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

Percentage Accurate: 99.9% → 99.9%

Time: 10.0s

Alternatives: 15

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-define 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. Add Preprocessing

5. Final simplification 99.9%

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

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. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \cos y \]
4. Add Preprocessing

Alternative 3: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.8 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(\cos y + \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.8) (not (<= z 3.5e-16)))
   (* z (+ (cos y) (/ x z)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.8) || !(z <= 3.5e-16)) {
		tmp = z * (cos(y) + (x / z));
	} 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 <= (-0.8d0)) .or. (.not. (z <= 3.5d-16))) then
        tmp = z * (cos(y) + (x / z))
    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 <= -0.8) || !(z <= 3.5e-16)) {
		tmp = z * (Math.cos(y) + (x / z));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.8) or not (z <= 3.5e-16):
		tmp = z * (math.cos(y) + (x / z))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.8) || !(z <= 3.5e-16))
		tmp = Float64(z * Float64(cos(y) + Float64(x / z)));
	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 <= -0.8) || ~((z <= 3.5e-16)))
		tmp = z * (cos(y) + (x / z));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.8], N[Not[LessEqual[z, 3.5e-16]], $MachinePrecision]], N[(z * N[(N[Cos[y], $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.80000000000000004 or 3.50000000000000017e-16 < z

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 80.4%

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

   7. Taylor expanded in z around -inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. neg-mul-1 80.4%

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

      4. neg-mul-1 80.4%

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

      5. unsub-neg 80.4%

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

   9. Simplified 80.4%

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

   10. Taylor expanded in x around inf 99.3%

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

       1. mul-1-neg 99.3%

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

       2. distribute-neg-frac2 99.3%

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

   12. Simplified 99.3%

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

   if -0.80000000000000004 < z < 3.50000000000000017e-16

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. 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 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.8 \lor \neg \left(z \leq 3.5 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(\cos y + \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+77} \lor \neg \left(z \leq 1.36 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.5e+77) (not (<= z 1.36e+88)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.5e+77) || !(z <= 1.36e+88)) {
		tmp = 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 <= (-5.5d+77)) .or. (.not. (z <= 1.36d+88))) then
        tmp = 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 <= -5.5e+77) || !(z <= 1.36e+88)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.5e+77) or not (z <= 1.36e+88):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.5e+77) || !(z <= 1.36e+88))
		tmp = 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 <= -5.5e+77) || ~((z <= 1.36e+88)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.5e+77], N[Not[LessEqual[z, 1.36e+88]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.50000000000000036e77 or 1.3600000000000001e88 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.8%

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

   if -5.50000000000000036e77 < z < 1.3600000000000001e88

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+77} \lor \neg \left(z \leq 1.36 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+105}:\\ \;\;\;\;x + \left(y + t\_0\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+87}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -6.5e+105)
     (+ x (+ y t_0))
     (if (<= z 9e+87) (+ z (+ x (sin y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -6.5e+105) {
		tmp = x + (y + t_0);
	} else if (z <= 9e+87) {
		tmp = z + (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 <= (-6.5d+105)) then
        tmp = x + (y + t_0)
    else if (z <= 9d+87) then
        tmp = z + (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 <= -6.5e+105) {
		tmp = x + (y + t_0);
	} else if (z <= 9e+87) {
		tmp = z + (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 <= -6.5e+105:
		tmp = x + (y + t_0)
	elif z <= 9e+87:
		tmp = z + (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 <= -6.5e+105)
		tmp = Float64(x + Float64(y + t_0));
	elseif (z <= 9e+87)
		tmp = Float64(z + 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 <= -6.5e+105)
		tmp = x + (y + t_0);
	elseif (z <= 9e+87)
		tmp = z + (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, -6.5e+105], N[(x + N[(y + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+87], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.50000000000000049e105

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 89.3%

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

   7. Taylor expanded in z around 0 89.4%

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

   if -6.50000000000000049e105 < z < 9.0000000000000005e87

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.1%

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

   if 9.0000000000000005e87 < z

   1. Initial program 99.7%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 83.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+105}:\\ \;\;\;\;x + \left(y + z \cdot \cos y\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+87}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+78} \lor \neg \left(z \leq 1.4 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05e+78) (not (<= z 1.4e+88))) (* z (cos y)) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05e+78) || !(z <= 1.4e+88)) {
		tmp = z * cos(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 ((z <= (-1.05d+78)) .or. (.not. (z <= 1.4d+88))) then
        tmp = z * cos(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 ((z <= -1.05e+78) || !(z <= 1.4e+88)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05e+78) or not (z <= 1.4e+88):
		tmp = z * math.cos(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05e+78) || !(z <= 1.4e+88))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05e+78) || ~((z <= 1.4e+88)))
		tmp = z * cos(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05e+78], N[Not[LessEqual[z, 1.4e+88]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e78 or 1.39999999999999994e88 < z

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.8%

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

   if -1.05e78 < z < 1.39999999999999994e88

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 68.9%

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

      1. +-commutative 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+78} \lor \neg \left(z \leq 1.4 \cdot 10^{+88}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+77} \lor \neg \left(z \leq 9.5 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e+77) (not (<= z 9.5e+16))) (* z (cos y)) (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e+77) || !(z <= 9.5e+16)) {
		tmp = 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 <= (-2.7d+77)) .or. (.not. (z <= 9.5d+16))) then
        tmp = 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 <= -2.7e+77) || !(z <= 9.5e+16)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.7e+77) or not (z <= 9.5e+16):
		tmp = z * math.cos(y)
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e+77) || !(z <= 9.5e+16))
		tmp = 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 <= -2.7e+77) || ~((z <= 9.5e+16)))
		tmp = z * cos(y);
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e+77], N[Not[LessEqual[z, 9.5e+16]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999998e77 or 9.5e16 < z

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 80.0%

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

   if -2.6999999999999998e77 < z < 9.5e16

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.2%

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

      1. +-commutative 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+77} \lor \neg \left(z \leq 9.5 \cdot 10^{+16}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23000000000 \lor \neg \left(y \leq 39000000000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right) + 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -23000000000.0) (not (<= y 39000000000000.0)))
   (+ z x)
   (+ x (+ z (* y (+ (* y (+ (* z -0.5) (* y -0.16666666666666666))) 1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -23000000000.0) || !(y <= 39000000000000.0)) {
		tmp = z + x;
	} else {
		tmp = x + (z + (y * ((y * ((z * -0.5) + (y * -0.16666666666666666))) + 1.0)));
	}
	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) :: tmp
    if ((y <= (-23000000000.0d0)) .or. (.not. (y <= 39000000000000.0d0))) then
        tmp = z + x
    else
        tmp = x + (z + (y * ((y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -23000000000.0) || !(y <= 39000000000000.0)) {
		tmp = z + x;
	} else {
		tmp = x + (z + (y * ((y * ((z * -0.5) + (y * -0.16666666666666666))) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -23000000000.0) or not (y <= 39000000000000.0):
		tmp = z + x
	else:
		tmp = x + (z + (y * ((y * ((z * -0.5) + (y * -0.16666666666666666))) + 1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -23000000000.0) || !(y <= 39000000000000.0))
		tmp = Float64(z + x);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666))) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -23000000000.0) || ~((y <= 39000000000000.0)))
		tmp = z + x;
	else
		tmp = x + (z + (y * ((y * ((z * -0.5) + (y * -0.16666666666666666))) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -23000000000.0], N[Not[LessEqual[y, 39000000000000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(x + N[(z + N[(y * N[(N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e10 or 3.9e13 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 39.6%

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

      1. +-commutative 39.6%

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

   5. Simplified 39.6%

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

   if -2.3e10 < y < 3.9e13

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 98.2%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23000000000 \lor \neg \left(y \leq 39000000000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right) + 1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+32} \lor \neg \left(y \leq 850\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(y \cdot \left(y \cdot -0.16666666666666666\right) + 1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e+32) (not (<= y 850.0)))
   (+ z x)
   (+ x (+ z (* y (+ (* y (* y -0.16666666666666666)) 1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+32) || !(y <= 850.0)) {
		tmp = z + x;
	} else {
		tmp = x + (z + (y * ((y * (y * -0.16666666666666666)) + 1.0)));
	}
	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) :: tmp
    if ((y <= (-3.7d+32)) .or. (.not. (y <= 850.0d0))) then
        tmp = z + x
    else
        tmp = x + (z + (y * ((y * (y * (-0.16666666666666666d0))) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+32) || !(y <= 850.0)) {
		tmp = z + x;
	} else {
		tmp = x + (z + (y * ((y * (y * -0.16666666666666666)) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e+32) or not (y <= 850.0):
		tmp = z + x
	else:
		tmp = x + (z + (y * ((y * (y * -0.16666666666666666)) + 1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e+32) || !(y <= 850.0))
		tmp = Float64(z + x);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(Float64(y * Float64(y * -0.16666666666666666)) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.7e+32) || ~((y <= 850.0)))
		tmp = z + x;
	else
		tmp = x + (z + (y * ((y * (y * -0.16666666666666666)) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e+32], N[Not[LessEqual[y, 850.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(x + N[(z + N[(y * N[(N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e32 or 850 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 38.4%

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

      1. +-commutative 38.4%

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

   5. Simplified 38.4%

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

   if -3.7e32 < y < 850

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.8%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]

   4. Taylor expanded in z around 0 97.3%

      \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \color{blue}{\left(-0.16666666666666666 \cdot y\right)}\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 97.3%

         \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \color{blue}{\left(y \cdot -0.16666666666666666\right)}\right)\right) \]

   6. Simplified 97.3%

      \[\leadsto x + \left(z + y \cdot \left(1 + y \cdot \color{blue}{\left(y \cdot -0.16666666666666666\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+32} \lor \neg \left(y \leq 850\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(y \cdot \left(y \cdot -0.16666666666666666\right) + 1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \lor \neg \left(y \leq 4.5 \cdot 10^{+16}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(-0.5 \cdot \left(z \cdot y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.42) (not (<= y 4.5e+16)))
   (+ z x)
   (+ (+ z x) (* y (+ (* -0.5 (* z y)) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42) || !(y <= 4.5e+16)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * ((-0.5 * (z * y)) + 1.0));
	}
	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) :: tmp
    if ((y <= (-1.42d0)) .or. (.not. (y <= 4.5d+16))) then
        tmp = z + x
    else
        tmp = (z + x) + (y * (((-0.5d0) * (z * y)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.42) || !(y <= 4.5e+16)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * ((-0.5 * (z * y)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.42) or not (y <= 4.5e+16):
		tmp = z + x
	else:
		tmp = (z + x) + (y * ((-0.5 * (z * y)) + 1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.42) || !(y <= 4.5e+16))
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(z + x) + Float64(y * Float64(Float64(-0.5 * Float64(z * y)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.42) || ~((y <= 4.5e+16)))
		tmp = z + x;
	else
		tmp = (z + x) + (y * ((-0.5 * (z * y)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.42], N[Not[LessEqual[y, 4.5e+16]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + N[(y * N[(N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4199999999999999 or 4.5e16 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 39.7%

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

      1. +-commutative 39.7%

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

   5. Simplified 39.7%

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

   if -1.4199999999999999 < y < 4.5e16

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 97.9%

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

      1. associate-+r+ 97.9%

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

      2. +-commutative 97.9%

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

      3. *-commutative 97.9%

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

   5. Simplified 97.9%

      \[\leadsto \color{blue}{\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \lor \neg \left(y \leq 4.5 \cdot 10^{+16}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(-0.5 \cdot \left(z \cdot y\right) + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+52} \lor \neg \left(y \leq 2.4 \cdot 10^{+66}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.7e+52) (not (<= y 2.4e+66))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.7e+52) || !(y <= 2.4e+66)) {
		tmp = z + x;
	} else {
		tmp = z + (y + 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 <= (-4.7d+52)) .or. (.not. (y <= 2.4d+66))) then
        tmp = z + x
    else
        tmp = z + (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.7e+52) || !(y <= 2.4e+66)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.7e+52) or not (y <= 2.4e+66):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.7e+52) || !(y <= 2.4e+66))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.7e+52) || ~((y <= 2.4e+66)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.7e+52], N[Not[LessEqual[y, 2.4e+66]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e52 or 2.4000000000000002e66 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 39.9%

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

      1. +-commutative 39.9%

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

   5. Simplified 39.9%

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

   if -4.7e52 < y < 2.4000000000000002e66

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.6%

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

      1. +-commutative 88.6%

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

      2. +-commutative 88.6%

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

      3. associate-+l+ 88.6%

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

   5. Simplified 88.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+52} \lor \neg \left(y \leq 2.4 \cdot 10^{+66}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.25 \cdot 10^{-21} \lor \neg \left(x \leq 5.3 \cdot 10^{-127}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.25e-21) (not (<= x 5.3e-127))) (+ z x) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.25e-21) || !(x <= 5.3e-127)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-9.25d-21)) .or. (.not. (x <= 5.3d-127))) then
        tmp = z + x
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.25e-21) || !(x <= 5.3e-127)) {
		tmp = z + x;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.25e-21) or not (x <= 5.3e-127):
		tmp = z + x
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.25e-21) || !(x <= 5.3e-127))
		tmp = Float64(z + x);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.25e-21) || ~((x <= 5.3e-127)))
		tmp = z + x;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.25e-21], N[Not[LessEqual[x, 5.3e-127]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2500000000000001e-21 or 5.3000000000000003e-127 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.5%

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

      1. +-commutative 76.5%

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

   5. Simplified 76.5%

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

   if -9.2500000000000001e-21 < x < 5.3000000000000003e-127

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 99.8%

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

   7. Taylor expanded in y around 0 52.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.25 \cdot 10^{-21} \lor \neg \left(x \leq 5.3 \cdot 10^{-127}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.4% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5400000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.4e-20) x (if (<= x 5400000.0) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.4e-20) {
		tmp = x;
	} else if (x <= 5400000.0) {
		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 <= (-8.4d-20)) then
        tmp = x
    else if (x <= 5400000.0d0) 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 <= -8.4e-20) {
		tmp = x;
	} else if (x <= 5400000.0) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -8.4e-20:
		tmp = x
	elif x <= 5400000.0:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.4e-20)
		tmp = x;
	elseif (x <= 5400000.0)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -8.4e-20)
		tmp = x;
	elseif (x <= 5400000.0)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.4e-20], x, If[LessEqual[x, 5400000.0], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.3999999999999996e-20 or 5.4e6 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 69.8%

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

   if -8.3999999999999996e-20 < x < 5.4e6

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 96.0%

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

   7. Taylor expanded in y around 0 51.4%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5400000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3300000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.8e-20) x (if (<= x 3300000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.8e-20) {
		tmp = x;
	} else if (x <= 3300000.0) {
		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 <= (-7.8d-20)) then
        tmp = x
    else if (x <= 3300000.0d0) 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 <= -7.8e-20) {
		tmp = x;
	} else if (x <= 3300000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.8e-20:
		tmp = x
	elif x <= 3300000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.8e-20)
		tmp = x;
	elseif (x <= 3300000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -7.8e-20)
		tmp = x;
	elseif (x <= 3300000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.8e-20], x, If[LessEqual[x, 3300000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.80000000000000014e-20 or 3.3e6 < x

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 69.8%

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

   if -7.80000000000000014e-20 < x < 3.3e6

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around 0 96.0%

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

   7. Taylor expanded in y around 0 45.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3300000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.5% 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. Add Preprocessing

3. Taylor expanded in x around inf 39.6%

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

4. Final simplification 39.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))))