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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 12

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

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

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]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-10} \lor \neg \left(x \leq 1.35 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -9.2e-10) (not (<= x 1.35e-6)))
     (- (+ 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 <= -9.2e-10) || !(x <= 1.35e-6)) {
		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 <= (-9.2d-10)) .or. (.not. (x <= 1.35d-6))) 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 <= -9.2e-10) || !(x <= 1.35e-6)) {
		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 <= -9.2e-10) or not (x <= 1.35e-6):
		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 <= -9.2e-10) || !(x <= 1.35e-6))
		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 <= -9.2e-10) || ~((x <= 1.35e-6)))
		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, -9.2e-10], N[Not[LessEqual[x, 1.35e-6]], $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 < -9.20000000000000028e-10 or 1.34999999999999999e-6 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. +-commutative 97.9%

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

   4. Simplified 97.9%

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

   if -9.20000000000000028e-10 < x < 1.34999999999999999e-6

   1. Initial program 99.9%

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

   2. 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 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-10} \lor \neg \left(x \leq 1.35 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]

Alternative 3: 91.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x + 1\right) - z \cdot \sin y\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-90} \lor \neg \left(z \leq 7.2 \cdot 10^{-148}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ x 1.0) (* z (sin y)))))
   (if (<= z -2.4e-12)
     t_0
     (if (<= z -2.8e-49)
       (cos y)
       (if (or (<= z -1.22e-90) (not (<= z 7.2e-148)))
         t_0
         (- (+ x (cos y)) (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * sin(y));
	double tmp;
	if (z <= -2.4e-12) {
		tmp = t_0;
	} else if (z <= -2.8e-49) {
		tmp = cos(y);
	} else if ((z <= -1.22e-90) || !(z <= 7.2e-148)) {
		tmp = t_0;
	} else {
		tmp = (x + cos(y)) - (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 = (x + 1.0d0) - (z * sin(y))
    if (z <= (-2.4d-12)) then
        tmp = t_0
    else if (z <= (-2.8d-49)) then
        tmp = cos(y)
    else if ((z <= (-1.22d-90)) .or. (.not. (z <= 7.2d-148))) then
        tmp = t_0
    else
        tmp = (x + cos(y)) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x + 1.0) - (z * Math.sin(y));
	double tmp;
	if (z <= -2.4e-12) {
		tmp = t_0;
	} else if (z <= -2.8e-49) {
		tmp = Math.cos(y);
	} else if ((z <= -1.22e-90) || !(z <= 7.2e-148)) {
		tmp = t_0;
	} else {
		tmp = (x + Math.cos(y)) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x + 1.0) - (z * math.sin(y))
	tmp = 0
	if z <= -2.4e-12:
		tmp = t_0
	elif z <= -2.8e-49:
		tmp = math.cos(y)
	elif (z <= -1.22e-90) or not (z <= 7.2e-148):
		tmp = t_0
	else:
		tmp = (x + math.cos(y)) - (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x + 1.0) - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -2.4e-12)
		tmp = t_0;
	elseif (z <= -2.8e-49)
		tmp = cos(y);
	elseif ((z <= -1.22e-90) || !(z <= 7.2e-148))
		tmp = t_0;
	else
		tmp = Float64(Float64(x + cos(y)) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x + 1.0) - (z * sin(y));
	tmp = 0.0;
	if (z <= -2.4e-12)
		tmp = t_0;
	elseif (z <= -2.8e-49)
		tmp = cos(y);
	elseif ((z <= -1.22e-90) || ~((z <= 7.2e-148)))
		tmp = t_0;
	else
		tmp = (x + cos(y)) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e-12], t$95$0, If[LessEqual[z, -2.8e-49], N[Cos[y], $MachinePrecision], If[Or[LessEqual[z, -1.22e-90], N[Not[LessEqual[z, 7.2e-148]], $MachinePrecision]], t$95$0, N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999987e-12 or -2.79999999999999997e-49 < z < -1.2199999999999999e-90 or 7.1999999999999997e-148 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 95.2%

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

      1. +-commutative 95.2%

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

   4. Simplified 95.2%

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

   if -2.39999999999999987e-12 < z < -2.79999999999999997e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   if -1.2199999999999999e-90 < z < 7.1999999999999997e-148

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-49}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-90} \lor \neg \left(z \leq 7.2 \cdot 10^{-148}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \]

Alternative 4: 71.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-72}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 35000000000000:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0)
   x
   (if (<= x 1.5e-72)
     (cos y)
     (if (<= x 35000000000000.0) (* (sin y) (- z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 1.5e-72) {
		tmp = cos(y);
	} else if (x <= 35000000000000.0) {
		tmp = sin(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 <= (-1.0d0)) then
        tmp = x
    else if (x <= 1.5d-72) then
        tmp = cos(y)
    else if (x <= 35000000000000.0d0) then
        tmp = sin(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 <= -1.0) {
		tmp = x;
	} else if (x <= 1.5e-72) {
		tmp = Math.cos(y);
	} else if (x <= 35000000000000.0) {
		tmp = Math.sin(y) * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x
	elif x <= 1.5e-72:
		tmp = math.cos(y)
	elif x <= 35000000000000.0:
		tmp = math.sin(y) * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 1.5e-72)
		tmp = cos(y);
	elseif (x <= 35000000000000.0)
		tmp = Float64(sin(y) * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 1.5e-72)
		tmp = cos(y);
	elseif (x <= 35000000000000.0)
		tmp = sin(y) * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], x, If[LessEqual[x, 1.5e-72], N[Cos[y], $MachinePrecision], If[LessEqual[x, 35000000000000.0], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 3.5e13 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.1%

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

   3. Taylor expanded in x around inf 89.4%

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

   if -1 < x < 1.5e-72

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.5%

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

   3. Taylor expanded in z around 0 71.4%

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

   if 1.5e-72 < x < 3.5e13

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 63.5%

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

   3. Taylor expanded in x around 0 60.3%

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

      1. associate-*r* 60.3%

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

      2. neg-mul-1 60.3%

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

   5. Simplified 60.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-72}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 35000000000000:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 86.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0028 \lor \neg \left(y \leq 10^{+35}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0028) (not (<= y 1e+35)))
   (- x (* z (sin y)))
   (- (+ 1.0 (+ x (* -0.5 (* y y)))) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0028) || !(y <= 1e+35)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (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 <= (-0.0028d0)) .or. (.not. (y <= 1d+35))) then
        tmp = x - (z * sin(y))
    else
        tmp = (1.0d0 + (x + ((-0.5d0) * (y * y)))) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0028) || !(y <= 1e+35)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0028) or not (y <= 1e+35):
		tmp = x - (z * math.sin(y))
	else:
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0028) || !(y <= 1e+35))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(Float64(1.0 + Float64(x + Float64(-0.5 * Float64(y * y)))) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0028) || ~((y <= 1e+35)))
		tmp = x - (z * sin(y));
	else
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0028], N[Not[LessEqual[y, 1e+35]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00279999999999999997 or 9.9999999999999997e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 71.2%

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

   if -0.00279999999999999997 < y < 9.9999999999999997e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.1%

      \[\leadsto \color{blue}{\left(1 + \left(x + -0.5 \cdot {y}^{2}\right)\right)} - z \cdot \sin y \]
   3. Step-by-step derivation

      1. unpow2 98.1%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in y around 0 97.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0028 \lor \neg \left(y \leq 10^{+35}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - y \cdot z\\ \end{array} \]

Alternative 6: 88.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) - z \cdot \sin y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x 1.0) (* z (sin y))))

C

double code(double x, double y, double z) {
	return (x + 1.0) - (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 + 1.0d0) - (z * sin(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x + 1.0) - (z * Math.sin(y));
}

Python

def code(x, y, z):
	return (x + 1.0) - (z * math.sin(y))

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + 1.0), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0 87.1%

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

   1. +-commutative 87.1%

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

4. Simplified 87.1%

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

5. Final simplification 87.1%

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

Alternative 7: 72.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.0) x (if (<= x 0.92) (cos y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 0.92) {
		tmp = cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = x
    else if (x <= 0.92d0) then
        tmp = cos(y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 0.92) {
		tmp = Math.cos(y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x
	elif x <= 0.92:
		tmp = math.cos(y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 0.92)
		tmp = cos(y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 0.92)
		tmp = cos(y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], x, If[LessEqual[x, 0.92], N[Cos[y], $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.92000000000000004 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.7%

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

   3. Taylor expanded in x around inf 88.4%

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

   if -1 < x < 0.92000000000000004

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.3%

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

   3. Taylor expanded in z around 0 67.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.92:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 69.4% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.75e+41)
   x
   (if (<= y 1e+35) (- (+ 1.0 (+ x (* -0.5 (* y y)))) (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.75e+41) {
		tmp = x;
	} else if (y <= 1e+35) {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (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 (y <= (-2.75d+41)) then
        tmp = x
    else if (y <= 1d+35) then
        tmp = (1.0d0 + (x + ((-0.5d0) * (y * y)))) - (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 (y <= -2.75e+41) {
		tmp = x;
	} else if (y <= 1e+35) {
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.75e+41:
		tmp = x
	elif y <= 1e+35:
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.75e+41)
		tmp = x;
	elseif (y <= 1e+35)
		tmp = Float64(Float64(1.0 + Float64(x + Float64(-0.5 * Float64(y * y)))) - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.75e+41)
		tmp = x;
	elseif (y <= 1e+35)
		tmp = (1.0 + (x + (-0.5 * (y * y)))) - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.75e+41], x, If[LessEqual[y, 1e+35], N[(N[(1.0 + N[(x + N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7500000000000002e41 or 9.9999999999999997e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 69.7%

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

   3. Taylor expanded in x around inf 41.7%

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

   if -2.7500000000000002e41 < y < 9.9999999999999997e34

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 97.5%

      \[\leadsto \color{blue}{\left(1 + \left(x + -0.5 \cdot {y}^{2}\right)\right)} - z \cdot \sin y \]
   3. Step-by-step derivation

      1. unpow2 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in y around 0 96.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+41}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;\left(1 + \left(x + -0.5 \cdot \left(y \cdot y\right)\right)\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 69.3% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+76) x (if (<= y 8.5e-6) (- (+ x 1.0) (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+76) {
		tmp = x;
	} else if (y <= 8.5e-6) {
		tmp = (x + 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 (y <= (-6.5d+76)) then
        tmp = x
    else if (y <= 8.5d-6) then
        tmp = (x + 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 (y <= -6.5e+76) {
		tmp = x;
	} else if (y <= 8.5e-6) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+76:
		tmp = x
	elif y <= 8.5e-6:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+76)
		tmp = x;
	elseif (y <= 8.5e-6)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+76)
		tmp = x;
	elseif (y <= 8.5e-6)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+76], x, If[LessEqual[y, 8.5e-6], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000005e76 or 8.4999999999999999e-6 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 68.8%

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

   3. Taylor expanded in x around inf 42.8%

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

   if -6.5000000000000005e76 < y < 8.4999999999999999e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

   4. Simplified 99.1%

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

   5. Taylor expanded in y around 0 97.2%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-6}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 67.3% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -16:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 35000000000000:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -16.0) x (if (<= x 35000000000000.0) (- 1.0 (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -16.0) {
		tmp = x;
	} else if (x <= 35000000000000.0) {
		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 <= (-16.0d0)) then
        tmp = x
    else if (x <= 35000000000000.0d0) 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 <= -16.0) {
		tmp = x;
	} else if (x <= 35000000000000.0) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -16.0:
		tmp = x
	elif x <= 35000000000000.0:
		tmp = 1.0 - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -16.0)
		tmp = x;
	elseif (x <= 35000000000000.0)
		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 <= -16.0)
		tmp = x;
	elseif (x <= 35000000000000.0)
		tmp = 1.0 - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -16.0], x, If[LessEqual[x, 35000000000000.0], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -16 or 3.5e13 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 98.1%

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

   3. Taylor expanded in x around inf 89.4%

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

   if -16 < x < 3.5e13

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 96.6%

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

   3. Taylor expanded in y around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. *-commutative 51.5%

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

   5. Simplified 51.5%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -16:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 35000000000000:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 61.9% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.98:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -0.98) x (if (<= x 1.2) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.98) {
		tmp = x;
	} else if (x <= 1.2) {
		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 <= (-0.98d0)) then
        tmp = x
    else if (x <= 1.2d0) 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 <= -0.98) {
		tmp = x;
	} else if (x <= 1.2) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.98:
		tmp = x
	elif x <= 1.2:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.98)
		tmp = x;
	elseif (x <= 1.2)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.98)
		tmp = x;
	elseif (x <= 1.2)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.98], x, If[LessEqual[x, 1.2], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.97999999999999998 or 1.19999999999999996 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 97.7%

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

   3. Taylor expanded in x around inf 88.4%

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

   if -0.97999999999999998 < x < 1.19999999999999996

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 97.3%

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

   3. Taylor expanded in y around 0 41.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.98:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 21.4% 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 100.0%

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

2. Taylor expanded in x around 0 51.1%

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

3. Taylor expanded in y around 0 20.6%

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

4. Final simplification 20.6%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023293 
(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))))