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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 8

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. Final simplification 99.9%

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

Alternative 2: 84.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.25 \cdot 10^{-283} \lor \neg \left(x \leq 1.7 \cdot 10^{-140}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.25e-283) (not (<= x 1.7e-140)))
   (+ x (* z (cos y)))
   (+ (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.25e-283) || !(x <= 1.7e-140)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = 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 ((x <= (-4.25d-283)) .or. (.not. (x <= 1.7d-140))) then
        tmp = x + (z * cos(y))
    else
        tmp = sin(y) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.25e-283) || !(x <= 1.7e-140)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = Math.sin(y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.25e-283) or not (x <= 1.7e-140):
		tmp = x + (z * math.cos(y))
	else:
		tmp = math.sin(y) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.25e-283) || !(x <= 1.7e-140))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(sin(y) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.25e-283) || ~((x <= 1.7e-140)))
		tmp = x + (z * cos(y));
	else
		tmp = sin(y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.25e-283], N[Not[LessEqual[x, 1.7e-140]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.24999999999999998e-283 or 1.70000000000000004e-140 < 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 89.5%

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

   if -4.24999999999999998e-283 < x < 1.70000000000000004e-140

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in y around 0 84.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.25 \cdot 10^{-283} \lor \neg \left(x \leq 1.7 \cdot 10^{-140}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -150000 \lor \neg \left(z \leq 7 \cdot 10^{-22}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -150000.0) (not (<= z 7e-22)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -150000.0) || !(z <= 7e-22)) {
		tmp = x + (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 <= (-150000.0d0)) .or. (.not. (z <= 7d-22))) then
        tmp = x + (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 <= -150000.0) || !(z <= 7e-22)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -150000.0) or not (z <= 7e-22):
		tmp = x + (z * math.cos(y))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -150000.0) || !(z <= 7e-22))
		tmp = Float64(x + 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 <= -150000.0) || ~((z <= 7e-22)))
		tmp = x + (z * cos(y));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -150000.0], N[Not[LessEqual[z, 7e-22]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e5 or 7.00000000000000011e-22 < 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 99.6%

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

   if -1.5e5 < z < 7.00000000000000011e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150000 \lor \neg \left(z \leq 7 \cdot 10^{-22}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-30}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-281}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-171}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.5e-30)
   (+ x z)
   (if (<= x 1.5e-281) (+ z (+ x y)) (if (<= x 7.6e-171) (sin y) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-30) {
		tmp = x + z;
	} else if (x <= 1.5e-281) {
		tmp = z + (x + y);
	} else if (x <= 7.6e-171) {
		tmp = sin(y);
	} 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 (x <= (-5.5d-30)) then
        tmp = x + z
    else if (x <= 1.5d-281) then
        tmp = z + (x + y)
    else if (x <= 7.6d-171) then
        tmp = sin(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.5e-30) {
		tmp = x + z;
	} else if (x <= 1.5e-281) {
		tmp = z + (x + y);
	} else if (x <= 7.6e-171) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.5e-30:
		tmp = x + z
	elif x <= 1.5e-281:
		tmp = z + (x + y)
	elif x <= 7.6e-171:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.5e-30)
		tmp = Float64(x + z);
	elseif (x <= 1.5e-281)
		tmp = Float64(z + Float64(x + y));
	elseif (x <= 7.6e-171)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.5e-30)
		tmp = x + z;
	elseif (x <= 1.5e-281)
		tmp = z + (x + y);
	elseif (x <= 7.6e-171)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.5e-30], N[(x + z), $MachinePrecision], If[LessEqual[x, 1.5e-281], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e-171], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.49999999999999976e-30 or 7.60000000000000043e-171 < 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 91.6%

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

   4. Taylor expanded in y around 0 77.4%

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

   if -5.49999999999999976e-30 < x < 1.49999999999999987e-281

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 68.4%

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

   4. Taylor expanded in y around 0 56.4%

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

      1. +-commutative 56.4%

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

   6. Simplified 56.4%

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

   if 1.49999999999999987e-281 < x < 7.60000000000000043e-171

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in y around 0 86.4%

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

   5. Taylor expanded in z around 0 69.0%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-30}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-281}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-171}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-91} \lor \neg \left(x \leq 8.8 \cdot 10^{-30}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.95e-91) (not (<= x 8.8e-30))) (+ x z) (+ (sin y) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.95e-91) || !(x <= 8.8e-30)) {
		tmp = x + z;
	} else {
		tmp = 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 ((x <= (-1.95d-91)) .or. (.not. (x <= 8.8d-30))) then
        tmp = x + z
    else
        tmp = sin(y) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.95e-91) || !(x <= 8.8e-30)) {
		tmp = x + z;
	} else {
		tmp = Math.sin(y) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.95e-91) or not (x <= 8.8e-30):
		tmp = x + z
	else:
		tmp = math.sin(y) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.95e-91) || !(x <= 8.8e-30))
		tmp = Float64(x + z);
	else
		tmp = Float64(sin(y) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.95e-91) || ~((x <= 8.8e-30)))
		tmp = x + z;
	else
		tmp = sin(y) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.95e-91], N[Not[LessEqual[x, 8.8e-30]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.94999999999999997e-91 or 8.79999999999999933e-30 < 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 96.2%

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

   4. Taylor expanded in y around 0 85.0%

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

   if -1.94999999999999997e-91 < x < 8.79999999999999933e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 94.3%

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

   4. Taylor expanded in y around 0 67.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-91} \lor \neg \left(x \leq 8.8 \cdot 10^{-30}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.5% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+72} \lor \neg \left(y \leq 1.02 \cdot 10^{+34}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1e+72) (not (<= y 1.02e+34))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+72) || !(y <= 1.02e+34)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.1d+72)) .or. (.not. (y <= 1.02d+34))) then
        tmp = x + z
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1e+72) || !(y <= 1.02e+34)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1e+72) or not (y <= 1.02e+34):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1e+72) || !(y <= 1.02e+34))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.1e+72) || ~((y <= 1.02e+34)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1e+72], N[Not[LessEqual[y, 1.02e+34]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e72 or 1.02e34 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.0%

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

   4. Taylor expanded in y around 0 38.4%

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

   if -1.1e72 < y < 1.02e34

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.2%

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

   4. Taylor expanded in y around 0 88.4%

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

      1. +-commutative 88.4%

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

   6. Simplified 88.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+72} \lor \neg \left(y \leq 1.02 \cdot 10^{+34}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-177} \lor \neg \left(x \leq 4 \cdot 10^{-142}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.6e-177) (not (<= x 4e-142))) (+ x z) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.6e-177) || !(x <= 4e-142)) {
		tmp = x + z;
	} else {
		tmp = 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 ((x <= (-6.6d-177)) .or. (.not. (x <= 4d-142))) then
        tmp = x + z
    else
        tmp = y + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.6e-177) || !(x <= 4e-142)) {
		tmp = x + z;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.6e-177) or not (x <= 4e-142):
		tmp = x + z
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.6e-177) || !(x <= 4e-142))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.6e-177) || ~((x <= 4e-142)))
		tmp = x + z;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.6e-177], N[Not[LessEqual[x, 4e-142]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5999999999999999e-177 or 4.0000000000000002e-142 < 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 90.1%

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

   4. Taylor expanded in y around 0 74.5%

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

   if -6.5999999999999999e-177 < x < 4.0000000000000002e-142

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in y around 0 74.1%

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

   5. Taylor expanded in y around 0 51.2%

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

      1. +-commutative 51.2%

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

   7. Simplified 51.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-177} \lor \neg \left(x \leq 4 \cdot 10^{-142}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.8% 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 x around inf 81.7%

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

4. Taylor expanded in y around 0 63.6%

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

5. Final simplification 63.6%

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

Reproduce

herbie shell --seed 2024013 
(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))))