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

Percentage Accurate: 99.9% → 99.9%

Time: 8.2s

Alternatives: 11

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. *-commutative 99.9%

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

   4. distribute-rgt-neg-in 99.9%

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

   5. fma-def 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(\sin y, -z, x + \cos y\right) \]

Alternative 2: 88.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+52}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+18)
   x
   (if (<= x 1.95e+52) (- (cos y) (* (sin y) z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+18) {
		tmp = x;
	} else if (x <= 1.95e+52) {
		tmp = cos(y) - (sin(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 <= (-4.6d+18)) then
        tmp = x
    else if (x <= 1.95d+52) then
        tmp = cos(y) - (sin(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 <= -4.6e+18) {
		tmp = x;
	} else if (x <= 1.95e+52) {
		tmp = Math.cos(y) - (Math.sin(y) * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+18:
		tmp = x
	elif x <= 1.95e+52:
		tmp = math.cos(y) - (math.sin(y) * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+18)
		tmp = x;
	elseif (x <= 1.95e+52)
		tmp = Float64(cos(y) - Float64(sin(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 <= -4.6e+18)
		tmp = x;
	elseif (x <= 1.95e+52)
		tmp = cos(y) - (sin(y) * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+18], x, If[LessEqual[x, 1.95e+52], N[(N[Cos[y], $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6e18

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 88.1%

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

   if -4.6e18 < x < 1.95e52

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 96.1%

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

   if 1.95e52 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.8%

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

      1. +-commutative 89.8%

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

   4. Simplified 89.8%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+52}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 4: 80.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \cos y\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+36} \lor \neg \left(y \leq 105000\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (cos y))))
   (if (or (<= y -3.2e+36) (not (<= y 105000.0))) t_0 (- t_0 (* y z)))))

C

double code(double x, double y, double z) {
	double t_0 = x + cos(y);
	double tmp;
	if ((y <= -3.2e+36) || !(y <= 105000.0)) {
		tmp = t_0;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x + cos(y)
    if ((y <= (-3.2d+36)) .or. (.not. (y <= 105000.0d0))) then
        tmp = t_0
    else
        tmp = t_0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.cos(y);
	double tmp;
	if ((y <= -3.2e+36) || !(y <= 105000.0)) {
		tmp = t_0;
	} else {
		tmp = t_0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.cos(y)
	tmp = 0
	if (y <= -3.2e+36) or not (y <= 105000.0):
		tmp = t_0
	else:
		tmp = t_0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + cos(y))
	tmp = 0.0
	if ((y <= -3.2e+36) || !(y <= 105000.0))
		tmp = t_0;
	else
		tmp = Float64(t_0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + cos(y);
	tmp = 0.0;
	if ((y <= -3.2e+36) || ~((y <= 105000.0)))
		tmp = t_0;
	else
		tmp = t_0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y, -3.2e+36], N[Not[LessEqual[y, 105000.0]], $MachinePrecision]], t$95$0, N[(t$95$0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999999e36 or 105000 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 65.1%

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

   if -3.1999999999999999e36 < y < 105000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.7%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+36} \lor \neg \left(y \leq 105000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \cos y\right) - y \cdot z\\ \end{array} \]

Alternative 5: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.024 \lor \neg \left(y \leq 13000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(-y, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.024) (not (<= y 13000.0)))
   (+ x (cos y))
   (+ 1.0 (fma (- y) z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.024) || !(y <= 13000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + fma(-y, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.024) || !(y <= 13000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + fma(Float64(-y), z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.024], N[Not[LessEqual[y, 13000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[((-y) * z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.024 or 13000 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 65.5%

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

   if -0.024 < y < 13000

   1. Initial program 100.0%

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

      1. add-cube-cbrt 99.7%

         \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{\left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{\sin y}\right)} \]

      2. pow3 99.7%

         \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{{\left(\sqrt[3]{\sin y}\right)}^{3}} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \left(x + \cos y\right) - z \cdot \color{blue}{{\left(\sqrt[3]{\sin y}\right)}^{3}} \]

   4. Taylor expanded in y around 0 98.4%

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

      1. associate-*r* 98.4%

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

      2. fma-def 98.4%

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

      3. mul-1-neg 98.4%

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

   6. Simplified 98.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.024 \lor \neg \left(y \leq 13000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(-y, z, x\right)\\ \end{array} \]

Alternative 6: 80.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.04 \lor \neg \left(y \leq 13000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.04) (not (<= y 13000.0)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.04) || !(y <= 13000.0)) {
		tmp = x + cos(y);
	} 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 <= (-0.04d0)) .or. (.not. (y <= 13000.0d0))) then
        tmp = x + cos(y)
    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 <= -0.04) || !(y <= 13000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.04) or not (y <= 13000.0):
		tmp = x + math.cos(y)
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.04) || !(y <= 13000.0))
		tmp = Float64(x + cos(y));
	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 <= -0.04) || ~((y <= 13000.0)))
		tmp = x + cos(y);
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.04], N[Not[LessEqual[y, 13000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0400000000000000008 or 13000 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 65.5%

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

   if -0.0400000000000000008 < y < 13000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.4%

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

      1. associate-+r+ 98.4%

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

      2. +-commutative 98.4%

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

      3. mul-1-neg 98.4%

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

      4. unsub-neg 98.4%

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

   4. Simplified 98.4%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.04 \lor \neg \left(y \leq 13000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 7: 69.3% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+36}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1220000000:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.2e+36)
   (+ x 1.0)
   (if (<= y 1220000000.0) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.2e+36) {
		tmp = x + 1.0;
	} else if (y <= 1220000000.0) {
		tmp = x + (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 (y <= (-3.2d+36)) then
        tmp = x + 1.0d0
    else if (y <= 1220000000.0d0) then
        tmp = x + (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 (y <= -3.2e+36) {
		tmp = x + 1.0;
	} else if (y <= 1220000000.0) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.2e+36:
		tmp = x + 1.0
	elif y <= 1220000000.0:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.2e+36)
		tmp = Float64(x + 1.0);
	elseif (y <= 1220000000.0)
		tmp = Float64(x + 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 (y <= -3.2e+36)
		tmp = x + 1.0;
	elseif (y <= 1220000000.0)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.2e+36], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1220000000.0], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999999e36 or 1.22e9 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 44.3%

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

      1. +-commutative 44.3%

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

   4. Simplified 44.3%

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

   if -3.1999999999999999e36 < y < 1.22e9

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.2%

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

      1. associate-+r+ 93.2%

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

      2. +-commutative 93.2%

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

      3. mul-1-neg 93.2%

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

      4. unsub-neg 93.2%

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

   4. Simplified 93.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+36}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1220000000:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8: 65.0% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-40}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e-40) (+ x 1.0) (if (<= x 4.8e+31) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-40) {
		tmp = x + 1.0;
	} else if (x <= 4.8e+31) {
		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 <= (-1.3d-40)) then
        tmp = x + 1.0d0
    else if (x <= 4.8d+31) 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 <= -1.3e-40) {
		tmp = x + 1.0;
	} else if (x <= 4.8e+31) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e-40:
		tmp = x + 1.0
	elif x <= 4.8e+31:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e-40)
		tmp = Float64(x + 1.0);
	elseif (x <= 4.8e+31)
		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 <= -1.3e-40)
		tmp = x + 1.0;
	elseif (x <= 4.8e+31)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e-40], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 4.8e+31], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e-40 or 4.79999999999999965e31 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 82.1%

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

      1. +-commutative 82.1%

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

   4. Simplified 82.1%

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

   if -1.3000000000000001e-40 < x < 4.79999999999999965e31

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 55.0%

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

      1. associate-+r+ 55.0%

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

      2. +-commutative 55.0%

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

      3. mul-1-neg 55.0%

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

      4. unsub-neg 55.0%

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

   4. Simplified 55.0%

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

   5. Taylor expanded in x around 0 54.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-40}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 62.1% accurate, 34.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.2 \cdot 10^{+250}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 3.2e+250) (+ x 1.0) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.2e+250) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 3.2d+250) then
        tmp = x + 1.0d0
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.2e+250) {
		tmp = x + 1.0;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.2e+250:
		tmp = x + 1.0
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.2e+250)
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.2e+250)
		tmp = x + 1.0;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.2e+250], N[(x + 1.0), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.1999999999999997e250

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 66.8%

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

      1. +-commutative 66.8%

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

   4. Simplified 66.8%

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

   if 3.1999999999999997e250 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 58.7%

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

   3. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.2 \cdot 10^{+250}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 10: 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. Taylor expanded in y around 0 64.5%

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

   1. +-commutative 64.5%

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

4. Simplified 64.5%

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

5. Final simplification 64.5%

   \[\leadsto x + 1 \]

Alternative 11: 41.8% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in x around inf 44.7%

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

3. Final simplification 44.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(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))))