp = x + z
    else if (y <= 3.4d+62) then
        tmp = y + (x + z)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -90000.0) {
		tmp = x + z;
	} else if (y <= 3.4e+62) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -90000.0:
		tmp = x + z
	elif y <= 3.4e+62:
		tmp = y + (x + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -90000.0)
		tmp = Float64(x + z);
	elseif (y <= 3.4e+62)
		tmp = Float64(y + Float64(x + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -90000.0)
		tmp = x + z;
	elseif (y <= 3.4e+62)
		tmp = y + (x + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -90000.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.4e+62], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9e4 or 3.40000000000000014e62 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 41.9%

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

   if -9e4 < y < 3.40000000000000014e62

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 90.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90000:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+62}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 58.9% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2500:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 95000:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2500.0) x (if (<= x 95000.0) (+ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2500.0) {
		tmp = x;
	} else if (x <= 95000.0) {
		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 <= (-2500.0d0)) then
        tmp = x
    else if (x <= 95000.0d0) 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 <= -2500.0) {
		tmp = x;
	} else if (x <= 95000.0) {
		tmp = y + z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2500.0:
		tmp = x
	elif x <= 95000.0:
		tmp = y + z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2500.0)
		tmp = x;
	elseif (x <= 95000.0)
		tmp = Float64(y + z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2500.0)
		tmp = x;
	elseif (x <= 95000.0)
		tmp = y + z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2500.0], x, If[LessEqual[x, 95000.0], N[(y + z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2500 or 95000 < 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* 99.7%

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

      4. fma-def 99.7%

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

      5. pow2 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 72.3%

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

   if -2500 < x < 95000

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.9%

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

   3. Taylor expanded in y around 0 51.5%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2500:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 95000:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 67.7% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-49}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-149}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e-49) (+ x z) (if (<= x 2.25e-149) (+ y z) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e-49) {
		tmp = x + z;
	} else if (x <= 2.25e-149) {
		tmp = y + z;
	} else {
		tmp = x + 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 (x <= (-5.8d-49)) then
        tmp = x + z
    else if (x <= 2.25d-149) then
        tmp = y + z
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e-49) {
		tmp = x + z;
	} else if (x <= 2.25e-149) {
		tmp = y + z;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e-49:
		tmp = x + z
	elif x <= 2.25e-149:
		tmp = y + z
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e-49)
		tmp = Float64(x + z);
	elseif (x <= 2.25e-149)
		tmp = Float64(y + z);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.8e-49)
		tmp = x + z;
	elseif (x <= 2.25e-149)
		tmp = y + z;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e-49], N[(x + z), $MachinePrecision], If[LessEqual[x, 2.25e-149], N[(y + z), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8e-49 or 2.2499999999999999e-149 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.8%

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

   if -5.8e-49 < x < 2.2499999999999999e-149

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.3%

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

   3. Taylor expanded in y around 0 54.7%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-49}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{-149}:\\ \;\;\;\;y + z\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 10: 55.8% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2500:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 225000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2500.0) x (if (<= x 225000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2500.0) {
		tmp = x;
	} else if (x <= 225000.0) {
		tmp = 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 <= (-2500.0d0)) then
        tmp = x
    else if (x <= 225000.0d0) then
        tmp = 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 <= -2500.0) {
		tmp = x;
	} else if (x <= 225000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2500.0:
		tmp = x
	elif x <= 225000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2500.0)
		tmp = x;
	elseif (x <= 225000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2500.0)
		tmp = x;
	elseif (x <= 225000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2500.0], x, If[LessEqual[x, 225000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2500 or 225000 < 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* 99.7%

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

      4. fma-def 99.7%

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

      5. pow2 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 72.3%

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

   if -2500 < x < 225000

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.9%

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

   3. Taylor expanded in y around 0 76.6%

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

   4. Taylor expanded in z around inf 38.4%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2500:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 225000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 43.0% 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 99.7%

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

   3. associate-*r* 99.7%

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

   4. fma-def 99.7%

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

   5. pow2 99.7%

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

3. Applied egg-rr 99.7%

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

4. Taylor expanded in x around inf 36.3%

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

5. Final simplification 36.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023216 
(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))))