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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + sin(y)) + (z * cos(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (z * cos(y)) + (x + sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 99.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0032 \lor \neg \left(z \leq 6.6 \cdot 10^{-6}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.0032) (not (<= z 6.6e-6)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0032) || !(z <= 6.6e-6)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.0032d0)) .or. (.not. (z <= 6.6d-6))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.0032) || !(z <= 6.6e-6)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.0032) or not (z <= 6.6e-6):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.0032) || !(z <= 6.6e-6))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.0032) || ~((z <= 6.6e-6)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.0032], N[Not[LessEqual[z, 6.6e-6]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00320000000000000015 or 6.60000000000000034e-6 < 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 99.2%

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

   if -0.00320000000000000015 < z < 6.60000000000000034e-6

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0032 \lor \neg \left(z \leq 6.6 \cdot 10^{-6}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-110} \lor \neg \left(z \leq 2.05 \cdot 10^{-38}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-110) (not (<= z 2.05e-38)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-110) || !(z <= 2.05e-38)) {
		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 <= (-2.4d-110)) .or. (.not. (z <= 2.05d-38))) 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 <= -2.4e-110) || !(z <= 2.05e-38)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-110) or not (z <= 2.05e-38):
		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 <= -2.4e-110) || !(z <= 2.05e-38))
		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 <= -2.4e-110) || ~((z <= 2.05e-38)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e-110], N[Not[LessEqual[z, 2.05e-38]], $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 < -2.40000000000000006e-110 or 2.0499999999999999e-38 < 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 95.7%

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

   if -2.40000000000000006e-110 < z < 2.0499999999999999e-38

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-110} \lor \neg \left(z \leq 2.05 \cdot 10^{-38}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+48} \lor \neg \left(z \leq 1.7 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e+48) (not (<= z 1.7e+15))) (* z (cos y)) (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+48) || !(z <= 1.7e+15)) {
		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 <= (-2.15d+48)) .or. (.not. (z <= 1.7d+15))) 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 <= -2.15e+48) || !(z <= 1.7e+15)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.15e+48) or not (z <= 1.7e+15):
		tmp = z * math.cos(y)
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e+48) || !(z <= 1.7e+15))
		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 <= -2.15e+48) || ~((z <= 1.7e+15)))
		tmp = z * cos(y);
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e+48], N[Not[LessEqual[z, 1.7e+15]], $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 < -2.14999999999999989e48 or 1.7e15 < 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 80.7%

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

   if -2.14999999999999989e48 < z < 1.7e15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 91.5%

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

      1. +-commutative 91.5%

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

   5. Simplified 91.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+48} \lor \neg \left(z \leq 1.7 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 10^{-24}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.05e+128) (* z (cos y)) (if (<= y 1e-24) (+ y (+ x z)) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+128) {
		tmp = z * cos(y);
	} else if (y <= 1e-24) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.05d+128)) then
        tmp = z * cos(y)
    else if (y <= 1d-24) then
        tmp = y + (x + z)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.05e+128) {
		tmp = z * Math.cos(y);
	} else if (y <= 1e-24) {
		tmp = y + (x + z);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.05e+128:
		tmp = z * math.cos(y)
	elif y <= 1e-24:
		tmp = y + (x + z)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.05e+128)
		tmp = Float64(z * cos(y));
	elseif (y <= 1e-24)
		tmp = Float64(y + Float64(x + z));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.05e+128)
		tmp = z * cos(y);
	elseif (y <= 1e-24)
		tmp = y + (x + z);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.05e+128], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-24], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e128

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 51.9%

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

   if -1.05e128 < y < 9.99999999999999924e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-+l+ 93.4%

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

   5. Simplified 93.4%

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

   if 9.99999999999999924e-25 < 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%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 10^{-24}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.2% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+37} \lor \neg \left(y \leq 5 \cdot 10^{+17}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+37) (not (<= y 5e+17)))
   (+ 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 <= -4e+37) || !(y <= 5e+17)) {
		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 <= (-4d+37)) .or. (.not. (y <= 5d+17))) 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 <= -4e+37) || !(y <= 5e+17)) {
		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 <= -4e+37) or not (y <= 5e+17):
		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 <= -4e+37) || !(y <= 5e+17))
		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 <= -4e+37) || ~((y <= 5e+17)))
		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, -4e+37], N[Not[LessEqual[y, 5e+17]], $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 < -3.99999999999999982e37 or 5e17 < 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 40.9%

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

      1. +-commutative 40.9%

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

   5. Simplified 40.9%

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

   if -3.99999999999999982e37 < y < 5e17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+37} \lor \neg \left(y \leq 5 \cdot 10^{+17}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+26} \lor \neg \left(y \leq 1.5 \cdot 10^{+21}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.4e+26) (not (<= y 1.5e+21)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (* y -0.16666666666666666))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.4e+26) || !(y <= 1.5e+21)) {
		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 <= (-4.4d+26)) .or. (.not. (y <= 1.5d+21))) 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 <= -4.4e+26) || !(y <= 1.5e+21)) {
		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 <= -4.4e+26) or not (y <= 1.5e+21):
		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 <= -4.4e+26) || !(y <= 1.5e+21))
		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 <= -4.4e+26) || ~((y <= 1.5e+21)))
		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, -4.4e+26], N[Not[LessEqual[y, 1.5e+21]], $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 < -4.40000000000000014e26 or 1.5e21 < 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 40.5%

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

      1. +-commutative 40.5%

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

   5. Simplified 40.5%

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

   if -4.40000000000000014e26 < y < 1.5e21

   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%

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

   4. Taylor expanded in z around 0 97.9%

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

      1. *-commutative 97.9%

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

   6. Simplified 97.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+26} \lor \neg \left(y \leq 1.5 \cdot 10^{+21}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+26} \lor \neg \left(y \leq 10^{-24}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e+26) (not (<= y 1e-24))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+26) || !(y <= 1e-24)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.2d+26)) .or. (.not. (y <= 1d-24))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e+26) || !(y <= 1e-24)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e+26) or not (y <= 1e-24):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e+26) || !(y <= 1e-24))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e+26) || ~((y <= 1e-24)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e+26], N[Not[LessEqual[y, 1e-24]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000029e26 or 9.99999999999999924e-25 < 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 41.9%

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

      1. +-commutative 41.9%

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

   5. Simplified 41.9%

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

   if -3.20000000000000029e26 < y < 9.99999999999999924e-25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+26} \lor \neg \left(y \leq 10^{-24}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.029:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.2e-9) x (if (<= x 0.029) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.2e-9) {
		tmp = x;
	} else if (x <= 0.029) {
		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-9)) then
        tmp = x
    else if (x <= 0.029d0) 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-9) {
		tmp = x;
	} else if (x <= 0.029) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.2e-9:
		tmp = x
	elif x <= 0.029:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.2e-9)
		tmp = x;
	elseif (x <= 0.029)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.2e-9)
		tmp = x;
	elseif (x <= 0.029)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.2e-9], x, If[LessEqual[x, 0.029], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e-9 or 0.0290000000000000015 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. +-commutative 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in z around 0 73.3%

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

   if -1.2e-9 < x < 0.0290000000000000015

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.6%

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

   4. Taylor expanded in z around inf 40.5%

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

Alternative 10: 44.6% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-116}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.32e-79) x (if (<= x 5.2e-116) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.32e-79) {
		tmp = x;
	} else if (x <= 5.2e-116) {
		tmp = 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 <= (-1.32d-79)) then
        tmp = x
    else if (x <= 5.2d-116) then
        tmp = 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 <= -1.32e-79) {
		tmp = x;
	} else if (x <= 5.2e-116) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.32e-79:
		tmp = x
	elif x <= 5.2e-116:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.32e-79)
		tmp = x;
	elseif (x <= 5.2e-116)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.32e-79)
		tmp = x;
	elseif (x <= 5.2e-116)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.32e-79], x, If[LessEqual[x, 5.2e-116], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.32e-79 or 5.2000000000000001e-116 < 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 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%

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

   6. Taylor expanded in z around 0 57.4%

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

   if -1.32e-79 < x < 5.2000000000000001e-116

   1. Initial program 100.0%

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

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

      3. associate-+l+ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 57.6%

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

   7. Taylor expanded in y around inf 16.9%

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

Alternative 11: 66.2% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 64.6%

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

   1. +-commutative 64.6%

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

5. Simplified 64.6%

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

6. Final simplification 64.6%

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

Alternative 12: 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 y around 0 64.6%

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

   1. +-commutative 64.6%

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

5. Simplified 64.6%

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

6. Taylor expanded in z around 0 40.3%

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

Reproduce

herbie shell --seed 2024135 
(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))))