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

Percentage Accurate: 99.9% → 99.9%

Time: 9.3s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in z around 0 99.9%

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

   1. mul-1-neg 99.9%

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

   2. sub-neg 99.9%

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

   3. associate-+r- 99.9%

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

   4. +-commutative 99.9%

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

   5. associate-+r- 99.9%

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

5. Simplified 99.9%

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

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-13} \lor \neg \left(x \leq 1.35 \cdot 10^{-5}\right):\\ \;\;\;\;\left(x + 1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -2.8e-13) (not (<= x 1.35e-5)))
     (- (+ x 1.0) t_0)
     (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -2.8e-13) || !(x <= 1.35e-5)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = cos(y) - 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 * sin(y)
    if ((x <= (-2.8d-13)) .or. (.not. (x <= 1.35d-5))) then
        tmp = (x + 1.0d0) - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -2.8e-13) || !(x <= 1.35e-5)) {
		tmp = (x + 1.0) - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -2.8e-13) or not (x <= 1.35e-5):
		tmp = (x + 1.0) - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -2.8e-13) || !(x <= 1.35e-5))
		tmp = Float64(Float64(x + 1.0) - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -2.8e-13) || ~((x <= 1.35e-5)))
		tmp = (x + 1.0) - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -2.8e-13], N[Not[LessEqual[x, 1.35e-5]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000002e-13 or 1.3499999999999999e-5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.9%

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

   if -2.8000000000000002e-13 < x < 1.3499999999999999e-5

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-13} \lor \neg \left(x \leq 1.35 \cdot 10^{-5}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+26} \lor \neg \left(z \leq 2.5 \cdot 10^{-38}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e+26) (not (<= z 2.5e-38)))
   (- (+ x 1.0) (* z (sin y)))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+26) || !(z <= 2.5e-38)) {
		tmp = (x + 1.0) - (z * sin(y));
	} else {
		tmp = cos(y) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-7.5d+26)) .or. (.not. (z <= 2.5d-38))) then
        tmp = (x + 1.0d0) - (z * sin(y))
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+26) || !(z <= 2.5e-38)) {
		tmp = (x + 1.0) - (z * Math.sin(y));
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e+26) or not (z <= 2.5e-38):
		tmp = (x + 1.0) - (z * math.sin(y))
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e+26) || !(z <= 2.5e-38))
		tmp = Float64(Float64(x + 1.0) - Float64(z * sin(y)));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.5e+26) || ~((z <= 2.5e-38)))
		tmp = (x + 1.0) - (z * sin(y));
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e+26], N[Not[LessEqual[z, 2.5e-38]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999941e26 or 2.50000000000000017e-38 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

   if -7.49999999999999941e26 < z < 2.50000000000000017e-38

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.1%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+26} \lor \neg \left(z \leq 2.5 \cdot 10^{-38}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+169} \lor \neg \left(z \leq 4.75 \cdot 10^{+145}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e+169) (not (<= z 4.75e+145)))
   (* (sin y) (- z))
   (+ (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e+169) || !(z <= 4.75e+145)) {
		tmp = sin(y) * -z;
	} else {
		tmp = cos(y) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.4d+169)) .or. (.not. (z <= 4.75d+145))) then
        tmp = sin(y) * -z
    else
        tmp = cos(y) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e+169) || !(z <= 4.75e+145)) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = Math.cos(y) + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e+169) or not (z <= 4.75e+145):
		tmp = math.sin(y) * -z
	else:
		tmp = math.cos(y) + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e+169) || !(z <= 4.75e+145))
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = Float64(cos(y) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.4e+169) || ~((z <= 4.75e+145)))
		tmp = sin(y) * -z;
	else
		tmp = cos(y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e+169], N[Not[LessEqual[z, 4.75e+145]], $MachinePrecision]], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000028e169 or 4.74999999999999974e145 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. *-commutative 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

   5. Simplified 75.2%

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

   if -3.40000000000000028e169 < z < 4.74999999999999974e145

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 90.7%

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

      1. +-commutative 90.7%

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

   5. Simplified 90.7%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+169} \lor \neg \left(z \leq 4.75 \cdot 10^{+145}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;\cos y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.25 \lor \neg \left(y \leq 3.05 \cdot 10^{-33}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\right) - y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.25) (not (<= y 3.05e-33)))
   (+ (cos y) x)
   (+ 1.0 (+ x (- (* y (* z (* y (* y 0.16666666666666666)))) (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.25) || !(y <= 3.05e-33)) {
		tmp = cos(y) + x;
	} else {
		tmp = 1.0 + (x + ((y * (z * (y * (y * 0.16666666666666666)))) - (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 <= (-0.25d0)) .or. (.not. (y <= 3.05d-33))) then
        tmp = cos(y) + x
    else
        tmp = 1.0d0 + (x + ((y * (z * (y * (y * 0.16666666666666666d0)))) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.25) || !(y <= 3.05e-33)) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = 1.0 + (x + ((y * (z * (y * (y * 0.16666666666666666)))) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.25) or not (y <= 3.05e-33):
		tmp = math.cos(y) + x
	else:
		tmp = 1.0 + (x + ((y * (z * (y * (y * 0.16666666666666666)))) - (y * z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.25) || !(y <= 3.05e-33))
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(1.0 + Float64(x + Float64(Float64(y * Float64(z * Float64(y * Float64(y * 0.16666666666666666)))) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.25) || ~((y <= 3.05e-33)))
		tmp = cos(y) + x;
	else
		tmp = 1.0 + (x + ((y * (z * (y * (y * 0.16666666666666666)))) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.25], N[Not[LessEqual[y, 3.05e-33]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(1.0 + N[(x + N[(N[(y * N[(z * N[(y * N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.25 or 3.0500000000000001e-33 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. +-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -0.25 < y < 3.0500000000000001e-33

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

   6. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

   8. Applied egg-rr 100.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.25 \lor \neg \left(y \leq 3.05 \cdot 10^{-33}\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + \left(y \cdot \left(z \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right)\right)\right) - y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.1% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+80} \lor \neg \left(y \leq 1.15 \cdot 10^{+148}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+80) (not (<= y 1.15e+148)))
   (+ x 1.0)
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+80) || !(y <= 1.15e+148)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (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 <= (-4.5d+80)) .or. (.not. (y <= 1.15d+148))) then
        tmp = x + 1.0d0
    else
        tmp = x + (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+80) || !(y <= 1.15e+148)) {
		tmp = x + 1.0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+80) or not (y <= 1.15e+148):
		tmp = x + 1.0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e+80) || !(y <= 1.15e+148))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.5e+80) || ~((y <= 1.15e+148)))
		tmp = x + 1.0;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+80], N[Not[LessEqual[y, 1.15e+148]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000007e80 or 1.15e148 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 55.2%

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative 55.2%

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{x + 1} \]

   if -4.50000000000000007e80 < y < 1.15e148

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.8%

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

      1. associate-+r+ 79.8%

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

      2. +-commutative 79.8%

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

      3. associate-+l+ 79.8%

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

      4. mul-1-neg 79.8%

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

      5. unsub-neg 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+80} \lor \neg \left(y \leq 1.15 \cdot 10^{+148}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-13}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 430000000:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.8e-13) (+ x 1.0) (if (<= x 430000000.0) (- 1.0 (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.8e-13) {
		tmp = x + 1.0;
	} else if (x <= 430000000.0) {
		tmp = 1.0 - (y * 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 <= (-2.8d-13)) then
        tmp = x + 1.0d0
    else if (x <= 430000000.0d0) then
        tmp = 1.0d0 - (y * 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 <= -2.8e-13) {
		tmp = x + 1.0;
	} else if (x <= 430000000.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.8e-13:
		tmp = x + 1.0
	elif x <= 430000000.0:
		tmp = 1.0 - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.8e-13)
		tmp = Float64(x + 1.0);
	elseif (x <= 430000000.0)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.8e-13)
		tmp = x + 1.0;
	elseif (x <= 430000000.0)
		tmp = 1.0 - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.8e-13], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 430000000.0], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8000000000000002e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.3%

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative 91.3%

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 91.3%

      \[\leadsto \color{blue}{x + 1} \]

   if -2.8000000000000002e-13 < x < 4.3e8

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 43.7%

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

      1. +-commutative 43.7%

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

      2. fma-define 43.7%

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

      3. *-commutative 43.7%

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

   5. Simplified 43.7%

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

   6. Taylor expanded in z around inf 45.2%

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

      1. mul-1-neg 45.2%

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

      2. distribute-rgt-neg-out 45.2%

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

   8. Simplified 45.2%

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

   if 4.3e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 88.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-13}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 430000000:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.4% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.76:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 430000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.76) x (if (<= x 430000000.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.76) {
		tmp = x;
	} else if (x <= 430000000.0) {
		tmp = 1.0;
	} 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 <= (-0.76d0)) then
        tmp = x
    else if (x <= 430000000.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.76) {
		tmp = x;
	} else if (x <= 430000000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.76:
		tmp = x
	elif x <= 430000000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.76)
		tmp = x;
	elseif (x <= 430000000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.76)
		tmp = x;
	elseif (x <= 430000000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.76], x, If[LessEqual[x, 430000000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.76000000000000001 or 4.3e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 89.0%

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

   if -0.76000000000000001 < x < 4.3e8

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 34.3%

      \[\leadsto \color{blue}{1 + x} \]
   4. Step-by-step derivation

      1. +-commutative 34.3%

         \[\leadsto \color{blue}{x + 1} \]

   5. Simplified 34.3%

      \[\leadsto \color{blue}{x + 1} \]

   6. Taylor expanded in x around 0 33.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 61.4% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

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 + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 65.2%

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative 65.2%

      \[\leadsto \color{blue}{x + 1} \]

5. Simplified 65.2%

   \[\leadsto \color{blue}{x + 1} \]
6. Add Preprocessing

Alternative 10: 21.5% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 1.0)

C

double code(double x, double y, double z) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 1.0;
}

Python

def code(x, y, z):
	return 1.0

Julia

function code(x, y, z)
	return 1.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 65.2%

   \[\leadsto \color{blue}{1 + x} \]
4. Step-by-step derivation

   1. +-commutative 65.2%

      \[\leadsto \color{blue}{x + 1} \]

5. Simplified 65.2%

   \[\leadsto \color{blue}{x + 1} \]

6. Taylor expanded in x around 0 16.4%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))