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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

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, 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 98.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+32} \lor \neg \left(z \leq 2.8 \cdot 10^{-23}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 + \sin y \cdot \frac{1}{x}\right) + \frac{z}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.42e+32) (not (<= z 2.8e-23)))
   (+ x (* z (cos y)))
   (* x (+ (+ 1.0 (* (sin y) (/ 1.0 x))) (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.42e+32) || !(z <= 2.8e-23)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = x * ((1.0 + (sin(y) * (1.0 / x))) + (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 <= (-1.42d+32)) .or. (.not. (z <= 2.8d-23))) then
        tmp = x + (z * cos(y))
    else
        tmp = x * ((1.0d0 + (sin(y) * (1.0d0 / x))) + (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.42e+32) || !(z <= 2.8e-23)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x * ((1.0 + (Math.sin(y) * (1.0 / x))) + (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.42e+32) or not (z <= 2.8e-23):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x * ((1.0 + (math.sin(y) * (1.0 / x))) + (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.42e+32) || !(z <= 2.8e-23))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x * Float64(Float64(1.0 + Float64(sin(y) * Float64(1.0 / x))) + Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.42e+32) || ~((z <= 2.8e-23)))
		tmp = x + (z * cos(y));
	else
		tmp = x * ((1.0 + (sin(y) * (1.0 / x))) + (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.42e+32], N[Not[LessEqual[z, 2.8e-23]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 + N[(N[Sin[y], $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.41999999999999992e32 or 2.7999999999999997e-23 < 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 99.5%

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

   if -1.41999999999999992e32 < z < 2.7999999999999997e-23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in y around 0 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.42 \cdot 10^{+32} \lor \neg \left(z \leq 2.8 \cdot 10^{-23}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 + \sin y \cdot \frac{1}{x}\right) + \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-44} \lor \neg \left(z \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e+107)
   (* z (cos y))
   (if (or (<= z -2.15e-44) (not (<= z 3.4e-66))) (+ x z) (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e+107) {
		tmp = z * cos(y);
	} else if ((z <= -2.15e-44) || !(z <= 3.4e-66)) {
		tmp = x + z;
	} 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 <= (-2.3d+107)) then
        tmp = z * cos(y)
    else if ((z <= (-2.15d-44)) .or. (.not. (z <= 3.4d-66))) then
        tmp = x + z
    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 <= -2.3e+107) {
		tmp = z * Math.cos(y);
	} else if ((z <= -2.15e-44) || !(z <= 3.4e-66)) {
		tmp = x + z;
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.3e+107:
		tmp = z * math.cos(y)
	elif (z <= -2.15e-44) or not (z <= 3.4e-66):
		tmp = x + z
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.3e+107)
		tmp = Float64(z * cos(y));
	elseif ((z <= -2.15e-44) || !(z <= 3.4e-66))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.3e+107)
		tmp = z * cos(y);
	elseif ((z <= -2.15e-44) || ~((z <= 3.4e-66)))
		tmp = x + z;
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.3e+107], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.15e-44], N[Not[LessEqual[z, 3.4e-66]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e107

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 74.2%

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

   if -2.3e107 < z < -2.15000000000000007e-44 or 3.39999999999999997e-66 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.5%

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

      1. +-commutative 83.5%

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

   5. Simplified 83.5%

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

   if -2.15000000000000007e-44 < z < 3.39999999999999997e-66

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-44} \lor \neg \left(z \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-44} \lor \neg \left(z \leq 7 \cdot 10^{-57}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e-44) (not (<= z 7e-57)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e-44) || !(z <= 7e-57)) {
		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 <= (-1.1d-44)) .or. (.not. (z <= 7d-57))) 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 <= -1.1e-44) || !(z <= 7e-57)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e-44) or not (z <= 7e-57):
		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 <= -1.1e-44) || !(z <= 7e-57))
		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 <= -1.1e-44) || ~((z <= 7e-57)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e-44], N[Not[LessEqual[z, 7e-57]], $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 < -1.10000000000000006e-44 or 6.99999999999999983e-57 < 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 98.3%

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

   if -1.10000000000000006e-44 < z < 6.99999999999999983e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-44} \lor \neg \left(z \leq 7 \cdot 10^{-57}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.4% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+19} \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+19) (not (<= y 0.195)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+19) || !(y <= 0.195)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	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 <= (-1.1d+19)) .or. (.not. (y <= 0.195d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+19) || !(y <= 0.195)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+19) or not (y <= 0.195):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+19) || !(y <= 0.195))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.1e+19) || ~((y <= 0.195)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+19], N[Not[LessEqual[y, 0.195]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e19 or 0.19500000000000001 < 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 48.7%

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

      1. +-commutative 48.7%

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

   5. Simplified 48.7%

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

   if -1.1e19 < y < 0.19500000000000001

   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%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+19} \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9000000 \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9000000.0) (not (<= y 0.195)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9000000.0) || !(y <= 0.195)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	}
	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 <= (-9000000.0d0)) .or. (.not. (y <= 0.195d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * (y * (-0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9000000.0) || !(y <= 0.195)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9000000.0) or not (y <= 0.195):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9000000.0) || !(y <= 0.195))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(y * -0.16666666666666666))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9000000.0) || ~((y <= 0.195)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * (y * -0.16666666666666666)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9000000.0], N[Not[LessEqual[y, 0.195]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e6 or 0.19500000000000001 < 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 49.5%

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

      1. +-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -9e6 < y < 0.19500000000000001

   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%

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

   4. Taylor expanded in z around 0 99.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9000000 \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.3% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+63} \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.6e+63) (not (<= y 0.195))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+63) || !(y <= 0.195)) {
		tmp = x + z;
	} else {
		tmp = z + (x + 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 <= (-1.6d+63)) .or. (.not. (y <= 0.195d0))) then
        tmp = x + z
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+63) || !(y <= 0.195)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.6e+63) or not (y <= 0.195):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.6e+63) || !(y <= 0.195))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.6e+63) || ~((y <= 0.195)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.6e+63], N[Not[LessEqual[y, 0.195]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000006e63 or 0.19500000000000001 < 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 47.3%

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

      1. +-commutative 47.3%

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

   5. Simplified 47.3%

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

   if -1.60000000000000006e63 < y < 0.19500000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.8%

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

      1. +-commutative 95.8%

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

      2. +-commutative 95.8%

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

      3. associate-+l+ 95.8%

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

   5. Simplified 95.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+63} \lor \neg \left(y \leq 0.195\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.8% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-192} \lor \neg \left(z \leq 5.2 \cdot 10^{-89}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e-192) (not (<= z 5.2e-89))) (+ x z) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-192) || !(z <= 5.2e-89)) {
		tmp = x + z;
	} else {
		tmp = x + 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 <= (-8.5d-192)) .or. (.not. (z <= 5.2d-89))) then
        tmp = x + z
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e-192) || !(z <= 5.2e-89)) {
		tmp = x + z;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e-192) or not (z <= 5.2e-89):
		tmp = x + z
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e-192) || !(z <= 5.2e-89))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e-192) || ~((z <= 5.2e-89)))
		tmp = x + z;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e-192], N[Not[LessEqual[z, 5.2e-89]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999985e-192 or 5.1999999999999997e-89 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. +-commutative 74.3%

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

   5. Simplified 74.3%

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

   if -8.49999999999999985e-192 < z < 5.1999999999999997e-89

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.4%

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

      1. +-commutative 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in y around 0 66.7%

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

      1. +-commutative 66.7%

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

   8. Simplified 66.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-192} \lor \neg \left(z \leq 5.2 \cdot 10^{-89}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.4% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-18}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e+14) x (if (<= x 7.5e-18) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e+14) {
		tmp = x;
	} else if (x <= 7.5e-18) {
		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 <= (-1.2d+14)) then
        tmp = x
    else if (x <= 7.5d-18) 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 <= -1.2e+14) {
		tmp = x;
	} else if (x <= 7.5e-18) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e+14:
		tmp = x
	elif x <= 7.5e-18:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e+14)
		tmp = x;
	elseif (x <= 7.5e-18)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.2e+14)
		tmp = x;
	elseif (x <= 7.5e-18)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e+14], x, If[LessEqual[x, 7.5e-18], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e14 or 7.50000000000000015e-18 < x

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. add-cube-cbrt 99.8%

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

      4. associate-*l* 99.8%

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

      5. fma-define 99.8%

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

      6. pow2 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 84.2%

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

   if -1.2e14 < x < 7.50000000000000015e-18

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. associate-+r+ 82.5%

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

      2. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in y around 0 31.7%

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

   7. Taylor expanded in x around 0 37.2%

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

Alternative 10: 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 100.0%

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

   1. +-commutative 100.0%

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

   2. *-commutative 100.0%

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

   3. add-cube-cbrt 99.7%

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

   4. associate-*l* 99.7%

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

   5. fma-define 99.7%

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

   6. pow2 99.7%

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

4. Applied egg-rr 99.7%

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

5. Taylor expanded in x around inf 49.4%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(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))))