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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 13

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(z * N[Cos[y], $MachinePrecision]), $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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 71.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -4 \cdot 10^{+169}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-134}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-257}:\\ \;\;\;\;\sin y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+104}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -4e+169)
     t_0
     (if (<= z -4e-134)
       (+ x z)
       (if (<= z -4.1e-257) (sin y) (if (<= z 2.7e+104) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -4e+169) {
		tmp = t_0;
	} else if (z <= -4e-134) {
		tmp = x + z;
	} else if (z <= -4.1e-257) {
		tmp = sin(y);
	} else if (z <= 2.7e+104) {
		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 <= (-4d+169)) then
        tmp = t_0
    else if (z <= (-4d-134)) then
        tmp = x + z
    else if (z <= (-4.1d-257)) then
        tmp = sin(y)
    else if (z <= 2.7d+104) 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 <= -4e+169) {
		tmp = t_0;
	} else if (z <= -4e-134) {
		tmp = x + z;
	} else if (z <= -4.1e-257) {
		tmp = Math.sin(y);
	} else if (z <= 2.7e+104) {
		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 <= -4e+169:
		tmp = t_0
	elif z <= -4e-134:
		tmp = x + z
	elif z <= -4.1e-257:
		tmp = math.sin(y)
	elif z <= 2.7e+104:
		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 <= -4e+169)
		tmp = t_0;
	elseif (z <= -4e-134)
		tmp = Float64(x + z);
	elseif (z <= -4.1e-257)
		tmp = sin(y);
	elseif (z <= 2.7e+104)
		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 <= -4e+169)
		tmp = t_0;
	elseif (z <= -4e-134)
		tmp = x + z;
	elseif (z <= -4.1e-257)
		tmp = sin(y);
	elseif (z <= 2.7e+104)
		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, -4e+169], t$95$0, If[LessEqual[z, -4e-134], N[(x + z), $MachinePrecision], If[LessEqual[z, -4.1e-257], N[Sin[y], $MachinePrecision], If[LessEqual[z, 2.7e+104], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999974e169 or 2.69999999999999985e104 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 83.3%

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

   if -3.99999999999999974e169 < z < -4.00000000000000016e-134 or -4.0999999999999997e-257 < z < 2.69999999999999985e104

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.8%

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

   if -4.00000000000000016e-134 < z < -4.0999999999999997e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.3%

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

   4. Taylor expanded in z around 0 78.7%

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

Alternative 3: 79.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \sin y\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -165:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 1200000000000:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (sin y))))
   (if (<= y -6.2e+76)
     t_0
     (if (<= y -165.0)
       (* z (cos y))
       (if (<= y 1200000000000.0)
         (+
          x
          (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x + sin(y);
	double tmp;
	if (y <= -6.2e+76) {
		tmp = t_0;
	} else if (y <= -165.0) {
		tmp = z * cos(y);
	} else if (y <= 1200000000000.0) {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	} 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 = x + sin(y)
    if (y <= (-6.2d+76)) then
        tmp = t_0
    else if (y <= (-165.0d0)) then
        tmp = z * cos(y)
    else if (y <= 1200000000000.0d0) then
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + Math.sin(y);
	double tmp;
	if (y <= -6.2e+76) {
		tmp = t_0;
	} else if (y <= -165.0) {
		tmp = z * Math.cos(y);
	} else if (y <= 1200000000000.0) {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + math.sin(y)
	tmp = 0
	if y <= -6.2e+76:
		tmp = t_0
	elif y <= -165.0:
		tmp = z * math.cos(y)
	elif y <= 1200000000000.0:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + sin(y))
	tmp = 0.0
	if (y <= -6.2e+76)
		tmp = t_0;
	elseif (y <= -165.0)
		tmp = Float64(z * cos(y));
	elseif (y <= 1200000000000.0)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + sin(y);
	tmp = 0.0;
	if (y <= -6.2e+76)
		tmp = t_0;
	elseif (y <= -165.0)
		tmp = z * cos(y);
	elseif (y <= 1200000000000.0)
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+76], t$95$0, If[LessEqual[y, -165.0], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1200000000000.0], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.20000000000000023e76 or 1.2e12 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 67.6%

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

      1. +-commutative 67.6%

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

   5. Simplified 67.6%

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

   if -6.20000000000000023e76 < y < -165

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 73.3%

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

   if -165 < y < 1.2e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;y \leq -165:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 1200000000000:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \lor \neg \left(z \leq 1.9\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.25) (not (<= z 1.9)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.25) || !(z <= 1.9)) {
		tmp = x + (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 <= (-1.25d0)) .or. (.not. (z <= 1.9d0))) then
        tmp = x + (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 <= -1.25) || !(z <= 1.9)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.25) or not (z <= 1.9):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.25) || !(z <= 1.9))
		tmp = Float64(x + 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 <= -1.25) || ~((z <= 1.9)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.25], N[Not[LessEqual[z, 1.9]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25 or 1.8999999999999999 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 97.6%

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

   if -1.25 < z < 1.8999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \lor \neg \left(z \leq 1.9\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-37} \lor \neg \left(z \leq 1.9 \cdot 10^{-81}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.8e-37) (not (<= z 1.9e-81)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e-37) || !(z <= 1.9e-81)) {
		tmp = x + (z * cos(y));
	} 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) :: tmp
    if ((z <= (-6.8d-37)) .or. (.not. (z <= 1.9d-81))) then
        tmp = x + (z * cos(y))
    else
        tmp = x + sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.8e-37) || !(z <= 1.9e-81)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.8e-37) or not (z <= 1.9e-81):
		tmp = x + (z * math.cos(y))
	else:
		tmp = x + math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -6.8e-37) || !(z <= 1.9e-81))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(x + sin(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -6.8e-37) || ~((z <= 1.9e-81)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -6.8e-37], N[Not[LessEqual[z, 1.9e-81]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.80000000000000037e-37 or 1.8999999999999999e-81 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 94.9%

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

   if -6.80000000000000037e-37 < z < 1.8999999999999999e-81

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.7%

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

      1. +-commutative 92.7%

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

   5. Simplified 92.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-37} \lor \neg \left(z \leq 1.9 \cdot 10^{-81}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -170:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -170.0)
   (+ x z)
   (if (<= y 2.1e+41)
     (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))
     (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -170.0) {
		tmp = x + z;
	} else if (y <= 2.1e+41) {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	} else {
		tmp = 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 (y <= (-170.0d0)) then
        tmp = x + z
    else if (y <= 2.1d+41) then
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    else
        tmp = sin(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -170.0) {
		tmp = x + z;
	} else if (y <= 2.1e+41) {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	} else {
		tmp = Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -170.0:
		tmp = x + z
	elif y <= 2.1e+41:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	else:
		tmp = math.sin(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -170.0)
		tmp = Float64(x + z);
	elseif (y <= 2.1e+41)
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	else
		tmp = sin(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -170.0)
		tmp = x + z;
	elseif (y <= 2.1e+41)
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	else
		tmp = sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -170.0], N[(x + z), $MachinePrecision], If[LessEqual[y, 2.1e+41], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[y], $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -170

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 44.4%

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

   if -170 < y < 2.1e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.0%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]

   if 2.1e41 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 78.5%

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

   4. Taylor expanded in z around 0 41.4%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -170:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -170 \lor \neg \left(y \leq 15000000000000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -170.0) (not (<= y 15000000000000.0)))
   (+ x z)
   (+ x (+ z (* y (+ 1.0 (* y (+ (* z -0.5) (* y -0.16666666666666666)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -170.0) || !(y <= 15000000000000.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	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 <= (-170.0d0)) .or. (.not. (y <= 15000000000000.0d0))) then
        tmp = x + z
    else
        tmp = x + (z + (y * (1.0d0 + (y * ((z * (-0.5d0)) + (y * (-0.16666666666666666d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -170.0) || !(y <= 15000000000000.0)) {
		tmp = x + z;
	} else {
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -170.0) or not (y <= 15000000000000.0):
		tmp = x + z
	else:
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -170.0) || !(y <= 15000000000000.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(x + Float64(z + Float64(y * Float64(1.0 + Float64(y * Float64(Float64(z * -0.5) + Float64(y * -0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -170.0) || ~((y <= 15000000000000.0)))
		tmp = x + z;
	else
		tmp = x + (z + (y * (1.0 + (y * ((z * -0.5) + (y * -0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -170.0], N[Not[LessEqual[y, 15000000000000.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(x + N[(z + N[(y * N[(1.0 + N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -170 or 1.5e13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 37.5%

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

   if -170 < y < 1.5e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

      \[\leadsto \color{blue}{x + \left(z + y \cdot \left(1 + y \cdot \left(-0.5 \cdot z + -0.16666666666666666 \cdot y\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -170 \lor \neg \left(y \leq 15000000000000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + y \cdot \left(1 + y \cdot \left(z \cdot -0.5 + y \cdot -0.16666666666666666\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -105 \lor \neg \left(y \leq 13000000000000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -105.0) (not (<= y 13000000000000.0)))
   (+ x z)
   (+ (+ x z) (* y (+ 1.0 (* -0.5 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -105.0) || !(y <= 13000000000000.0)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-105.0d0)) .or. (.not. (y <= 13000000000000.0d0))) then
        tmp = x + z
    else
        tmp = (x + z) + (y * (1.0d0 + ((-0.5d0) * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -105.0) || !(y <= 13000000000000.0)) {
		tmp = x + z;
	} else {
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -105.0) or not (y <= 13000000000000.0):
		tmp = x + z
	else:
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -105.0) || !(y <= 13000000000000.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(Float64(x + z) + Float64(y * Float64(1.0 + Float64(-0.5 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -105.0) || ~((y <= 13000000000000.0)))
		tmp = x + z;
	else
		tmp = (x + z) + (y * (1.0 + (-0.5 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -105.0], N[Not[LessEqual[y, 13000000000000.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[(x + z), $MachinePrecision] + N[(y * N[(1.0 + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -105 or 1.3e13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 37.5%

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

   if -105 < y < 1.3e13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. associate-+r+ 99.3%

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

   5. Simplified 99.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -105 \lor \neg \left(y \leq 13000000000000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + y \cdot \left(1 + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+46} \lor \neg \left(y \leq 3.2\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e+46) (not (<= y 3.2))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e+46) || !(y <= 3.2)) {
		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 <= (-2.9d+46)) .or. (.not. (y <= 3.2d0))) 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 <= -2.9e+46) || !(y <= 3.2)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e+46) or not (y <= 3.2):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e+46) || !(y <= 3.2))
		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 <= -2.9e+46) || ~((y <= 3.2)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e+46], N[Not[LessEqual[y, 3.2]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000002e46 or 3.2000000000000002 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 38.0%

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

   if -2.9000000000000002e46 < y < 3.2000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.2%

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

      1. associate-+r+ 97.2%

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

      2. +-commutative 97.2%

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

   5. Simplified 97.2%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+46} \lor \neg \left(y \leq 3.2\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 68.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-102} \lor \neg \left(x \leq 8.5 \cdot 10^{-132}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e-102) (not (<= x 8.5e-132))) (+ x z) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-102) || !(x <= 8.5e-132)) {
		tmp = x + z;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.7d-102)) .or. (.not. (x <= 8.5d-132))) then
        tmp = x + z
    else
        tmp = y + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-102) || !(x <= 8.5e-132)) {
		tmp = x + z;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e-102) or not (x <= 8.5e-132):
		tmp = x + z
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e-102) || !(x <= 8.5e-132))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.7e-102) || ~((x <= 8.5e-132)))
		tmp = x + z;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e-102], N[Not[LessEqual[x, 8.5e-132]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7e-102 or 8.49999999999999988e-132 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

   if -2.7e-102 < x < 8.49999999999999988e-132

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.7%

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

   4. Taylor expanded in y around 0 55.6%

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

      1. +-commutative 55.6%

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

   6. Simplified 55.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-102} \lor \neg \left(x \leq 8.5 \cdot 10^{-132}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -75:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 130000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -75.0) x (if (<= x 130000000.0) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -75.0) {
		tmp = x;
	} else if (x <= 130000000.0) {
		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 <= (-75.0d0)) then
        tmp = x
    else if (x <= 130000000.0d0) 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 <= -75.0) {
		tmp = x;
	} else if (x <= 130000000.0) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -75.0:
		tmp = x
	elif x <= 130000000.0:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -75.0)
		tmp = x;
	elseif (x <= 130000000.0)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -75.0)
		tmp = x;
	elseif (x <= 130000000.0)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -75.0], x, If[LessEqual[x, 130000000.0], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -75 or 1.3e8 < x

   1. Initial program 100.0%

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

      1. expm1-log1p-u 100.0%

         \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

   5. Taylor expanded in x around inf 80.6%

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

   if -75 < x < 1.3e8

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 58.7%

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

   4. Taylor expanded in y around 0 40.4%

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

Alternative 12: 66.8% 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. Add Preprocessing

3. Taylor expanded in y around 0 64.9%

   \[\leadsto \color{blue}{x + z} \]
4. Add Preprocessing

Alternative 13: 42.5% 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. Step-by-step derivation

   1. expm1-log1p-u 99.9%

      \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

4. Applied egg-rr 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y\right)\right)} \]

5. Taylor expanded in x around inf 40.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024152 
(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))))