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

Percentage Accurate: 99.9% → 99.9%

Time: 8.6s

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. Taylor expanded in x around 0 99.9%

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

   1. associate-+r- 99.9%

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

4. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 90.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;x \leq 130000:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e-11)
   (+ (cos y) x)
   (if (<= x 130000.0) (- (cos y) (* z (sin y))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-11) {
		tmp = cos(y) + x;
	} else if (x <= 130000.0) {
		tmp = cos(y) - (z * sin(y));
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-1.05d-11)) then
        tmp = cos(y) + x
    else if (x <= 130000.0d0) then
        tmp = cos(y) - (z * sin(y))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e-11) {
		tmp = Math.cos(y) + x;
	} else if (x <= 130000.0) {
		tmp = Math.cos(y) - (z * Math.sin(y));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e-11:
		tmp = math.cos(y) + x
	elif x <= 130000.0:
		tmp = math.cos(y) - (z * math.sin(y))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e-11)
		tmp = Float64(cos(y) + x);
	elseif (x <= 130000.0)
		tmp = Float64(cos(y) - Float64(z * sin(y)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e-11)
		tmp = cos(y) + x;
	elseif (x <= 130000.0)
		tmp = cos(y) - (z * sin(y));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e-11], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 130000.0], N[(N[Cos[y], $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0499999999999999e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.9%

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

   if -1.0499999999999999e-11 < x < 1.3e5

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.3%

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

   if 1.3e5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

   4. Simplified 86.7%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-11}:\\ \;\;\;\;\cos y + x\\ \mathbf{elif}\;x \leq 130000:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 3: 80.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+106}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.46e+106)
   (+ 1.0 (- x (* y z)))
   (if (<= z 3.7e+101) (+ (cos y) x) (* (sin y) (- z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.46e+106) {
		tmp = 1.0 + (x - (y * z));
	} else if (z <= 3.7e+101) {
		tmp = cos(y) + x;
	} 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 (z <= (-1.46d+106)) then
        tmp = 1.0d0 + (x - (y * z))
    else if (z <= 3.7d+101) then
        tmp = cos(y) + x
    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 (z <= -1.46e+106) {
		tmp = 1.0 + (x - (y * z));
	} else if (z <= 3.7e+101) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = Math.sin(y) * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.46e+106:
		tmp = 1.0 + (x - (y * z))
	elif z <= 3.7e+101:
		tmp = math.cos(y) + x
	else:
		tmp = math.sin(y) * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.46e+106)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	elseif (z <= 3.7e+101)
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(sin(y) * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.46e+106)
		tmp = 1.0 + (x - (y * z));
	elseif (z <= 3.7e+101)
		tmp = cos(y) + x;
	else
		tmp = sin(y) * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.46e+106], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+101], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.46000000000000005e106

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. associate-+r- 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. +-commutative 67.7%

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

      2. mul-1-neg 67.7%

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

      3. unsub-neg 67.7%

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

   7. Simplified 67.7%

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

   if -1.46000000000000005e106 < z < 3.6999999999999997e101

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 93.4%

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

   if 3.6999999999999997e101 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 79.9%

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

      1. associate-*r* 79.9%

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

      2. neg-mul-1 79.9%

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

      3. *-commutative 79.9%

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

   4. Simplified 79.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+106}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+101}:\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 69.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4500000000:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+29)
   (+ x 1.0)
   (if (<= y 4500000000.0)
     (+ 1.0 (- x (* y z)))
     (if (<= y 9e+69) (cos y) (+ x 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+29) {
		tmp = x + 1.0;
	} else if (y <= 4500000000.0) {
		tmp = 1.0 + (x - (y * z));
	} else if (y <= 9e+69) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (y <= (-2.5d+29)) then
        tmp = x + 1.0d0
    else if (y <= 4500000000.0d0) then
        tmp = 1.0d0 + (x - (y * z))
    else if (y <= 9d+69) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+29) {
		tmp = x + 1.0;
	} else if (y <= 4500000000.0) {
		tmp = 1.0 + (x - (y * z));
	} else if (y <= 9e+69) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e+29:
		tmp = x + 1.0
	elif y <= 4500000000.0:
		tmp = 1.0 + (x - (y * z))
	elif y <= 9e+69:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+29)
		tmp = Float64(x + 1.0);
	elseif (y <= 4500000000.0)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	elseif (y <= 9e+69)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.5e+29)
		tmp = x + 1.0;
	elseif (y <= 4500000000.0)
		tmp = 1.0 + (x - (y * z));
	elseif (y <= 9e+69)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e+29], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 4500000000.0], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+69], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5e29 or 8.9999999999999999e69 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 43.8%

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

      1. +-commutative 43.8%

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

   4. Simplified 43.8%

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

   if -2.5e29 < y < 4.5e9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. associate-+r- 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 95.1%

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

      1. +-commutative 95.1%

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

      2. mul-1-neg 95.1%

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

      3. unsub-neg 95.1%

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

   7. Simplified 95.1%

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

   if 4.5e9 < y < 8.9999999999999999e69

   1. Initial program 99.7%

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

      1. add-log-exp 62.7%

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

      2. associate--l+ 62.7%

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

   3. Applied egg-rr 62.7%

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

   4. Taylor expanded in x around 0 59.5%

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

   5. Taylor expanded in z around 0 55.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+29}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4500000000:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+69}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 5: 80.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+18} \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.7e+18) (not (<= y 0.0065)))
   (+ (cos y) x)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.7e+18) || !(y <= 0.0065)) {
		tmp = cos(y) + x;
	} else {
		tmp = 1.0 + (x - (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 <= (-7.7d+18)) .or. (.not. (y <= 0.0065d0))) then
        tmp = cos(y) + x
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.7e+18) || !(y <= 0.0065)) {
		tmp = Math.cos(y) + x;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.7e+18) or not (y <= 0.0065):
		tmp = math.cos(y) + x
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.7e+18) || !(y <= 0.0065))
		tmp = Float64(cos(y) + x);
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.7e+18) || ~((y <= 0.0065)))
		tmp = cos(y) + x;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.7e+18], N[Not[LessEqual[y, 0.0065]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] + x), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.7e18 or 0.0064999999999999997 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 61.0%

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

   if -7.7e18 < y < 0.0064999999999999997

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. associate-+r- 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.7 \cdot 10^{+18} \lor \neg \left(y \leq 0.0065\right):\\ \;\;\;\;\cos y + x\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 6: 69.5% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+29}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+59}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+29)
   (+ x 1.0)
   (if (<= y 1.36e+59) (+ 1.0 (- x (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+29) {
		tmp = x + 1.0;
	} else if (y <= 1.36e+59) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (y <= (-1.25d+29)) then
        tmp = x + 1.0d0
    else if (y <= 1.36d+59) then
        tmp = 1.0d0 + (x - (y * z))
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+29) {
		tmp = x + 1.0;
	} else if (y <= 1.36e+59) {
		tmp = 1.0 + (x - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+29:
		tmp = x + 1.0
	elif y <= 1.36e+59:
		tmp = 1.0 + (x - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+29)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.36e+59)
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+29)
		tmp = x + 1.0;
	elseif (y <= 1.36e+59)
		tmp = 1.0 + (x - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+29], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.36e+59], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e29 or 1.36e59 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 43.3%

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

      1. +-commutative 43.3%

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

   4. Simplified 43.3%

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

   if -1.25e29 < y < 1.36e59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

      1. associate-+r- 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 90.7%

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

      1. +-commutative 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

   7. Simplified 90.7%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+29}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+59}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 7: 66.2% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-29}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-33}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e-29)
   (+ x 1.0)
   (if (<= x 2.55e-33) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-29) {
		tmp = x + 1.0;
	} else if (x <= 2.55e-33) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if (x <= (-1.95d-29)) then
        tmp = x + 1.0d0
    else if (x <= 2.55d-33) then
        tmp = 1.0d0 - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e-29) {
		tmp = x + 1.0;
	} else if (x <= 2.55e-33) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e-29:
		tmp = x + 1.0
	elif x <= 2.55e-33:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e-29)
		tmp = Float64(x + 1.0);
	elseif (x <= 2.55e-33)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e-29)
		tmp = x + 1.0;
	elseif (x <= 2.55e-33)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e-29], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 2.55e-33], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9499999999999999e-29 or 2.55000000000000004e-33 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.6%

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

      1. +-commutative 80.6%

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

   4. Simplified 80.6%

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

   if -1.9499999999999999e-29 < x < 2.55000000000000004e-33

   1. Initial program 99.9%

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

      1. add-log-exp 64.9%

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

      2. associate--l+ 64.9%

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

   3. Applied egg-rr 64.9%

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

   4. Taylor expanded in x around 0 64.9%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. unsub-neg 62.7%

         \[\leadsto \color{blue}{1 - y \cdot z} \]

   7. Simplified 62.7%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-29}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-33}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 60.3% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 125000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e-10) x (if (<= x 125000.0) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e-10) {
		tmp = x;
	} else if (x <= 125000.0) {
		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 <= (-1.7d-10)) then
        tmp = x
    else if (x <= 125000.0d0) 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 <= -1.7e-10) {
		tmp = x;
	} else if (x <= 125000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.7e-10:
		tmp = x
	elif x <= 125000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e-10)
		tmp = x;
	elseif (x <= 125000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.7e-10)
		tmp = x;
	elseif (x <= 125000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e-10], x, If[LessEqual[x, 125000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000007e-10 or 125000 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 84.0%

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

   if -1.70000000000000007e-10 < x < 125000

   1. Initial program 99.9%

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

      1. add-log-exp 65.5%

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

      2. associate--l+ 65.5%

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

   3. Applied egg-rr 65.5%

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

   4. Taylor expanded in x around 0 64.7%

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

   5. Taylor expanded in y around 0 46.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 125000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 61.3% 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. Taylor expanded in y around 0 64.3%

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

   1. +-commutative 64.3%

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

4. Simplified 64.3%

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

5. Final simplification 64.3%

   \[\leadsto x + 1 \]

Alternative 10: 21.3% 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. Step-by-step derivation

   1. add-log-exp 38.7%

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

   2. associate--l+ 38.7%

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

3. Applied egg-rr 38.7%

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

4. Taylor expanded in x around 0 36.9%

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

5. Taylor expanded in y around 0 26.8%

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

6. Final simplification 26.8%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023174 
(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))))