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

Percentage Accurate: 99.9% → 99.9%

Time: 8.3s

Alternatives: 10

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 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 3: 69.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+194}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{+48}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+27}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+286} \lor \neg \left(y \leq 7.5 \cdot 10^{+304}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= y -1.9e+194)
     (+ z x)
     (if (<= y -1.18e+48)
       t_0
       (if (<= y 2e+27)
         (+ z (+ y x))
         (if (or (<= y 4.5e+286) (not (<= y 7.5e+304))) t_0 (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (y <= -1.9e+194) {
		tmp = z + x;
	} else if (y <= -1.18e+48) {
		tmp = t_0;
	} else if (y <= 2e+27) {
		tmp = z + (y + x);
	} else if ((y <= 4.5e+286) || !(y <= 7.5e+304)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (y <= (-1.9d+194)) then
        tmp = z + x
    else if (y <= (-1.18d+48)) then
        tmp = t_0
    else if (y <= 2d+27) then
        tmp = z + (y + x)
    else if ((y <= 4.5d+286) .or. (.not. (y <= 7.5d+304))) then
        tmp = t_0
    else
        tmp = z + x
    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 (y <= -1.9e+194) {
		tmp = z + x;
	} else if (y <= -1.18e+48) {
		tmp = t_0;
	} else if (y <= 2e+27) {
		tmp = z + (y + x);
	} else if ((y <= 4.5e+286) || !(y <= 7.5e+304)) {
		tmp = t_0;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if y <= -1.9e+194:
		tmp = z + x
	elif y <= -1.18e+48:
		tmp = t_0
	elif y <= 2e+27:
		tmp = z + (y + x)
	elif (y <= 4.5e+286) or not (y <= 7.5e+304):
		tmp = t_0
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (y <= -1.9e+194)
		tmp = Float64(z + x);
	elseif (y <= -1.18e+48)
		tmp = t_0;
	elseif (y <= 2e+27)
		tmp = Float64(z + Float64(y + x));
	elseif ((y <= 4.5e+286) || !(y <= 7.5e+304))
		tmp = t_0;
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (y <= -1.9e+194)
		tmp = z + x;
	elseif (y <= -1.18e+48)
		tmp = t_0;
	elseif (y <= 2e+27)
		tmp = z + (y + x);
	elseif ((y <= 4.5e+286) || ~((y <= 7.5e+304)))
		tmp = t_0;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+194], N[(z + x), $MachinePrecision], If[LessEqual[y, -1.18e+48], t$95$0, If[LessEqual[y, 2e+27], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 4.5e+286], N[Not[LessEqual[y, 7.5e+304]], $MachinePrecision]], t$95$0, N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8999999999999999e194 or 4.4999999999999998e286 < y < 7.49999999999999954e304

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 53.5%

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

      1. +-commutative 53.5%

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

   5. Simplified 53.5%

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

   if -1.8999999999999999e194 < y < -1.18000000000000007e48 or 2e27 < y < 4.4999999999999998e286 or 7.49999999999999954e304 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 51.6%

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

   if -1.18000000000000007e48 < y < 2e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.4%

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

      1. +-commutative 95.4%

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

      2. +-commutative 95.4%

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

      3. associate-+l+ 95.4%

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

   5. Simplified 95.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+194}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq -1.18 \cdot 10^{+48}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+27}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+286} \lor \neg \left(y \leq 7.5 \cdot 10^{+304}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+150}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+44}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -5000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+129}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.8e+150)
     t_0
     (if (<= z -2.1e+44)
       (+ z x)
       (if (<= z -5000000.0)
         t_0
         (if (<= z 1.5e-34)
           (+ x (sin y))
           (if (<= z 1.02e+129) (+ z x) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.8e+150) {
		tmp = t_0;
	} else if (z <= -2.1e+44) {
		tmp = z + x;
	} else if (z <= -5000000.0) {
		tmp = t_0;
	} else if (z <= 1.5e-34) {
		tmp = x + sin(y);
	} else if (z <= 1.02e+129) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.8d+150)) then
        tmp = t_0
    else if (z <= (-2.1d+44)) then
        tmp = z + x
    else if (z <= (-5000000.0d0)) then
        tmp = t_0
    else if (z <= 1.5d-34) then
        tmp = x + sin(y)
    else if (z <= 1.02d+129) then
        tmp = z + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.8e+150) {
		tmp = t_0;
	} else if (z <= -2.1e+44) {
		tmp = z + x;
	} else if (z <= -5000000.0) {
		tmp = t_0;
	} else if (z <= 1.5e-34) {
		tmp = x + Math.sin(y);
	} else if (z <= 1.02e+129) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.8e+150:
		tmp = t_0
	elif z <= -2.1e+44:
		tmp = z + x
	elif z <= -5000000.0:
		tmp = t_0
	elif z <= 1.5e-34:
		tmp = x + math.sin(y)
	elif z <= 1.02e+129:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.8e+150)
		tmp = t_0;
	elseif (z <= -2.1e+44)
		tmp = Float64(z + x);
	elseif (z <= -5000000.0)
		tmp = t_0;
	elseif (z <= 1.5e-34)
		tmp = Float64(x + sin(y));
	elseif (z <= 1.02e+129)
		tmp = Float64(z + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.8e+150)
		tmp = t_0;
	elseif (z <= -2.1e+44)
		tmp = z + x;
	elseif (z <= -5000000.0)
		tmp = t_0;
	elseif (z <= 1.5e-34)
		tmp = x + sin(y);
	elseif (z <= 1.02e+129)
		tmp = z + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+150], t$95$0, If[LessEqual[z, -2.1e+44], N[(z + x), $MachinePrecision], If[LessEqual[z, -5000000.0], t$95$0, If[LessEqual[z, 1.5e-34], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+129], N[(z + x), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.79999999999999993e150 or -2.09999999999999987e44 < z < -5e6 or 1.01999999999999996e129 < 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 84.0%

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

   if -1.79999999999999993e150 < z < -2.09999999999999987e44 or 1.5e-34 < z < 1.01999999999999996e129

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 82.5%

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

      1. +-commutative 82.5%

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

   5. Simplified 82.5%

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

   if -5e6 < z < 1.5e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.1%

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

      1. +-commutative 93.1%

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

   5. Simplified 93.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+44}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq -5000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-34}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+129}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-76} \lor \neg \left(z \leq 1.45 \cdot 10^{-34}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e-76) (not (<= z 1.45e-34)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-76) || !(z <= 1.45e-34)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x + sin(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.35d-76)) .or. (.not. (z <= 1.45d-34))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-76) || !(z <= 1.45e-34)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e-76) or not (z <= 1.45e-34):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e-76) || !(z <= 1.45e-34))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e-76) || ~((z <= 1.45e-34)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e-76], N[Not[LessEqual[z, 1.45e-34]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.35e-76 or 1.4500000000000001e-34 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.4%

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

      1. associate-+r+ 77.4%

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

      2. associate-/l* 77.3%

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

   5. Simplified 77.3%

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

      1. associate-+l+ 77.3%

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

      2. distribute-rgt-in 77.3%

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

      3. *-un-lft-identity 77.3%

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

      4. clear-num 77.3%

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

      5. un-div-inv 77.4%

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

   7. Applied egg-rr 77.4%

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

   8. Taylor expanded in z around inf 97.1%

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

   if -1.35e-76 < z < 1.4500000000000001e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.6%

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

      1. +-commutative 95.6%

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

   5. Simplified 95.6%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-76} \lor \neg \left(z \leq 1.45 \cdot 10^{-34}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \lor \neg \left(y \leq 1.2 \cdot 10^{+16}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.5) (not (<= y 1.2e+16)))
   (+ z x)
   (+ (+ z x) (* y (+ 1.0 (* -0.5 (* z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.5) || !(y <= 1.2e+16)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * (1.0 + (-0.5 * (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 ((y <= (-3.5d0)) .or. (.not. (y <= 1.2d+16))) then
        tmp = z + x
    else
        tmp = (z + x) + (y * (1.0d0 + ((-0.5d0) * (z * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.5) || !(y <= 1.2e+16)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.5) or not (y <= 1.2e+16):
		tmp = z + x
	else:
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.5) || !(y <= 1.2e+16))
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(z + x) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.5) || ~((y <= 1.2e+16)))
		tmp = z + x;
	else
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.5], N[Not[LessEqual[y, 1.2e+16]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5 or 1.2e16 < 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 35.6%

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

      1. +-commutative 35.6%

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

   5. Simplified 35.6%

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

   if -3.5 < y < 1.2e16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

      1. associate-+r+ 98.8%

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

      2. +-commutative 98.8%

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

      3. *-commutative 98.8%

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

   5. Simplified 98.8%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \lor \neg \left(y \leq 1.2 \cdot 10^{+16}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.4% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+32} \lor \neg \left(y \leq 5.8 \cdot 10^{+107}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e+32) (not (<= y 5.8e+107))) (+ z x) (+ z (+ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e+32) || !(y <= 5.8e+107)) {
		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 <= (-1.25d+32)) .or. (.not. (y <= 5.8d+107))) 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 <= -1.25e+32) || !(y <= 5.8e+107)) {
		tmp = z + x;
	} else {
		tmp = z + (y + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e+32) or not (y <= 5.8e+107):
		tmp = z + x
	else:
		tmp = z + (y + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e+32) || !(y <= 5.8e+107))
		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 <= -1.25e+32) || ~((y <= 5.8e+107)))
		tmp = z + x;
	else
		tmp = z + (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e+32], N[Not[LessEqual[y, 5.8e+107]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e32 or 5.79999999999999975e107 < 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 36.7%

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

      1. +-commutative 36.7%

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

   5. Simplified 36.7%

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

   if -1.2499999999999999e32 < y < 5.79999999999999975e107

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.0%

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

      1. +-commutative 91.0%

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

      2. +-commutative 91.0%

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

      3. associate-+l+ 91.0%

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

   5. Simplified 91.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+32} \lor \neg \left(y \leq 5.8 \cdot 10^{+107}\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z + \left(y + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.1% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -165:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+196}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -165.0) x (if (<= y 8.2e+196) (+ y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -165.0) {
		tmp = x;
	} else if (y <= 8.2e+196) {
		tmp = y + x;
	} 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 (y <= (-165.0d0)) then
        tmp = x
    else if (y <= 8.2d+196) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -165.0) {
		tmp = x;
	} else if (y <= 8.2e+196) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -165.0:
		tmp = x
	elif y <= 8.2e+196:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -165.0)
		tmp = x;
	elseif (y <= 8.2e+196)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -165.0)
		tmp = x;
	elseif (y <= 8.2e+196)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -165.0], x, If[LessEqual[y, 8.2e+196], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -165 or 8.1999999999999993e196 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 37.8%

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

   if -165 < y < 8.1999999999999993e196

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.6%

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

      1. associate-+r+ 88.6%

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

      2. associate-/l* 88.5%

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

   5. Simplified 88.5%

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

      1. associate-+l+ 88.5%

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

      2. distribute-rgt-in 88.5%

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

      3. *-un-lft-identity 88.5%

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

      4. clear-num 88.5%

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

      5. un-div-inv 88.6%

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

   7. Applied egg-rr 88.6%

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

   8. Taylor expanded in y around 0 80.2%

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

   9. Taylor expanded in y around inf 58.7%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -165:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+196}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 65.5%

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

   1. +-commutative 65.5%

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

5. Simplified 65.5%

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

6. Final simplification 65.5%

   \[\leadsto z + x \]
7. Add Preprocessing

Alternative 10: 42.3% 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 46.2%

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

4. Final simplification 46.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024066 
(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))))