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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 82.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-16}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+37}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -6e+51)
     t_0
     (if (<= z -3.2e-16)
       (+ y (+ z x))
       (if (<= z 1.02e+37) (+ x (sin y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -6e+51) {
		tmp = t_0;
	} else if (z <= -3.2e-16) {
		tmp = y + (z + x);
	} else if (z <= 1.02e+37) {
		tmp = x + sin(y);
	} else {
		tmp = 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 * cos(y)
    if (z <= (-6d+51)) then
        tmp = t_0
    else if (z <= (-3.2d-16)) then
        tmp = y + (z + x)
    else if (z <= 1.02d+37) then
        tmp = x + sin(y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -6e+51) {
		tmp = t_0;
	} else if (z <= -3.2e-16) {
		tmp = y + (z + x);
	} else if (z <= 1.02e+37) {
		tmp = x + Math.sin(y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -6e+51:
		tmp = t_0
	elif z <= -3.2e-16:
		tmp = y + (z + x)
	elif z <= 1.02e+37:
		tmp = x + math.sin(y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -6e+51)
		tmp = t_0;
	elseif (z <= -3.2e-16)
		tmp = Float64(y + Float64(z + x));
	elseif (z <= 1.02e+37)
		tmp = Float64(x + sin(y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -6e+51)
		tmp = t_0;
	elseif (z <= -3.2e-16)
		tmp = y + (z + x);
	elseif (z <= 1.02e+37)
		tmp = x + sin(y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+51], t$95$0, If[LessEqual[z, -3.2e-16], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+37], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e51 or 1.01999999999999995e37 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 99.1%

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

      4. associate-*l* 99.0%

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

      5. fma-def 99.0%

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

      6. pow2 99.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 85.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 85.3%

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

      2. *-commutative 85.3%

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

      3. *-lft-identity 85.3%

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

   6. Simplified 85.3%

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

   if -6e51 < z < -3.20000000000000023e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.8%

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

   if -3.20000000000000023e-16 < z < 1.01999999999999995e37

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 87.7%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-16}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+37}:\\ \;\;\;\;x + \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 87.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+51} \lor \neg \left(z \leq 1.55 \cdot 10^{+42}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.8e+51) (not (<= z 1.55e+42)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.8e+51) || !(z <= 1.55e+42)) {
		tmp = z * cos(y);
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-8.8d+51)) .or. (.not. (z <= 1.55d+42))) then
        tmp = z * cos(y)
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.8e+51) || !(z <= 1.55e+42)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.8e+51) or not (z <= 1.55e+42):
		tmp = z * math.cos(y)
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.8e+51) || !(z <= 1.55e+42))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.8e+51) || ~((z <= 1.55e+42)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.8e+51], N[Not[LessEqual[z, 1.55e+42]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.79999999999999967e51 or 1.5500000000000001e42 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 99.1%

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

      4. associate-*l* 99.0%

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

      5. fma-def 99.0%

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

      6. pow2 99.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 85.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 85.3%

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

      2. *-commutative 85.3%

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

      3. *-lft-identity 85.3%

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

   6. Simplified 85.3%

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

   if -8.79999999999999967e51 < z < 1.5500000000000001e42

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+51} \lor \neg \left(z \leq 1.55 \cdot 10^{+42}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 5: 89.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1 \cdot 10^{+57}:\\ \;\;\;\;\left(y + x\right) + t_0\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1e+57)
     (+ (+ y x) t_0)
     (if (<= z 4.5e+43) (+ z (+ x (sin y))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1e+57) {
		tmp = (y + x) + t_0;
	} else if (z <= 4.5e+43) {
		tmp = z + (x + sin(y));
	} else {
		tmp = 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 * cos(y)
    if (z <= (-1d+57)) then
        tmp = (y + x) + t_0
    else if (z <= 4.5d+43) then
        tmp = z + (x + sin(y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.cos(y);
	double tmp;
	if (z <= -1e+57) {
		tmp = (y + x) + t_0;
	} else if (z <= 4.5e+43) {
		tmp = z + (x + Math.sin(y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -1e+57:
		tmp = (y + x) + t_0
	elif z <= 4.5e+43:
		tmp = z + (x + math.sin(y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -1e+57)
		tmp = Float64(Float64(y + x) + t_0);
	elseif (z <= 4.5e+43)
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -1e+57)
		tmp = (y + x) + t_0;
	elseif (z <= 4.5e+43)
		tmp = z + (x + sin(y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+57], N[(N[(y + x), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[z, 4.5e+43], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000005e57

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 88.2%

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

   if -1.00000000000000005e57 < z < 4.5e43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.8%

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

   if 4.5e43 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. add-cube-cbrt 99.1%

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

      4. associate-*l* 99.0%

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

      5. fma-def 99.0%

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

      6. pow2 99.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 85.8%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 85.8%

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

      2. *-commutative 85.8%

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

      3. *-lft-identity 85.8%

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

   6. Simplified 85.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+57}:\\ \;\;\;\;\left(y + x\right) + z \cdot \cos y\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 6: 71.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+52} \lor \neg \left(z \leq 4.5 \cdot 10^{+43}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1e+52) (not (<= z 4.5e+43))) (* z (cos y)) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+52) || !(z <= 4.5e+43)) {
		tmp = z * cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1d+52)) .or. (.not. (z <= 4.5d+43))) then
        tmp = z * cos(y)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1e+52) || !(z <= 4.5e+43)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1e+52) or not (z <= 4.5e+43):
		tmp = z * math.cos(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1e+52) || !(z <= 4.5e+43))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1e+52) || ~((z <= 4.5e+43)))
		tmp = z * cos(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1e+52], N[Not[LessEqual[z, 4.5e+43]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999999e51 or 4.5e43 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 99.1%

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

      4. associate-*l* 99.0%

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

      5. fma-def 99.0%

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

      6. pow2 99.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{2}}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right) \]

   3. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\cos y}\right)}^{2}, \sqrt[3]{\cos y} \cdot z, x + \sin y\right)} \]

   4. Taylor expanded in z around inf 85.3%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(z \cdot \cos y\right)} \]
   5. Step-by-step derivation

      1. pow-base-1 85.3%

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

      2. *-commutative 85.3%

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

      3. *-lft-identity 85.3%

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

   6. Simplified 85.3%

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

   if -9.9999999999999999e51 < z < 4.5e43

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 68.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+52} \lor \neg \left(z \leq 4.5 \cdot 10^{+43}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 7: 70.8% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.2e+48) (+ z x) (if (<= y 8.2e+17) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+48) {
		tmp = z + x;
	} else if (y <= 8.2e+17) {
		tmp = y + (z + x);
	} else {
		tmp = z + 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 <= (-6.2d+48)) then
        tmp = z + x
    else if (y <= 8.2d+17) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+48) {
		tmp = z + x;
	} else if (y <= 8.2e+17) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.2e+48:
		tmp = z + x
	elif y <= 8.2e+17:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.2e+48)
		tmp = Float64(z + x);
	elseif (y <= 8.2e+17)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.2e+48)
		tmp = z + x;
	elseif (y <= 8.2e+17)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.2e+48], N[(z + x), $MachinePrecision], If[LessEqual[y, 8.2e+17], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000011e48 or 8.2e17 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 39.0%

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

   if -6.20000000000000011e48 < y < 8.2e17

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.5%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+48}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 47.0% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+35}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+50) x (if (<= y 3e+35) (+ y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+50) {
		tmp = x;
	} else if (y <= 3e+35) {
		tmp = y + x;
	} 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 <= (-2.8d+50)) then
        tmp = x
    else if (y <= 3d+35) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+50) {
		tmp = x;
	} else if (y <= 3e+35) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+50:
		tmp = x
	elif y <= 3e+35:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+50)
		tmp = x;
	elseif (y <= 3e+35)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+50)
		tmp = x;
	elseif (y <= 3e+35)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+50], x, If[LessEqual[y, 3e+35], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999998e50 or 2.99999999999999991e35 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 35.0%

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

   if -2.7999999999999998e50 < y < 2.99999999999999991e35

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 53.3%

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

   3. Taylor expanded in y around 0 50.7%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+35}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 66.5% accurate, 69.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + 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 = z + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Taylor expanded in y around 0 64.7%

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

3. Final simplification 64.7%

   \[\leadsto z + x \]

Alternative 10: 43.0% 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%

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

2. Taylor expanded in x around inf 39.5%

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

3. Final simplification 39.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))