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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

Alternatives: 9

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + 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. associate-+l+ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

   1. fma-undefine 99.9%

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

6. Applied egg-rr 99.9%

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

Alternative 2: 95.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -480 \lor \neg \left(z \leq 9.5 \cdot 10^{-24}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -480.0) (not (<= z 9.5e-24)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -480.0) || !(z <= 9.5e-24)) {
		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 <= (-480.0d0)) .or. (.not. (z <= 9.5d-24))) 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 <= -480.0) || !(z <= 9.5e-24)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -480.0) or not (z <= 9.5e-24):
		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 <= -480.0) || !(z <= 9.5e-24))
		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 <= -480.0) || ~((z <= 9.5e-24)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -480.0], N[Not[LessEqual[z, 9.5e-24]], $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 < -480 or 9.50000000000000029e-24 < z

   1. Initial program 99.9%

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

      1. associate-+l+ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 99.9%

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

   if -480 < z < 9.50000000000000029e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.6%

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

      1. +-commutative 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -480 \lor \neg \left(z \leq 9.5 \cdot 10^{-24}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -300000000 \lor \neg \left(z \leq 1.55 \cdot 10^{+36}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -300000000.0) (not (<= z 1.55e+36)))
   (* z (cos y))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -300000000.0) || !(z <= 1.55e+36)) {
		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 <= (-300000000.0d0)) .or. (.not. (z <= 1.55d+36))) 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 <= -300000000.0) || !(z <= 1.55e+36)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -300000000.0) or not (z <= 1.55e+36):
		tmp = z * math.cos(y)
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -300000000.0) || !(z <= 1.55e+36))
		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 <= -300000000.0) || ~((z <= 1.55e+36)))
		tmp = z * cos(y);
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -300000000.0], N[Not[LessEqual[z, 1.55e+36]], $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 < -3e8 or 1.55e36 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 81.0%

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

   if -3e8 < z < 1.55e36

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.3%

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

      1. +-commutative 92.3%

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

   5. Simplified 92.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -300000000 \lor \neg \left(z \leq 1.55 \cdot 10^{+36}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-13} \lor \neg \left(x \leq 2.1 \cdot 10^{-27}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-13) (not (<= x 2.1e-27))) (+ x z) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-13) || !(x <= 2.1e-27)) {
		tmp = x + z;
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-5.8d-13)) .or. (.not. (x <= 2.1d-27))) then
        tmp = x + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-13) || !(x <= 2.1e-27)) {
		tmp = x + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-13) or not (x <= 2.1e-27):
		tmp = x + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-13) || !(x <= 2.1e-27))
		tmp = Float64(x + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.8e-13) || ~((x <= 2.1e-27)))
		tmp = x + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-13], N[Not[LessEqual[x, 2.1e-27]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999995e-13 or 2.10000000000000015e-27 < 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 88.8%

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

      1. +-commutative 88.8%

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

   5. Simplified 88.8%

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

   if -5.7999999999999995e-13 < x < 2.10000000000000015e-27

   1. Initial program 99.9%

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

   3. Taylor expanded in z around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. distribute-rgt-neg-in 99.8%

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

      3. distribute-lft-out 99.8%

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

      4. mul-1-neg 99.8%

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

      5. remove-double-neg 99.8%

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

      6. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around inf 65.8%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-13} \lor \neg \left(x \leq 2.1 \cdot 10^{-27}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.7% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -57000000000 \lor \neg \left(y \leq 3.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -57000000000.0) (not (<= y 3.1e+51))) (+ x z) (+ x (+ z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -57000000000.0) || !(y <= 3.1e+51)) {
		tmp = x + z;
	} else {
		tmp = x + (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 <= (-57000000000.0d0)) .or. (.not. (y <= 3.1d+51))) then
        tmp = x + z
    else
        tmp = x + (z + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -57000000000.0) || !(y <= 3.1e+51)) {
		tmp = x + z;
	} else {
		tmp = x + (z + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -57000000000.0) or not (y <= 3.1e+51):
		tmp = x + z
	else:
		tmp = x + (z + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -57000000000.0) || !(y <= 3.1e+51))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -57000000000.0) || ~((y <= 3.1e+51)))
		tmp = x + z;
	else
		tmp = x + (z + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -57000000000.0], N[Not[LessEqual[y, 3.1e+51]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7e10 or 3.10000000000000011e51 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 47.1%

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

      1. +-commutative 47.1%

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

   5. Simplified 47.1%

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

   if -5.7e10 < y < 3.10000000000000011e51

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.5%

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

      1. +-commutative 93.5%

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

   5. Simplified 93.5%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -57000000000 \lor \neg \left(y \leq 3.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-163} \lor \neg \left(x \leq 2.3 \cdot 10^{-96}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e-163) (not (<= x 2.3e-96))) (+ x z) (+ z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-163) || !(x <= 2.3e-96)) {
		tmp = x + z;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4d-163)) .or. (.not. (x <= 2.3d-96))) then
        tmp = x + z
    else
        tmp = z + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e-163) || !(x <= 2.3e-96)) {
		tmp = x + z;
	} else {
		tmp = z + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e-163) or not (x <= 2.3e-96):
		tmp = x + z
	else:
		tmp = z + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e-163) || !(x <= 2.3e-96))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e-163) || ~((x <= 2.3e-96)))
		tmp = x + z;
	else
		tmp = z + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e-163], N[Not[LessEqual[x, 2.3e-96]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999969e-163 or 2.3e-96 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 76.6%

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

      1. +-commutative 76.6%

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

   5. Simplified 76.6%

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

   if -3.99999999999999969e-163 < x < 2.3e-96

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.6%

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

      2. pow3 98.6%

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

   4. Applied egg-rr 98.6%

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

   5. Taylor expanded in x around 0 98.0%

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   6. Step-by-step derivation

      1. +-commutative 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in y around 0 55.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-163} \lor \neg \left(x \leq 2.3 \cdot 10^{-96}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.4% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1150000000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.65e+50) x (if (<= x 1150000000.0) (+ z y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e+50) {
		tmp = x;
	} else if (x <= 1150000000.0) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.65d+50)) then
        tmp = x
    else if (x <= 1150000000.0d0) then
        tmp = z + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e+50) {
		tmp = x;
	} else if (x <= 1150000000.0) {
		tmp = z + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.65e+50:
		tmp = x
	elif x <= 1150000000.0:
		tmp = z + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.65e+50)
		tmp = x;
	elseif (x <= 1150000000.0)
		tmp = Float64(z + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.65e+50)
		tmp = x;
	elseif (x <= 1150000000.0)
		tmp = z + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.65e+50], x, If[LessEqual[x, 1150000000.0], N[(z + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e50 or 1.15e9 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.7%

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

   if -1.65e50 < x < 1.15e9

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.5%

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

      2. pow3 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   6. Step-by-step derivation

      1. +-commutative 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in y around 0 49.0%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1150000000:\\ \;\;\;\;z + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 175000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.65e+48) x (if (<= x 175000000000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e+48) {
		tmp = x;
	} else if (x <= 175000000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.65d+48)) then
        tmp = x
    else if (x <= 175000000000.0d0) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e+48) {
		tmp = x;
	} else if (x <= 175000000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.65e+48:
		tmp = x
	elif x <= 175000000000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.65e+48)
		tmp = x;
	elseif (x <= 175000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.65e+48)
		tmp = x;
	elseif (x <= 175000000000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.65e+48], x, If[LessEqual[x, 175000000000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000011e48 or 1.75e11 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 78.7%

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

   if -1.65000000000000011e48 < x < 1.75e11

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.5%

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

      2. pow3 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{\sin y + z \cdot \cos y} \]
   6. Step-by-step derivation

      1. +-commutative 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in y around 0 41.9%

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

Alternative 9: 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 41.0%

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

Reproduce

herbie shell --seed 2024085 
(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))))