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

Percentage Accurate: 99.9% → 99.9%

Time: 8.1s

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-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. Final simplification 99.9%

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

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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 3: 72.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-145}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-129}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+141}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.12e+108)
     t_0
     (if (<= z 2.6e-145)
       (+ z x)
       (if (<= z 1.36e-129) (sin y) (if (<= z 1.05e+141) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.12e+108) {
		tmp = t_0;
	} else if (z <= 2.6e-145) {
		tmp = z + x;
	} else if (z <= 1.36e-129) {
		tmp = sin(y);
	} else if (z <= 1.05e+141) {
		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 <= (-1.12d+108)) then
        tmp = t_0
    else if (z <= 2.6d-145) then
        tmp = z + x
    else if (z <= 1.36d-129) then
        tmp = sin(y)
    else if (z <= 1.05d+141) 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 <= -1.12e+108) {
		tmp = t_0;
	} else if (z <= 2.6e-145) {
		tmp = z + x;
	} else if (z <= 1.36e-129) {
		tmp = Math.sin(y);
	} else if (z <= 1.05e+141) {
		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 <= -1.12e+108:
		tmp = t_0
	elif z <= 2.6e-145:
		tmp = z + x
	elif z <= 1.36e-129:
		tmp = math.sin(y)
	elif z <= 1.05e+141:
		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 <= -1.12e+108)
		tmp = t_0;
	elseif (z <= 2.6e-145)
		tmp = Float64(z + x);
	elseif (z <= 1.36e-129)
		tmp = sin(y);
	elseif (z <= 1.05e+141)
		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 <= -1.12e+108)
		tmp = t_0;
	elseif (z <= 2.6e-145)
		tmp = z + x;
	elseif (z <= 1.36e-129)
		tmp = sin(y);
	elseif (z <= 1.05e+141)
		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, -1.12e+108], t$95$0, If[LessEqual[z, 2.6e-145], N[(z + x), $MachinePrecision], If[LessEqual[z, 1.36e-129], N[Sin[y], $MachinePrecision], If[LessEqual[z, 1.05e+141], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.11999999999999994e108 or 1.0499999999999999e141 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 92.3%

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

   if -1.11999999999999994e108 < z < 2.6e-145 or 1.36000000000000002e-129 < z < 1.0499999999999999e141

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.7%

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

      1. +-commutative 75.7%

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

   5. Simplified 75.7%

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

   if 2.6e-145 < z < 1.36000000000000002e-129

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in z around 0 100.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-145}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-129}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+141}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-22}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-56}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.7 \cdot 10^{+142}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.6e+108)
     t_0
     (if (<= z -2.15e-22)
       (+ z x)
       (if (<= z 1.3e-56) (+ x (sin y)) (if (<= z 8.7e+142) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.6e+108) {
		tmp = t_0;
	} else if (z <= -2.15e-22) {
		tmp = z + x;
	} else if (z <= 1.3e-56) {
		tmp = x + sin(y);
	} else if (z <= 8.7e+142) {
		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 <= (-1.6d+108)) then
        tmp = t_0
    else if (z <= (-2.15d-22)) then
        tmp = z + x
    else if (z <= 1.3d-56) then
        tmp = x + sin(y)
    else if (z <= 8.7d+142) 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 <= -1.6e+108) {
		tmp = t_0;
	} else if (z <= -2.15e-22) {
		tmp = z + x;
	} else if (z <= 1.3e-56) {
		tmp = x + Math.sin(y);
	} else if (z <= 8.7e+142) {
		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 <= -1.6e+108:
		tmp = t_0
	elif z <= -2.15e-22:
		tmp = z + x
	elif z <= 1.3e-56:
		tmp = x + math.sin(y)
	elif z <= 8.7e+142:
		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 <= -1.6e+108)
		tmp = t_0;
	elseif (z <= -2.15e-22)
		tmp = Float64(z + x);
	elseif (z <= 1.3e-56)
		tmp = Float64(x + sin(y));
	elseif (z <= 8.7e+142)
		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 <= -1.6e+108)
		tmp = t_0;
	elseif (z <= -2.15e-22)
		tmp = z + x;
	elseif (z <= 1.3e-56)
		tmp = x + sin(y);
	elseif (z <= 8.7e+142)
		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, -1.6e+108], t$95$0, If[LessEqual[z, -2.15e-22], N[(z + x), $MachinePrecision], If[LessEqual[z, 1.3e-56], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.7e+142], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6e108 or 8.6999999999999999e142 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 92.3%

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

   if -1.6e108 < z < -2.15000000000000019e-22 or 1.29999999999999998e-56 < z < 8.6999999999999999e142

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. +-commutative 80.5%

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

   5. Simplified 80.5%

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

   if -2.15000000000000019e-22 < z < 1.29999999999999998e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.1%

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

      1. +-commutative 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-22}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-56}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 8.7 \cdot 10^{+142}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+108} \lor \neg \left(z \leq 1.4 \cdot 10^{+140}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.02e+108) (not (<= z 1.4e+140)))
   (* z (cos y))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02e+108) || !(z <= 1.4e+140)) {
		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 <= (-1.02d+108)) .or. (.not. (z <= 1.4d+140))) 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 <= -1.02e+108) || !(z <= 1.4e+140)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.02e+108) or not (z <= 1.4e+140):
		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 <= -1.02e+108) || !(z <= 1.4e+140))
		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 <= -1.02e+108) || ~((z <= 1.4e+140)))
		tmp = z * cos(y);
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.02e+108], N[Not[LessEqual[z, 1.4e+140]], $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 < -1.02e108 or 1.39999999999999991e140 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 92.3%

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

   if -1.02e108 < z < 1.39999999999999991e140

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+108} \lor \neg \left(z \leq 1.4 \cdot 10^{+140}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+42} \lor \neg \left(y \leq 380000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.22e+42) (not (<= y 380000000.0)))
   (+ z x)
   (+ (+ z x) (* y (+ 1.0 (* -0.5 (* z y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.22e+42) || !(y <= 380000000.0)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * 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 <= (-1.22d+42)) .or. (.not. (y <= 380000000.0d0))) then
        tmp = z + x
    else
        tmp = (z + x) + (y * (1.0d0 + ((-0.5d0) * (z * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.22e+42) || !(y <= 380000000.0)) {
		tmp = z + x;
	} else {
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.22e+42) or not (y <= 380000000.0):
		tmp = z + x
	else:
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.22e+42) || !(y <= 380000000.0))
		tmp = Float64(z + x);
	else
		tmp = Float64(Float64(z + x) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.22e+42) || ~((y <= 380000000.0)))
		tmp = z + x;
	else
		tmp = (z + x) + (y * (1.0 + (-0.5 * (z * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.22e+42], N[Not[LessEqual[y, 380000000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(N[(z + x), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e42 or 3.8e8 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 41.1%

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

      1. +-commutative 41.1%

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

   5. Simplified 41.1%

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

   if -1.22e42 < y < 3.8e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.8%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ 92.8%

         \[\leadsto \color{blue}{\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)} \]

      2. +-commutative 92.8%

         \[\leadsto \color{blue}{\left(z + x\right)} + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right) \]

      3. *-commutative 92.8%

         \[\leadsto \left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

   5. Simplified 92.8%

      \[\leadsto \color{blue}{\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+42} \lor \neg \left(y \leq 380000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + y \cdot \left(1 + -0.5 \cdot \left(z \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+80} \lor \neg \left(y \leq 430000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.5e+80) (not (<= y 430000000.0))) (+ z x) (+ y (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5e+80) || !(y <= 430000000.0)) {
		tmp = z + x;
	} else {
		tmp = y + (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 <= (-8.5d+80)) .or. (.not. (y <= 430000000.0d0))) then
        tmp = z + x
    else
        tmp = y + (z + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5e+80) || !(y <= 430000000.0)) {
		tmp = z + x;
	} else {
		tmp = y + (z + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.5e+80) or not (y <= 430000000.0):
		tmp = z + x
	else:
		tmp = y + (z + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.5e+80) || !(y <= 430000000.0))
		tmp = Float64(z + x);
	else
		tmp = Float64(y + Float64(z + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.5e+80) || ~((y <= 430000000.0)))
		tmp = z + x;
	else
		tmp = y + (z + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.5e+80], N[Not[LessEqual[y, 430000000.0]], $MachinePrecision]], N[(z + x), $MachinePrecision], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000007e80 or 4.3e8 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 38.3%

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

      1. +-commutative 38.3%

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

   5. Simplified 38.3%

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

   if -8.50000000000000007e80 < y < 4.3e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-+l+ 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+80} \lor \neg \left(y \leq 430000000\right):\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;y + \left(z + x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.2% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-20}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -9.5e-48) x (if (<= x 1.5e-20) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -9.5e-48) {
		tmp = x;
	} else if (x <= 1.5e-20) {
		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 <= (-9.5d-48)) then
        tmp = x
    else if (x <= 1.5d-20) 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 <= -9.5e-48) {
		tmp = x;
	} else if (x <= 1.5e-20) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -9.5e-48:
		tmp = x
	elif x <= 1.5e-20:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -9.5e-48)
		tmp = x;
	elseif (x <= 1.5e-20)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -9.5e-48)
		tmp = x;
	elseif (x <= 1.5e-20)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -9.5e-48], x, If[LessEqual[x, 1.5e-20], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000036e-48 or 1.50000000000000014e-20 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.4%

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

   if -9.50000000000000036e-48 < x < 1.50000000000000014e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 92.0%

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

   4. Taylor expanded in y around 0 38.2%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-20}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% 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. Add Preprocessing

3. Taylor expanded in y around 0 64.4%

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

   1. +-commutative 64.4%

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

5. Simplified 64.4%

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

6. Final simplification 64.4%

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

Alternative 10: 41.6% 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. Add Preprocessing

3. Taylor expanded in x around inf 44.1%

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

4. Final simplification 44.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024112 
(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))))