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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 14

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

Alternative 2: 95.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-27} \lor \neg \left(x \leq 0.036\right):\\ \;\;\;\;x \cdot \left(1 + \cos y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-27) (not (<= x 0.036)))
   (* x (+ 1.0 (* (cos y) (/ z x))))
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-27) || !(x <= 0.036)) {
		tmp = x * (1.0 + (cos(y) * (z / x)));
	} else {
		tmp = sin(y) + (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 <= (-2.1d-27)) .or. (.not. (x <= 0.036d0))) then
        tmp = x * (1.0d0 + (cos(y) * (z / x)))
    else
        tmp = sin(y) + (z * cos(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-27) || !(x <= 0.036)) {
		tmp = x * (1.0 + (Math.cos(y) * (z / x)));
	} else {
		tmp = Math.sin(y) + (z * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-27) or not (x <= 0.036):
		tmp = x * (1.0 + (math.cos(y) * (z / x)))
	else:
		tmp = math.sin(y) + (z * math.cos(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-27) || !(x <= 0.036))
		tmp = Float64(x * Float64(1.0 + Float64(cos(y) * Float64(z / x))));
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-27) || ~((x <= 0.036)))
		tmp = x * (1.0 + (cos(y) * (z / x)));
	else
		tmp = sin(y) + (z * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-27], N[Not[LessEqual[x, 0.036]], $MachinePrecision]], N[(x * N[(1.0 + N[(N[Cos[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.10000000000000015e-27 or 0.0359999999999999973 < 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 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-/l* 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 77.8%

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

   7. Taylor expanded in z around inf 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

   if -2.10000000000000015e-27 < x < 0.0359999999999999973

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 93.5%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-27} \lor \neg \left(x \leq 0.036\right):\\ \;\;\;\;x \cdot \left(1 + \cos y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \cos y + \left(x + y\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+26} \lor \neg \left(z \leq 5.5 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(1 + \cos y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+202)
   (+ (* z (cos y)) (+ x y))
   (if (or (<= z -6e+26) (not (<= z 5.5e-32)))
     (* x (+ 1.0 (* (cos y) (/ z x))))
     (+ (+ x (sin y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+202) {
		tmp = (z * cos(y)) + (x + y);
	} else if ((z <= -6e+26) || !(z <= 5.5e-32)) {
		tmp = x * (1.0 + (cos(y) * (z / x)));
	} else {
		tmp = (x + sin(y)) + 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 (z <= (-1.8d+202)) then
        tmp = (z * cos(y)) + (x + y)
    else if ((z <= (-6d+26)) .or. (.not. (z <= 5.5d-32))) then
        tmp = x * (1.0d0 + (cos(y) * (z / x)))
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+202) {
		tmp = (z * Math.cos(y)) + (x + y);
	} else if ((z <= -6e+26) || !(z <= 5.5e-32)) {
		tmp = x * (1.0 + (Math.cos(y) * (z / x)));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+202:
		tmp = (z * math.cos(y)) + (x + y)
	elif (z <= -6e+26) or not (z <= 5.5e-32):
		tmp = x * (1.0 + (math.cos(y) * (z / x)))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+202)
		tmp = Float64(Float64(z * cos(y)) + Float64(x + y));
	elseif ((z <= -6e+26) || !(z <= 5.5e-32))
		tmp = Float64(x * Float64(1.0 + Float64(cos(y) * Float64(z / x))));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e+202)
		tmp = (z * cos(y)) + (x + y);
	elseif ((z <= -6e+26) || ~((z <= 5.5e-32)))
		tmp = x * (1.0 + (cos(y) * (z / x)));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+202], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6e+26], N[Not[LessEqual[z, 5.5e-32]], $MachinePrecision]], N[(x * N[(1.0 + N[(N[Cos[y], $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000004e202

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 96.1%

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

      1. +-commutative 96.1%

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

   5. Simplified 96.1%

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

   if -1.80000000000000004e202 < z < -5.99999999999999994e26 or 5.50000000000000024e-32 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 85.5%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in y around 0 58.2%

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

   7. Taylor expanded in z around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-/l* 85.5%

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

   9. Simplified 85.5%

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

   if -5.99999999999999994e26 < z < 5.50000000000000024e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.6%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+202}:\\ \;\;\;\;z \cdot \cos y + \left(x + y\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+26} \lor \neg \left(z \leq 5.5 \cdot 10^{-32}\right):\\ \;\;\;\;x \cdot \left(1 + \cos y \cdot \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \cos y + \left(x + y\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+26} \lor \neg \left(z \leq 6.6 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot \frac{\cos y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+205)
   (+ (* z (cos y)) (+ x y))
   (if (or (<= z -6e+26) (not (<= z 6.6e+18)))
     (* x (+ 1.0 (* z (/ (cos y) x))))
     (+ (+ x (sin y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+205) {
		tmp = (z * cos(y)) + (x + y);
	} else if ((z <= -6e+26) || !(z <= 6.6e+18)) {
		tmp = x * (1.0 + (z * (cos(y) / x)));
	} else {
		tmp = (x + sin(y)) + 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 (z <= (-5d+205)) then
        tmp = (z * cos(y)) + (x + y)
    else if ((z <= (-6d+26)) .or. (.not. (z <= 6.6d+18))) then
        tmp = x * (1.0d0 + (z * (cos(y) / x)))
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+205) {
		tmp = (z * Math.cos(y)) + (x + y);
	} else if ((z <= -6e+26) || !(z <= 6.6e+18)) {
		tmp = x * (1.0 + (z * (Math.cos(y) / x)));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+205:
		tmp = (z * math.cos(y)) + (x + y)
	elif (z <= -6e+26) or not (z <= 6.6e+18):
		tmp = x * (1.0 + (z * (math.cos(y) / x)))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+205)
		tmp = Float64(Float64(z * cos(y)) + Float64(x + y));
	elseif ((z <= -6e+26) || !(z <= 6.6e+18))
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(cos(y) / x))));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+205)
		tmp = (z * cos(y)) + (x + y);
	elseif ((z <= -6e+26) || ~((z <= 6.6e+18)))
		tmp = x * (1.0 + (z * (cos(y) / x)));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+205], N[(N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(x + y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6e+26], N[Not[LessEqual[z, 6.6e+18]], $MachinePrecision]], N[(x * N[(1.0 + N[(z * N[(N[Cos[y], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000002e205

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 95.9%

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

      1. +-commutative 95.9%

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

   5. Simplified 95.9%

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

   if -5.0000000000000002e205 < z < -5.99999999999999994e26 or 6.6e18 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 84.4%

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

      1. associate-/l* 84.2%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in y around 0 57.8%

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

   7. Taylor expanded in z around inf 84.4%

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

      1. associate-/l* 84.2%

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

   9. Simplified 84.2%

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

   if -5.99999999999999994e26 < z < 6.6e18

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+205}:\\ \;\;\;\;z \cdot \cos y + \left(x + y\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+26} \lor \neg \left(z \leq 6.6 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot \frac{\cos y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+209}:\\ \;\;\;\;t\_0 + \left(x + y\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+27} \lor \neg \left(z \leq 2.2 \cdot 10^{+111}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.25e+209)
     (+ t_0 (+ x y))
     (if (or (<= z -2.8e+27) (not (<= z 2.2e+111))) t_0 (+ (+ x (sin y)) z)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.25e+209) {
		tmp = t_0 + (x + y);
	} else if ((z <= -2.8e+27) || !(z <= 2.2e+111)) {
		tmp = t_0;
	} else {
		tmp = (x + sin(y)) + 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.25d+209)) then
        tmp = t_0 + (x + y)
    else if ((z <= (-2.8d+27)) .or. (.not. (z <= 2.2d+111))) then
        tmp = t_0
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.25e+209) {
		tmp = t_0 + (x + y);
	} else if ((z <= -2.8e+27) || !(z <= 2.2e+111)) {
		tmp = t_0;
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.25e+209:
		tmp = t_0 + (x + y)
	elif (z <= -2.8e+27) or not (z <= 2.2e+111):
		tmp = t_0
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.25e+209)
		tmp = Float64(t_0 + Float64(x + y));
	elseif ((z <= -2.8e+27) || !(z <= 2.2e+111))
		tmp = t_0;
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.25e+209)
		tmp = t_0 + (x + y);
	elseif ((z <= -2.8e+27) || ~((z <= 2.2e+111)))
		tmp = t_0;
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+209], N[(t$95$0 + N[(x + y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.8e+27], N[Not[LessEqual[z, 2.2e+111]], $MachinePrecision]], t$95$0, N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999991e209

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 95.2%

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

      1. +-commutative 95.2%

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

   5. Simplified 95.2%

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

   if -1.24999999999999991e209 < z < -2.7999999999999999e27 or 2.19999999999999999e111 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 79.6%

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

   if -2.7999999999999999e27 < z < 2.19999999999999999e111

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+209}:\\ \;\;\;\;z \cdot \cos y + \left(x + y\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+27} \lor \neg \left(z \leq 2.2 \cdot 10^{+111}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-204}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.9e+27)
     t_0
     (if (<= z 8.6e-204) (+ z (+ x y)) (if (<= z 1.15e+111) (+ x z) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.9e+27) {
		tmp = t_0;
	} else if (z <= 8.6e-204) {
		tmp = z + (x + y);
	} else if (z <= 1.15e+111) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-1.9d+27)) then
        tmp = t_0
    else if (z <= 8.6d-204) then
        tmp = z + (x + y)
    else if (z <= 1.15d+111) then
        tmp = x + z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1.9e+27) {
		tmp = t_0;
	} else if (z <= 8.6e-204) {
		tmp = z + (x + y);
	} else if (z <= 1.15e+111) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1.9e+27:
		tmp = t_0
	elif z <= 8.6e-204:
		tmp = z + (x + y)
	elif z <= 1.15e+111:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1.9e+27)
		tmp = t_0;
	elseif (z <= 8.6e-204)
		tmp = Float64(z + Float64(x + y));
	elseif (z <= 1.15e+111)
		tmp = Float64(x + z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1.9e+27)
		tmp = t_0;
	elseif (z <= 8.6e-204)
		tmp = z + (x + y);
	elseif (z <= 1.15e+111)
		tmp = x + z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+27], t$95$0, If[LessEqual[z, 8.6e-204], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+111], N[(x + z), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000011e27 or 1.15000000000000001e111 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -1.90000000000000011e27 < z < 8.6000000000000005e-204

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. +-commutative 68.0%

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

      3. associate-+l+ 68.0%

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

   5. Simplified 68.0%

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

   if 8.6000000000000005e-204 < z < 1.15000000000000001e111

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.6%

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

      1. +-commutative 71.6%

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

   5. Simplified 71.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+27}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-204}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+111}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+27} \lor \neg \left(z \leq 1.55 \cdot 10^{+111}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.05e+27) (not (<= z 1.55e+111)))
   (* z (cos y))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.05e+27) || !(z <= 1.55e+111)) {
		tmp = z * cos(y);
	} else {
		tmp = (x + sin(y)) + 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 ((z <= (-3.05d+27)) .or. (.not. (z <= 1.55d+111))) then
        tmp = z * cos(y)
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.05e+27) || !(z <= 1.55e+111)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.05e+27) or not (z <= 1.55e+111):
		tmp = z * math.cos(y)
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.05e+27) || !(z <= 1.55e+111))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.05e+27) || ~((z <= 1.55e+111)))
		tmp = z * cos(y);
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.05e+27], N[Not[LessEqual[z, 1.55e+111]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0499999999999999e27 or 1.55e111 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 78.2%

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

   if -3.0499999999999999e27 < z < 1.55e111

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+27} \lor \neg \left(z \leq 1.55 \cdot 10^{+111}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+22} \lor \neg \left(z \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e+22) (not (<= z 4.3e+15))) (* z (cos y)) (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e+22) || !(z <= 4.3e+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 <= (-1.3d+22)) .or. (.not. (z <= 4.3d+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 <= -1.3e+22) || !(z <= 4.3e+15)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e+22) or not (z <= 4.3e+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 <= -1.3e+22) || !(z <= 4.3e+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 <= -1.3e+22) || ~((z <= 4.3e+15)))
		tmp = z * cos(y);
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e+22], N[Not[LessEqual[z, 4.3e+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 < -1.3e22 or 4.3e15 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 75.9%

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

   if -1.3e22 < z < 4.3e15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.3%

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

      1. +-commutative 89.3%

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

   5. Simplified 89.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+22} \lor \neg \left(z \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+17} \lor \neg \left(y \leq 7600\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.85e+17) (not (<= y 7600.0)))
   (+ x z)
   (+ (+ x z) (* y (+ 1.0 (* -0.5 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.85e+17) || !(y <= 7600.0)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * 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 <= (-2.85d+17)) .or. (.not. (y <= 7600.0d0))) then
        tmp = x + z
    else
        tmp = (x + z) + (y * (1.0d0 + ((-0.5d0) * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.85e+17) || !(y <= 7600.0)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.85e+17) or not (y <= 7600.0):
		tmp = x + z
	else:
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.85e+17) || !(y <= 7600.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.85e+17) || ~((y <= 7600.0)))
		tmp = x + z;
	else
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.85e+17], N[Not[LessEqual[y, 7600.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.85e17 or 7600 < 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 42.8%

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

      1. +-commutative 42.8%

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

   5. Simplified 42.8%

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

   if -2.85e17 < y < 7600

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.9%

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

      1. associate-+r+ 97.9%

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

      2. +-commutative 97.9%

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

      3. *-commutative 97.9%

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

   5. Simplified 97.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+17} \lor \neg \left(y \leq 7600\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.1% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+41} \lor \neg \left(y \leq 9.5 \cdot 10^{+25}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+41) (not (<= y 9.5e+25))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+41) || !(y <= 9.5e+25)) {
		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 <= (-5.5d+41)) .or. (.not. (y <= 9.5d+25))) 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 <= -5.5e+41) || !(y <= 9.5e+25)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+41) or not (y <= 9.5e+25):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+41) || !(y <= 9.5e+25))
		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 <= -5.5e+41) || ~((y <= 9.5e+25)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+41], N[Not[LessEqual[y, 9.5e+25]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000003e41 or 9.5000000000000005e25 < 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 42.3%

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

      1. +-commutative 42.3%

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

   5. Simplified 42.3%

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

   if -5.5000000000000003e41 < y < 9.5000000000000005e25

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.3%

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

      1. +-commutative 94.3%

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

      2. +-commutative 94.3%

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

      3. associate-+l+ 94.3%

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

   5. Simplified 94.3%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+41} \lor \neg \left(y \leq 9.5 \cdot 10^{+25}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+111}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -9.6e+30) x (if (<= y 1.4e+111) (+ x y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.6e+30) {
		tmp = x;
	} else if (y <= 1.4e+111) {
		tmp = x + 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 (y <= (-9.6d+30)) then
        tmp = x
    else if (y <= 1.4d+111) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.6e+30) {
		tmp = x;
	} else if (y <= 1.4e+111) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -9.6e+30:
		tmp = x
	elif y <= 1.4e+111:
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -9.6e+30)
		tmp = x;
	elseif (y <= 1.4e+111)
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -9.6e+30)
		tmp = x;
	elseif (y <= 1.4e+111)
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -9.6e+30], x, If[LessEqual[y, 1.4e+111], N[(x + y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5999999999999997e30 or 1.4e111 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 38.8%

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

   if -9.5999999999999997e30 < y < 1.4e111

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 55.2%

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

      1. +-commutative 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in y around 0 50.4%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+111}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.4% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-222}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e-38) x (if (<= x 1.6e-222) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e-38) {
		tmp = x;
	} else if (x <= 1.6e-222) {
		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 <= (-2.5d-38)) then
        tmp = x
    else if (x <= 1.6d-222) 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 <= -2.5e-38) {
		tmp = x;
	} else if (x <= 1.6e-222) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e-38:
		tmp = x
	elif x <= 1.6e-222:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e-38)
		tmp = x;
	elseif (x <= 1.6e-222)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e-38)
		tmp = x;
	elseif (x <= 1.6e-222)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e-38], x, If[LessEqual[x, 1.6e-222], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000017e-38 or 1.6e-222 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 55.3%

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

   if -2.50000000000000017e-38 < x < 1.6e-222

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 73.6%

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

      1. associate-/l* 73.6%

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

   5. Simplified 73.6%

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

   6. Taylor expanded in y around 0 43.6%

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

   7. Taylor expanded in y around inf 16.8%

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

Alternative 13: 67.1% 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 64.3%

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

   1. +-commutative 64.3%

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

5. Simplified 64.3%

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

6. Final simplification 64.3%

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

Alternative 14: 43.1% 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 40.8%

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

Reproduce

herbie shell --seed 2024111 
(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))))