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

Percentage Accurate: 99.9% → 99.9%

Time: 10.6s

Alternatives: 11

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: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-28} \lor \neg \left(x \leq 1.1 \cdot 10^{-139}\right):\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.9e-28) (not (<= x 1.1e-139)))
   (+ z (+ x (sin y)))
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e-28) || !(x <= 1.1e-139)) {
		tmp = z + (x + sin(y));
	} else {
		tmp = sin(y) + (z * cos(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 ((x <= (-3.9d-28)) .or. (.not. (x <= 1.1d-139))) then
        tmp = z + (x + sin(y))
    else
        tmp = sin(y) + (z * cos(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.9e-28) || !(x <= 1.1e-139)) {
		tmp = z + (x + Math.sin(y));
	} else {
		tmp = Math.sin(y) + (z * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.9e-28) or not (x <= 1.1e-139):
		tmp = z + (x + math.sin(y))
	else:
		tmp = math.sin(y) + (z * math.cos(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.9e-28) || !(x <= 1.1e-139))
		tmp = Float64(z + Float64(x + sin(y)));
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.9e-28) || ~((x <= 1.1e-139)))
		tmp = z + (x + sin(y));
	else
		tmp = sin(y) + (z * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.9e-28], N[Not[LessEqual[x, 1.1e-139]], $MachinePrecision]], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.89999999999999999e-28 or 1.10000000000000005e-139 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 89.8%

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

   if -3.89999999999999999e-28 < x < 1.10000000000000005e-139

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-28} \lor \neg \left(x \leq 1.1 \cdot 10^{-139}\right):\\ \;\;\;\;z + \left(x + \sin y\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]

Alternative 3: 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 4: 69.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-260}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-130}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+18}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= x -2.8e-28)
     (+ z x)
     (if (<= x -3.6e-197)
       t_0
       (if (<= x -6.5e-260)
         (sin y)
         (if (<= x -2.4e-281)
           t_0
           (if (<= x 7.5e-258)
             (sin y)
             (if (<= x 3.4e-130)
               t_0
               (if (<= x 6e+18)
                 (+ z (+ y x))
                 (if (<= x 4.5e+38) t_0 (+ z x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (x <= -2.8e-28) {
		tmp = z + x;
	} else if (x <= -3.6e-197) {
		tmp = t_0;
	} else if (x <= -6.5e-260) {
		tmp = sin(y);
	} else if (x <= -2.4e-281) {
		tmp = t_0;
	} else if (x <= 7.5e-258) {
		tmp = sin(y);
	} else if (x <= 3.4e-130) {
		tmp = t_0;
	} else if (x <= 6e+18) {
		tmp = z + (y + x);
	} else if (x <= 4.5e+38) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (x <= (-2.8d-28)) then
        tmp = z + x
    else if (x <= (-3.6d-197)) then
        tmp = t_0
    else if (x <= (-6.5d-260)) then
        tmp = sin(y)
    else if (x <= (-2.4d-281)) then
        tmp = t_0
    else if (x <= 7.5d-258) then
        tmp = sin(y)
    else if (x <= 3.4d-130) then
        tmp = t_0
    else if (x <= 6d+18) then
        tmp = z + (y + x)
    else if (x <= 4.5d+38) then
        tmp = t_0
    else
        tmp = z + x
    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 (x <= -2.8e-28) {
		tmp = z + x;
	} else if (x <= -3.6e-197) {
		tmp = t_0;
	} else if (x <= -6.5e-260) {
		tmp = Math.sin(y);
	} else if (x <= -2.4e-281) {
		tmp = t_0;
	} else if (x <= 7.5e-258) {
		tmp = Math.sin(y);
	} else if (x <= 3.4e-130) {
		tmp = t_0;
	} else if (x <= 6e+18) {
		tmp = z + (y + x);
	} else if (x <= 4.5e+38) {
		tmp = t_0;
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if x <= -2.8e-28:
		tmp = z + x
	elif x <= -3.6e-197:
		tmp = t_0
	elif x <= -6.5e-260:
		tmp = math.sin(y)
	elif x <= -2.4e-281:
		tmp = t_0
	elif x <= 7.5e-258:
		tmp = math.sin(y)
	elif x <= 3.4e-130:
		tmp = t_0
	elif x <= 6e+18:
		tmp = z + (y + x)
	elif x <= 4.5e+38:
		tmp = t_0
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (x <= -2.8e-28)
		tmp = Float64(z + x);
	elseif (x <= -3.6e-197)
		tmp = t_0;
	elseif (x <= -6.5e-260)
		tmp = sin(y);
	elseif (x <= -2.4e-281)
		tmp = t_0;
	elseif (x <= 7.5e-258)
		tmp = sin(y);
	elseif (x <= 3.4e-130)
		tmp = t_0;
	elseif (x <= 6e+18)
		tmp = Float64(z + Float64(y + x));
	elseif (x <= 4.5e+38)
		tmp = t_0;
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (x <= -2.8e-28)
		tmp = z + x;
	elseif (x <= -3.6e-197)
		tmp = t_0;
	elseif (x <= -6.5e-260)
		tmp = sin(y);
	elseif (x <= -2.4e-281)
		tmp = t_0;
	elseif (x <= 7.5e-258)
		tmp = sin(y);
	elseif (x <= 3.4e-130)
		tmp = t_0;
	elseif (x <= 6e+18)
		tmp = z + (y + x);
	elseif (x <= 4.5e+38)
		tmp = t_0;
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e-28], N[(z + x), $MachinePrecision], If[LessEqual[x, -3.6e-197], t$95$0, If[LessEqual[x, -6.5e-260], N[Sin[y], $MachinePrecision], If[LessEqual[x, -2.4e-281], t$95$0, If[LessEqual[x, 7.5e-258], N[Sin[y], $MachinePrecision], If[LessEqual[x, 3.4e-130], t$95$0, If[LessEqual[x, 6e+18], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+38], t$95$0, N[(z + x), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.7999999999999998e-28 or 4.4999999999999998e38 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 88.4%

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

      1. +-commutative 88.4%

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

   4. Simplified 88.4%

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

   if -2.7999999999999998e-28 < x < -3.5999999999999998e-197 or -6.50000000000000002e-260 < x < -2.4e-281 or 7.4999999999999998e-258 < x < 3.40000000000000005e-130 or 6e18 < x < 4.4999999999999998e38

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 76.5%

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

   if -3.5999999999999998e-197 < x < -6.50000000000000002e-260 or -2.4e-281 < x < 7.4999999999999998e-258

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 78.8%

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

      1. +-commutative 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in x around 0 78.7%

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

   if 3.40000000000000005e-130 < x < 6e18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. +-commutative 55.5%

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

      3. associate-+l+ 55.5%

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

   4. Simplified 55.5%

      \[\leadsto \color{blue}{z + \left(y + x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-28}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-260}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-281}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-258}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-130}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+18}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 5: 84.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -7 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-6}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+167}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -7e+79)
     t_0
     (if (<= z -4.6e-6)
       (+ z x)
       (if (<= z 7.5) (+ x (sin y)) (if (<= z 8.2e+167) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -7e+79) {
		tmp = t_0;
	} else if (z <= -4.6e-6) {
		tmp = z + x;
	} else if (z <= 7.5) {
		tmp = x + sin(y);
	} else if (z <= 8.2e+167) {
		tmp = z + x;
	} 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 <= (-7d+79)) then
        tmp = t_0
    else if (z <= (-4.6d-6)) then
        tmp = z + x
    else if (z <= 7.5d0) then
        tmp = x + sin(y)
    else if (z <= 8.2d+167) then
        tmp = z + x
    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 <= -7e+79) {
		tmp = t_0;
	} else if (z <= -4.6e-6) {
		tmp = z + x;
	} else if (z <= 7.5) {
		tmp = x + Math.sin(y);
	} else if (z <= 8.2e+167) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -7e+79:
		tmp = t_0
	elif z <= -4.6e-6:
		tmp = z + x
	elif z <= 7.5:
		tmp = x + math.sin(y)
	elif z <= 8.2e+167:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -7e+79)
		tmp = t_0;
	elseif (z <= -4.6e-6)
		tmp = Float64(z + x);
	elseif (z <= 7.5)
		tmp = Float64(x + sin(y));
	elseif (z <= 8.2e+167)
		tmp = Float64(z + x);
	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 <= -7e+79)
		tmp = t_0;
	elseif (z <= -4.6e-6)
		tmp = z + x;
	elseif (z <= 7.5)
		tmp = x + sin(y);
	elseif (z <= 8.2e+167)
		tmp = z + x;
	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, -7e+79], t$95$0, If[LessEqual[z, -4.6e-6], N[(z + x), $MachinePrecision], If[LessEqual[z, 7.5], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e+167], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999961e79 or 8.2e167 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -6.99999999999999961e79 < z < -4.6e-6 or 7.5 < z < 8.2e167

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.6%

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

      1. +-commutative 81.6%

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

   4. Simplified 81.6%

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

   if -4.6e-6 < z < 7.5

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 96.5%

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

      1. +-commutative 96.5%

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

   4. Simplified 96.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-6}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 7.5:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+167}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 6: 89.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+80} \lor \neg \left(z \leq 1.25 \cdot 10^{+167}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7e+80) (not (<= z 1.25e+167)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7e+80) || !(z <= 1.25e+167)) {
		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 <= (-7d+80)) .or. (.not. (z <= 1.25d+167))) 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 <= -7e+80) || !(z <= 1.25e+167)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7e+80) or not (z <= 1.25e+167):
		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 <= -7e+80) || !(z <= 1.25e+167))
		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 <= -7e+80) || ~((z <= 1.25e+167)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7e+80], N[Not[LessEqual[z, 1.25e+167]], $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 < -6.99999999999999987e80 or 1.2499999999999999e167 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 85.2%

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

   if -6.99999999999999987e80 < z < 1.2499999999999999e167

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+80} \lor \neg \left(z \leq 1.25 \cdot 10^{+167}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 66.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-195}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-156}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-5}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.3e-195)
   (+ z x)
   (if (<= x 3.2e-156) (sin y) (if (<= x 2.15e-5) (+ z (+ y x)) (+ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.3e-195) {
		tmp = z + x;
	} else if (x <= 3.2e-156) {
		tmp = sin(y);
	} else if (x <= 2.15e-5) {
		tmp = z + (y + 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 (x <= (-1.3d-195)) then
        tmp = z + x
    else if (x <= 3.2d-156) then
        tmp = sin(y)
    else if (x <= 2.15d-5) then
        tmp = z + (y + 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 (x <= -1.3e-195) {
		tmp = z + x;
	} else if (x <= 3.2e-156) {
		tmp = Math.sin(y);
	} else if (x <= 2.15e-5) {
		tmp = z + (y + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.3e-195:
		tmp = z + x
	elif x <= 3.2e-156:
		tmp = math.sin(y)
	elif x <= 2.15e-5:
		tmp = z + (y + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.3e-195)
		tmp = Float64(z + x);
	elseif (x <= 3.2e-156)
		tmp = sin(y);
	elseif (x <= 2.15e-5)
		tmp = Float64(z + Float64(y + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.3e-195)
		tmp = z + x;
	elseif (x <= 3.2e-156)
		tmp = sin(y);
	elseif (x <= 2.15e-5)
		tmp = z + (y + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.3e-195], N[(z + x), $MachinePrecision], If[LessEqual[x, 3.2e-156], N[Sin[y], $MachinePrecision], If[LessEqual[x, 2.15e-5], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3000000000000001e-195 or 2.1500000000000001e-5 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.2%

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

      1. +-commutative 80.2%

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

   4. Simplified 80.2%

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

   if -1.3000000000000001e-195 < x < 3.19999999999999982e-156

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 53.4%

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

      1. +-commutative 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in x around 0 53.4%

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

   if 3.19999999999999982e-156 < x < 2.1500000000000001e-5

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 57.6%

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

      1. +-commutative 57.6%

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

      2. +-commutative 57.6%

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

      3. associate-+l+ 57.6%

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

   4. Simplified 57.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-195}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-156}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-5}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 70.3% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.7e-21) (+ z x) (if (<= x 1.22e-8) (+ z (+ y x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.7e-21) {
		tmp = z + x;
	} else if (x <= 1.22e-8) {
		tmp = z + (y + 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 (x <= (-2.7d-21)) then
        tmp = z + x
    else if (x <= 1.22d-8) then
        tmp = z + (y + 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 (x <= -2.7e-21) {
		tmp = z + x;
	} else if (x <= 1.22e-8) {
		tmp = z + (y + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.7e-21:
		tmp = z + x
	elif x <= 1.22e-8:
		tmp = z + (y + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.7e-21)
		tmp = Float64(z + x);
	elseif (x <= 1.22e-8)
		tmp = Float64(z + Float64(y + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.7e-21)
		tmp = z + x;
	elseif (x <= 1.22e-8)
		tmp = z + (y + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.7e-21], N[(z + x), $MachinePrecision], If[LessEqual[x, 1.22e-8], N[(z + N[(y + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7000000000000001e-21 or 1.22e-8 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.8%

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

      1. +-commutative 87.8%

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

   4. Simplified 87.8%

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

   if -2.7000000000000001e-21 < x < 1.22e-8

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 48.8%

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

      1. +-commutative 48.8%

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

      2. +-commutative 48.8%

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

      3. associate-+l+ 48.8%

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

   4. Simplified 48.8%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-21}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-8}:\\ \;\;\;\;z + \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9: 55.8% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.5e-22) x (if (<= x 6.8e-33) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.5e-22) {
		tmp = x;
	} else if (x <= 6.8e-33) {
		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 <= (-2.5d-22)) then
        tmp = x
    else if (x <= 6.8d-33) 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 <= -2.5e-22) {
		tmp = x;
	} else if (x <= 6.8e-33) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.5e-22:
		tmp = x
	elif x <= 6.8e-33:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.5e-22)
		tmp = x;
	elseif (x <= 6.8e-33)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.5e-22)
		tmp = x;
	elseif (x <= 6.8e-33)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.5e-22], x, If[LessEqual[x, 6.8e-33], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999977e-22 or 6.8000000000000001e-33 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 76.2%

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

   if -2.49999999999999977e-22 < x < 6.8000000000000001e-33

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 55.7%

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

   3. Taylor expanded in y around 0 35.1%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-33}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 66.9% 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 64.0%

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

   1. +-commutative 64.0%

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

4. Simplified 64.0%

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

5. Final simplification 64.0%

   \[\leadsto z + x \]

Alternative 11: 42.8% 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%

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

2. Taylor expanded in x around inf 45.2%

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

3. Final simplification 45.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(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))))