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

Percentage Accurate: 99.9% → 99.9%

Time: 11.2s

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: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{-60} \lor \neg \left(x \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;x + t_0\\ \mathbf{else}:\\ \;\;\;\;\sin y + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (or (<= x -1.45e-60) (not (<= x 4e-21))) (+ x t_0) (+ (sin y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if ((x <= -1.45e-60) || !(x <= 4e-21)) {
		tmp = x + t_0;
	} else {
		tmp = sin(y) + 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 ((x <= (-1.45d-60)) .or. (.not. (x <= 4d-21))) then
        tmp = x + t_0
    else
        tmp = sin(y) + 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 ((x <= -1.45e-60) || !(x <= 4e-21)) {
		tmp = x + t_0;
	} else {
		tmp = Math.sin(y) + t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if (x <= -1.45e-60) or not (x <= 4e-21):
		tmp = x + t_0
	else:
		tmp = math.sin(y) + t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if ((x <= -1.45e-60) || !(x <= 4e-21))
		tmp = Float64(x + t_0);
	else
		tmp = Float64(sin(y) + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if ((x <= -1.45e-60) || ~((x <= 4e-21)))
		tmp = x + t_0;
	else
		tmp = sin(y) + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.45e-60], N[Not[LessEqual[x, 4e-21]], $MachinePrecision]], N[(x + t$95$0), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.45e-60 or 3.99999999999999963e-21 < x

   1. Initial program 99.9%

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

      1. add-cube-cbrt_binary64 99.3%

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

   3. Applied rewrite-once 99.3%

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

      1. pow3 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. flip-+ 56.6%

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

      2. unpow2 56.6%

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

      3. div-inv 56.5%

         \[\leadsto \color{blue}{\left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y}} + {\left(\sqrt[3]{z \cdot \cos y}\right)}^{3} \]

      4. rem-cube-cbrt 57.0%

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

      5. fma-udef 57.0%

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

   7. Applied egg-rr 57.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot x - {\sin y}^{2}, \frac{1}{x - \sin y}, z \cdot \cos y\right)} \]
   8. Step-by-step derivation

      1. fma-udef 57.0%

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

      2. +-commutative 57.0%

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

      3. associate-*r/ 57.1%

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

      4. *-commutative 57.1%

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

      5. *-lft-identity 57.1%

         \[\leadsto z \cdot \cos y + \frac{\color{blue}{x \cdot x - {\sin y}^{2}}}{x - \sin y} \]

   9. Simplified 57.1%

      \[\leadsto \color{blue}{z \cdot \cos y + \frac{x \cdot x - {\sin y}^{2}}{x - \sin y}} \]

   10. Taylor expanded in x around inf 98.2%

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

   if -1.45e-60 < x < 3.99999999999999963e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.2%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{-60} \lor \neg \left(x \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]

Alternative 3: 68.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -3 \cdot 10^{+57}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= x -3e+57)
     (+ x z)
     (if (<= x 7e-173)
       t_0
       (if (<= x 1.9e-45) (sin y) (if (<= x 4.6e+17) t_0 (+ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (x <= -3e+57) {
		tmp = x + z;
	} else if (x <= 7e-173) {
		tmp = t_0;
	} else if (x <= 1.9e-45) {
		tmp = sin(y);
	} else if (x <= 4.6e+17) {
		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 = z * cos(y)
    if (x <= (-3d+57)) then
        tmp = x + z
    else if (x <= 7d-173) then
        tmp = t_0
    else if (x <= 1.9d-45) then
        tmp = sin(y)
    else if (x <= 4.6d+17) 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 = z * Math.cos(y);
	double tmp;
	if (x <= -3e+57) {
		tmp = x + z;
	} else if (x <= 7e-173) {
		tmp = t_0;
	} else if (x <= 1.9e-45) {
		tmp = Math.sin(y);
	} else if (x <= 4.6e+17) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if x <= -3e+57:
		tmp = x + z
	elif x <= 7e-173:
		tmp = t_0
	elif x <= 1.9e-45:
		tmp = math.sin(y)
	elif x <= 4.6e+17:
		tmp = t_0
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -3e+57)
		tmp = Float64(x + z);
	elseif (x <= 7e-173)
		tmp = t_0;
	elseif (x <= 1.9e-45)
		tmp = sin(y);
	elseif (x <= 4.6e+17)
		tmp = t_0;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (x <= -3e+57)
		tmp = x + z;
	elseif (x <= 7e-173)
		tmp = t_0;
	elseif (x <= 1.9e-45)
		tmp = sin(y);
	elseif (x <= 4.6e+17)
		tmp = t_0;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+57], N[(x + z), $MachinePrecision], If[LessEqual[x, 7e-173], t$95$0, If[LessEqual[x, 1.9e-45], N[Sin[y], $MachinePrecision], If[LessEqual[x, 4.6e+17], t$95$0, N[(x + z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3e57 or 4.6e17 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.9%

      \[\leadsto \color{blue}{x + z} \]
   3. Step-by-step derivation

      1. +-commutative 91.9%

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

   4. Simplified 91.9%

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

   if -3e57 < x < 7.00000000000000029e-173 or 1.89999999999999999e-45 < x < 4.6e17

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 68.7%

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

   if 7.00000000000000029e-173 < x < 1.89999999999999999e-45

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.3%

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

   3. Taylor expanded in z around 0 62.9%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+57}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-173}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 4: 84.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-56}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+138}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.3e+33)
     t_0
     (if (<= z -3.15e-49)
       (+ x z)
       (if (<= z 1.75e-56) (+ x (sin y)) (if (<= z 1.3e+138) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.3e+33) {
		tmp = t_0;
	} else if (z <= -3.15e-49) {
		tmp = x + z;
	} else if (z <= 1.75e-56) {
		tmp = x + sin(y);
	} else if (z <= 1.3e+138) {
		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 <= (-2.3d+33)) then
        tmp = t_0
    else if (z <= (-3.15d-49)) then
        tmp = x + z
    else if (z <= 1.75d-56) then
        tmp = x + sin(y)
    else if (z <= 1.3d+138) 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 <= -2.3e+33) {
		tmp = t_0;
	} else if (z <= -3.15e-49) {
		tmp = x + z;
	} else if (z <= 1.75e-56) {
		tmp = x + Math.sin(y);
	} else if (z <= 1.3e+138) {
		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 <= -2.3e+33:
		tmp = t_0
	elif z <= -3.15e-49:
		tmp = x + z
	elif z <= 1.75e-56:
		tmp = x + math.sin(y)
	elif z <= 1.3e+138:
		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 <= -2.3e+33)
		tmp = t_0;
	elseif (z <= -3.15e-49)
		tmp = Float64(x + z);
	elseif (z <= 1.75e-56)
		tmp = Float64(x + sin(y));
	elseif (z <= 1.3e+138)
		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 <= -2.3e+33)
		tmp = t_0;
	elseif (z <= -3.15e-49)
		tmp = x + z;
	elseif (z <= 1.75e-56)
		tmp = x + sin(y);
	elseif (z <= 1.3e+138)
		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, -2.3e+33], t$95$0, If[LessEqual[z, -3.15e-49], N[(x + z), $MachinePrecision], If[LessEqual[z, 1.75e-56], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+138], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000011e33 or 1.3e138 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 79.9%

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

   if -2.30000000000000011e33 < z < -3.1499999999999998e-49 or 1.7499999999999999e-56 < z < 1.3e138

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 83.2%

      \[\leadsto \color{blue}{x + z} \]
   3. Step-by-step derivation

      1. +-commutative 83.2%

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

   4. Simplified 83.2%

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

   if -3.1499999999999998e-49 < z < 1.7499999999999999e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.6%

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

      1. +-commutative 95.6%

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

   4. Simplified 95.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.15 \cdot 10^{-49}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-56}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+138}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 94.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-49} \lor \neg \left(z \leq 2.3 \cdot 10^{-56}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e-49) (not (<= z 2.3e-56)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e-49) || !(z <= 2.3e-56)) {
		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 <= (-4.6d-49)) .or. (.not. (z <= 2.3d-56))) 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 <= -4.6e-49) || !(z <= 2.3e-56)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e-49) or not (z <= 2.3e-56):
		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 <= -4.6e-49) || !(z <= 2.3e-56))
		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 <= -4.6e-49) || ~((z <= 2.3e-56)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e-49], N[Not[LessEqual[z, 2.3e-56]], $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 < -4.5999999999999998e-49 or 2.30000000000000002e-56 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt_binary64 98.7%

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

   3. Applied rewrite-once 98.7%

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

      1. pow3 98.7%

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

   5. Applied egg-rr 98.7%

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

      1. flip-+ 73.9%

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

      2. unpow2 73.9%

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

      3. div-inv 73.8%

         \[\leadsto \color{blue}{\left(x \cdot x - {\sin y}^{2}\right) \cdot \frac{1}{x - \sin y}} + {\left(\sqrt[3]{z \cdot \cos y}\right)}^{3} \]

      4. rem-cube-cbrt 75.0%

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

      5. fma-udef 75.0%

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

   7. Applied egg-rr 75.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot x - {\sin y}^{2}, \frac{1}{x - \sin y}, z \cdot \cos y\right)} \]
   8. Step-by-step derivation

      1. fma-udef 75.0%

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

      2. +-commutative 75.0%

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

      3. associate-*r/ 75.1%

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

      4. *-commutative 75.1%

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

      5. *-lft-identity 75.1%

         \[\leadsto z \cdot \cos y + \frac{\color{blue}{x \cdot x - {\sin y}^{2}}}{x - \sin y} \]

   9. Simplified 75.1%

      \[\leadsto \color{blue}{z \cdot \cos y + \frac{x \cdot x - {\sin y}^{2}}{x - \sin y}} \]

   10. Taylor expanded in x around inf 97.4%

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

   if -4.5999999999999998e-49 < z < 2.30000000000000002e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.6%

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

      1. +-commutative 95.6%

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

   4. Simplified 95.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-49} \lor \neg \left(z \leq 2.3 \cdot 10^{-56}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 68.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-55}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2e-55)
   (+ x z)
   (if (<= x 2.15e-172) (+ z (+ x y)) (if (<= x 1.9e-45) (sin y) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2e-55) {
		tmp = x + z;
	} else if (x <= 2.15e-172) {
		tmp = z + (x + y);
	} else if (x <= 1.9e-45) {
		tmp = sin(y);
	} 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 <= (-2d-55)) then
        tmp = x + z
    else if (x <= 2.15d-172) then
        tmp = z + (x + y)
    else if (x <= 1.9d-45) then
        tmp = sin(y)
    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 <= -2e-55) {
		tmp = x + z;
	} else if (x <= 2.15e-172) {
		tmp = z + (x + y);
	} else if (x <= 1.9e-45) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2e-55:
		tmp = x + z
	elif x <= 2.15e-172:
		tmp = z + (x + y)
	elif x <= 1.9e-45:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2e-55)
		tmp = Float64(x + z);
	elseif (x <= 2.15e-172)
		tmp = Float64(z + Float64(x + y));
	elseif (x <= 1.9e-45)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2e-55)
		tmp = x + z;
	elseif (x <= 2.15e-172)
		tmp = z + (x + y);
	elseif (x <= 1.9e-45)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2e-55], N[(x + z), $MachinePrecision], If[LessEqual[x, 2.15e-172], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-45], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.99999999999999999e-55 or 1.89999999999999999e-45 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.6%

      \[\leadsto \color{blue}{x + z} \]
   3. Step-by-step derivation

      1. +-commutative 82.6%

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

   4. Simplified 82.6%

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

   if -1.99999999999999999e-55 < x < 2.1499999999999999e-172

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 53.0%

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

      1. associate-+r+ 53.0%

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

      2. +-commutative 53.0%

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

      3. +-commutative 53.0%

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

   4. Simplified 53.0%

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

   if 2.1499999999999999e-172 < x < 1.89999999999999999e-45

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.3%

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

   3. Taylor expanded in z around 0 62.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-55}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-172}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-45}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 7: 69.3% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-52}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;x + \left(\left(y + z\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e-52)
   (+ x z)
   (if (<= x 1.9e-64) (+ x (+ (+ y z) (* -0.5 (* z (* y y))))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e-52) {
		tmp = x + z;
	} else if (x <= 1.9e-64) {
		tmp = x + ((y + z) + (-0.5 * (z * (y * y))));
	} 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 <= (-4.6d-52)) then
        tmp = x + z
    else if (x <= 1.9d-64) then
        tmp = x + ((y + z) + ((-0.5d0) * (z * (y * y))))
    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 <= -4.6e-52) {
		tmp = x + z;
	} else if (x <= 1.9e-64) {
		tmp = x + ((y + z) + (-0.5 * (z * (y * y))));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e-52:
		tmp = x + z
	elif x <= 1.9e-64:
		tmp = x + ((y + z) + (-0.5 * (z * (y * y))))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e-52)
		tmp = Float64(x + z);
	elseif (x <= 1.9e-64)
		tmp = Float64(x + Float64(Float64(y + z) + Float64(-0.5 * Float64(z * Float64(y * y)))));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e-52)
		tmp = x + z;
	elseif (x <= 1.9e-64)
		tmp = x + ((y + z) + (-0.5 * (z * (y * y))));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e-52], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.9e-64], N[(x + N[(N[(y + z), $MachinePrecision] + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.59999999999999989e-52 or 1.9000000000000001e-64 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.3%

      \[\leadsto \color{blue}{x + z} \]
   3. Step-by-step derivation

      1. +-commutative 82.3%

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

   4. Simplified 82.3%

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

   if -4.59999999999999989e-52 < x < 1.9000000000000001e-64

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 48.5%

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

      1. associate-+r+ 48.5%

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

      2. +-commutative 48.5%

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

      3. *-commutative 48.5%

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

      4. unpow2 48.5%

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

   4. Simplified 48.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-52}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-64}:\\ \;\;\;\;x + \left(\left(y + z\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 8: 69.7% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e-56) (+ x z) (if (<= x 2.4e-67) (+ z (+ x y)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-56) {
		tmp = x + z;
	} else if (x <= 2.4e-67) {
		tmp = z + (x + y);
	} 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 <= (-3.5d-56)) then
        tmp = x + z
    else if (x <= 2.4d-67) then
        tmp = z + (x + y)
    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 <= -3.5e-56) {
		tmp = x + z;
	} else if (x <= 2.4e-67) {
		tmp = z + (x + y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e-56:
		tmp = x + z
	elif x <= 2.4e-67:
		tmp = z + (x + y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e-56)
		tmp = Float64(x + z);
	elseif (x <= 2.4e-67)
		tmp = Float64(z + Float64(x + y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.5e-56)
		tmp = x + z;
	elseif (x <= 2.4e-67)
		tmp = z + (x + y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e-56], N[(x + z), $MachinePrecision], If[LessEqual[x, 2.4e-67], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999998e-56 or 2.4e-67 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.8%

      \[\leadsto \color{blue}{x + z} \]
   3. Step-by-step derivation

      1. +-commutative 81.8%

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

   4. Simplified 81.8%

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

   if -3.4999999999999998e-56 < x < 2.4e-67

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 48.9%

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

      1. associate-+r+ 48.9%

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

      2. +-commutative 48.9%

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

      3. +-commutative 48.9%

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

   4. Simplified 48.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 9: 55.3% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -23000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -23000000000.0) x (if (<= x 5e-8) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -23000000000.0) {
		tmp = x;
	} else if (x <= 5e-8) {
		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 <= (-23000000000.0d0)) then
        tmp = x
    else if (x <= 5d-8) 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 <= -23000000000.0) {
		tmp = x;
	} else if (x <= 5e-8) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -23000000000.0:
		tmp = x
	elif x <= 5e-8:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -23000000000.0)
		tmp = x;
	elseif (x <= 5e-8)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -23000000000.0)
		tmp = x;
	elseif (x <= 5e-8)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -23000000000.0], x, If[LessEqual[x, 5e-8], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e10 or 4.9999999999999998e-8 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 74.3%

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

   if -2.3e10 < x < 4.9999999999999998e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 60.9%

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

   3. Taylor expanded in y around 0 39.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -23000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 66.2% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x z))

C

double code(double x, double y, double z) {
	return x + 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 + z
end function

Java

public static double code(double x, double y, double z) {
	return x + z;
}

Python

def code(x, y, z):
	return x + z

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 67.7%

   \[\leadsto \color{blue}{x + z} \]
3. Step-by-step derivation

   1. +-commutative 67.7%

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

4. Simplified 67.7%

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

5. Final simplification 67.7%

   \[\leadsto x + z \]

Alternative 11: 42.1% 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. Taylor expanded in x around inf 44.1%

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

3. Final simplification 44.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023297 
(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))))