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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 8

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, 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 71.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-221}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -3.2e+147)
     t_0
     (if (<= z -3.5e+51)
       (+ x z)
       (if (<= z -1.6e+30)
         t_0
         (if (<= z -8.8e-221)
           (+ z (+ x y))
           (if (<= z 1.15e+112) (+ x z) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -3.2e+147) {
		tmp = t_0;
	} else if (z <= -3.5e+51) {
		tmp = x + z;
	} else if (z <= -1.6e+30) {
		tmp = t_0;
	} else if (z <= -8.8e-221) {
		tmp = z + (x + y);
	} else if (z <= 1.15e+112) {
		tmp = x + z;
	} 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 <= (-3.2d+147)) then
        tmp = t_0
    else if (z <= (-3.5d+51)) then
        tmp = x + z
    else if (z <= (-1.6d+30)) then
        tmp = t_0
    else if (z <= (-8.8d-221)) then
        tmp = z + (x + y)
    else if (z <= 1.15d+112) then
        tmp = x + z
    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 <= -3.2e+147) {
		tmp = t_0;
	} else if (z <= -3.5e+51) {
		tmp = x + z;
	} else if (z <= -1.6e+30) {
		tmp = t_0;
	} else if (z <= -8.8e-221) {
		tmp = z + (x + y);
	} else if (z <= 1.15e+112) {
		tmp = x + z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -3.2e+147:
		tmp = t_0
	elif z <= -3.5e+51:
		tmp = x + z
	elif z <= -1.6e+30:
		tmp = t_0
	elif z <= -8.8e-221:
		tmp = z + (x + y)
	elif z <= 1.15e+112:
		tmp = x + z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -3.2e+147)
		tmp = t_0;
	elseif (z <= -3.5e+51)
		tmp = Float64(x + z);
	elseif (z <= -1.6e+30)
		tmp = t_0;
	elseif (z <= -8.8e-221)
		tmp = Float64(z + Float64(x + y));
	elseif (z <= 1.15e+112)
		tmp = Float64(x + z);
	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 <= -3.2e+147)
		tmp = t_0;
	elseif (z <= -3.5e+51)
		tmp = x + z;
	elseif (z <= -1.6e+30)
		tmp = t_0;
	elseif (z <= -8.8e-221)
		tmp = z + (x + y);
	elseif (z <= 1.15e+112)
		tmp = x + z;
	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, -3.2e+147], t$95$0, If[LessEqual[z, -3.5e+51], N[(x + z), $MachinePrecision], If[LessEqual[z, -1.6e+30], t$95$0, If[LessEqual[z, -8.8e-221], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+112], N[(x + z), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.19999999999999979e147 or -3.5e51 < z < -1.59999999999999986e30 or 1.15e112 < 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. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.8%

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

   if -3.19999999999999979e147 < z < -3.5e51 or -8.80000000000000005e-221 < z < 1.15e112

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 75.5%

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

      1. +-commutative 75.5%

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

   7. Simplified 75.5%

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

   if -1.59999999999999986e30 < z < -8.80000000000000005e-221

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 66.9%

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

      1. +-commutative 66.9%

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

      2. +-commutative 66.9%

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

      3. associate-+l+ 66.9%

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

   7. Simplified 66.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-221}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+147}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -18 \lor \neg \left(z \leq 3 \cdot 10^{+95}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -6.5e+147)
     t_0
     (if (<= z -4.5e+51)
       (+ x z)
       (if (or (<= z -18.0) (not (<= z 3e+95))) t_0 (+ x (sin y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -6.5e+147) {
		tmp = t_0;
	} else if (z <= -4.5e+51) {
		tmp = x + z;
	} else if ((z <= -18.0) || !(z <= 3e+95)) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-6.5d+147)) then
        tmp = t_0
    else if (z <= (-4.5d+51)) then
        tmp = x + z
    else if ((z <= (-18.0d0)) .or. (.not. (z <= 3d+95))) then
        tmp = t_0
    else
        tmp = x + sin(y)
    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 <= -6.5e+147) {
		tmp = t_0;
	} else if (z <= -4.5e+51) {
		tmp = x + z;
	} else if ((z <= -18.0) || !(z <= 3e+95)) {
		tmp = t_0;
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -6.5e+147:
		tmp = t_0
	elif z <= -4.5e+51:
		tmp = x + z
	elif (z <= -18.0) or not (z <= 3e+95):
		tmp = t_0
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -6.5e+147)
		tmp = t_0;
	elseif (z <= -4.5e+51)
		tmp = Float64(x + z);
	elseif ((z <= -18.0) || !(z <= 3e+95))
		tmp = t_0;
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -6.5e+147)
		tmp = t_0;
	elseif (z <= -4.5e+51)
		tmp = x + z;
	elseif ((z <= -18.0) || ~((z <= 3e+95)))
		tmp = t_0;
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+147], t$95$0, If[LessEqual[z, -4.5e+51], N[(x + z), $MachinePrecision], If[Or[LessEqual[z, -18.0], N[Not[LessEqual[z, 3e+95]], $MachinePrecision]], t$95$0, N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e147 or -4.5e51 < z < -18 or 2.99999999999999991e95 < 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. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.2%

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

   if -6.5e147 < z < -4.5e51

   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-define 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. Add Preprocessing

   5. Taylor expanded in y around 0 77.4%

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

      1. +-commutative 77.4%

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

   7. Simplified 77.4%

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

   if -18 < z < 2.99999999999999991e95

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 92.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -18 \lor \neg \left(z \leq 3 \cdot 10^{+95}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+146} \lor \neg \left(z \leq 1.5 \cdot 10^{+107}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.1e+146) (not (<= z 1.5e+107)))
   (* z (cos y))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e+146) || !(z <= 1.5e+107)) {
		tmp = z * cos(y);
	} else {
		tmp = (x + 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 <= (-3.1d+146)) .or. (.not. (z <= 1.5d+107))) then
        tmp = z * cos(y)
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.1e+146) || !(z <= 1.5e+107)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.1e+146) or not (z <= 1.5e+107):
		tmp = z * math.cos(y)
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.1e+146) || !(z <= 1.5e+107))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.1e+146) || ~((z <= 1.5e+107)))
		tmp = z * cos(y);
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.1e+146], N[Not[LessEqual[z, 1.5e+107]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000002e146 or 1.50000000000000012e107 < 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. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.1%

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

   if -3.1000000000000002e146 < z < 1.50000000000000012e107

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.2%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+146} \lor \neg \left(z \leq 1.5 \cdot 10^{+107}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+20} \lor \neg \left(y \leq 6.2 \cdot 10^{-19}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+20) (not (<= y 6.2e-19))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+20) || !(y <= 6.2e-19)) {
		tmp = x + z;
	} else {
		tmp = z + (x + 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 ((y <= (-4d+20)) .or. (.not. (y <= 6.2d-19))) then
        tmp = x + z
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+20) || !(y <= 6.2e-19)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+20) or not (y <= 6.2e-19):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+20) || !(y <= 6.2e-19))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+20) || ~((y <= 6.2e-19)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+20], N[Not[LessEqual[y, 6.2e-19]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e20 or 6.1999999999999998e-19 < y

   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-define 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. Add Preprocessing

   5. Taylor expanded in y around 0 48.5%

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

      1. +-commutative 48.5%

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

   7. Simplified 48.5%

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

   if -4e20 < y < 6.1999999999999998e-19

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.1%

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

      1. +-commutative 98.1%

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

      2. +-commutative 98.1%

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

      3. associate-+l+ 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+20} \lor \neg \left(y \leq 6.2 \cdot 10^{-19}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.55e-8) x (if (<= x 3.7e-48) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.55e-8) {
		tmp = x;
	} else if (x <= 3.7e-48) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.55d-8)) then
        tmp = x
    else if (x <= 3.7d-48) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.55e-8) {
		tmp = x;
	} else if (x <= 3.7e-48) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.55e-8:
		tmp = x
	elif x <= 3.7e-48:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.55e-8)
		tmp = x;
	elseif (x <= 3.7e-48)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.55e-8)
		tmp = x;
	elseif (x <= 3.7e-48)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.55e-8], x, If[LessEqual[x, 3.7e-48], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.55e-8 or 3.6999999999999998e-48 < x

   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-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 74.2%

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

   if -2.55e-8 < x < 3.6999999999999998e-48

   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-define 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. Add Preprocessing

   5. Taylor expanded in z around inf 56.8%

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

   6. Taylor expanded in y around 0 38.2%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-48}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.9% accurate, 69.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + z), $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-define 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. Add Preprocessing

5. Taylor expanded in y around 0 67.9%

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

   1. +-commutative 67.9%

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

7. Simplified 67.9%

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

8. Final simplification 67.9%

   \[\leadsto x + z \]
9. Add Preprocessing

Alternative 8: 42.7% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-define 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. Add Preprocessing

5. Taylor expanded in x around inf 46.6%

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

6. Final simplification 46.6%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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))))