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

Percentage Accurate: 99.9% → 99.9%

Time: 7.7s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.5e-21)
   (+ (+ x (sin y)) z)
   (if (<= x 4.1e+14) (+ (sin y) (* z (cos y))) (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-21) {
		tmp = (x + sin(y)) + z;
	} else if (x <= 4.1e+14) {
		tmp = sin(y) + (z * cos(y));
	} else {
		tmp = x + 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 <= (-4.5d-21)) then
        tmp = (x + sin(y)) + z
    else if (x <= 4.1d+14) then
        tmp = sin(y) + (z * cos(y))
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.5e-21) {
		tmp = (x + Math.sin(y)) + z;
	} else if (x <= 4.1e+14) {
		tmp = Math.sin(y) + (z * Math.cos(y));
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.5e-21:
		tmp = (x + math.sin(y)) + z
	elif x <= 4.1e+14:
		tmp = math.sin(y) + (z * math.cos(y))
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.5e-21)
		tmp = Float64(Float64(x + sin(y)) + z);
	elseif (x <= 4.1e+14)
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.5e-21)
		tmp = (x + sin(y)) + z;
	elseif (x <= 4.1e+14)
		tmp = sin(y) + (z * cos(y));
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.5e-21], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 4.1e+14], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.49999999999999968e-21

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 89.5%

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

   if -4.49999999999999968e-21 < x < 4.1e14

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 92.5%

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

   if 4.1e14 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.4%

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

      1. +-commutative 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+29} \lor \neg \left(z \leq 1.1 \cdot 10^{+42}\right) \land \left(z \leq 9.2 \cdot 10^{+144} \lor \neg \left(z \leq 1.35 \cdot 10^{+181}\right)\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e+29)
         (and (not (<= z 1.1e+42))
              (or (<= z 9.2e+144) (not (<= z 1.35e+181)))))
   (* z (cos y))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+29) || (!(z <= 1.1e+42) && ((z <= 9.2e+144) || !(z <= 1.35e+181)))) {
		tmp = z * cos(y);
	} else {
		tmp = (x + sin(y)) + z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.8d+29)) .or. (.not. (z <= 1.1d+42)) .and. (z <= 9.2d+144) .or. (.not. (z <= 1.35d+181))) then
        tmp = z * cos(y)
    else
        tmp = (x + sin(y)) + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e+29) || (!(z <= 1.1e+42) && ((z <= 9.2e+144) || !(z <= 1.35e+181)))) {
		tmp = z * Math.cos(y);
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e+29) or (not (z <= 1.1e+42) and ((z <= 9.2e+144) or not (z <= 1.35e+181))):
		tmp = z * math.cos(y)
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e+29) || (!(z <= 1.1e+42) && ((z <= 9.2e+144) || !(z <= 1.35e+181))))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(Float64(x + sin(y)) + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e+29) || (~((z <= 1.1e+42)) && ((z <= 9.2e+144) || ~((z <= 1.35e+181)))))
		tmp = z * cos(y);
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e+29], And[N[Not[LessEqual[z, 1.1e+42]], $MachinePrecision], Or[LessEqual[z, 9.2e+144], N[Not[LessEqual[z, 1.35e+181]], $MachinePrecision]]]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.79999999999999988e29 or 1.1000000000000001e42 < z < 9.2000000000000006e144 or 1.35000000000000004e181 < 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 87.8%

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

   if -1.79999999999999988e29 < z < 1.1000000000000001e42 or 9.2000000000000006e144 < z < 1.35000000000000004e181

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+29} \lor \neg \left(z \leq 1.1 \cdot 10^{+42}\right) \land \left(z \leq 9.2 \cdot 10^{+144} \lor \neg \left(z \leq 1.35 \cdot 10^{+181}\right)\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -20.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+145} \lor \neg \left(z \leq 1.25 \cdot 10^{+181}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -20.5)
     t_0
     (if (<= z 4.3e+39)
       (+ x (sin y))
       (if (or (<= z 1.25e+145) (not (<= z 1.25e+181))) t_0 (+ x z))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -20.5) {
		tmp = t_0;
	} else if (z <= 4.3e+39) {
		tmp = x + sin(y);
	} else if ((z <= 1.25e+145) || !(z <= 1.25e+181)) {
		tmp = t_0;
	} else {
		tmp = x + 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (z <= (-20.5d0)) then
        tmp = t_0
    else if (z <= 4.3d+39) then
        tmp = x + sin(y)
    else if ((z <= 1.25d+145) .or. (.not. (z <= 1.25d+181))) then
        tmp = t_0
    else
        tmp = x + z
    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 <= -20.5) {
		tmp = t_0;
	} else if (z <= 4.3e+39) {
		tmp = x + Math.sin(y);
	} else if ((z <= 1.25e+145) || !(z <= 1.25e+181)) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -20.5:
		tmp = t_0
	elif z <= 4.3e+39:
		tmp = x + math.sin(y)
	elif (z <= 1.25e+145) or not (z <= 1.25e+181):
		tmp = t_0
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -20.5)
		tmp = t_0;
	elseif (z <= 4.3e+39)
		tmp = Float64(x + sin(y));
	elseif ((z <= 1.25e+145) || !(z <= 1.25e+181))
		tmp = t_0;
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (z <= -20.5)
		tmp = t_0;
	elseif (z <= 4.3e+39)
		tmp = x + sin(y);
	elseif ((z <= 1.25e+145) || ~((z <= 1.25e+181)))
		tmp = t_0;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -20.5], t$95$0, If[LessEqual[z, 4.3e+39], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.25e+145], N[Not[LessEqual[z, 1.25e+181]], $MachinePrecision]], t$95$0, N[(x + z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -20.5 or 4.3e39 < z < 1.24999999999999992e145 or 1.2500000000000001e181 < 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 85.4%

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

   if -20.5 < z < 4.3e39

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.1%

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

      1. +-commutative 92.1%

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

   5. Simplified 92.1%

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

   if 1.24999999999999992e145 < z < 1.2500000000000001e181

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 88.1%

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

      1. +-commutative 88.1%

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

   5. Simplified 88.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20.5:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+39}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+145} \lor \neg \left(z \leq 1.25 \cdot 10^{+181}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-93}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.4e-48)
   (+ x z)
   (if (<= x 7.2e-93)
     (+ (sin y) z)
     (if (<= x 19000000.0) (* z (cos y)) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-48) {
		tmp = x + z;
	} else if (x <= 7.2e-93) {
		tmp = sin(y) + z;
	} else if (x <= 19000000.0) {
		tmp = z * cos(y);
	} else {
		tmp = x + 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 <= (-2.4d-48)) then
        tmp = x + z
    else if (x <= 7.2d-93) then
        tmp = sin(y) + z
    else if (x <= 19000000.0d0) then
        tmp = z * cos(y)
    else
        tmp = x + z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.4e-48) {
		tmp = x + z;
	} else if (x <= 7.2e-93) {
		tmp = Math.sin(y) + z;
	} else if (x <= 19000000.0) {
		tmp = z * Math.cos(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.4e-48:
		tmp = x + z
	elif x <= 7.2e-93:
		tmp = math.sin(y) + z
	elif x <= 19000000.0:
		tmp = z * math.cos(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.4e-48)
		tmp = Float64(x + z);
	elseif (x <= 7.2e-93)
		tmp = Float64(sin(y) + z);
	elseif (x <= 19000000.0)
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.4e-48)
		tmp = x + z;
	elseif (x <= 7.2e-93)
		tmp = sin(y) + z;
	elseif (x <= 19000000.0)
		tmp = z * cos(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.4e-48], N[(x + z), $MachinePrecision], If[LessEqual[x, 7.2e-93], N[(N[Sin[y], $MachinePrecision] + z), $MachinePrecision], If[LessEqual[x, 19000000.0], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.4e-48 or 1.9e7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 86.0%

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

      1. +-commutative 86.0%

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

   5. Simplified 86.0%

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

   if -2.4e-48 < x < 7.2000000000000003e-93

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 74.6%

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

   4. Taylor expanded in x around 0 68.0%

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

   if 7.2000000000000003e-93 < x < 1.9e7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 86.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-93}:\\ \;\;\;\;\sin y + z\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-20} \lor \neg \left(x \leq 14500000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e-20) (not (<= x 14500000.0))) (+ x z) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e-20) || !(x <= 14500000.0)) {
		tmp = x + z;
	} else {
		tmp = 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 <= (-6.2d-20)) .or. (.not. (x <= 14500000.0d0))) then
        tmp = x + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e-20) || !(x <= 14500000.0)) {
		tmp = x + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e-20) or not (x <= 14500000.0):
		tmp = x + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e-20) || !(x <= 14500000.0))
		tmp = Float64(x + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.2e-20) || ~((x <= 14500000.0)))
		tmp = x + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e-20], N[Not[LessEqual[x, 14500000.0]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.19999999999999999e-20 or 1.45e7 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. +-commutative 87.2%

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

   5. Simplified 87.2%

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

   if -6.19999999999999999e-20 < x < 1.45e7

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 67.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-20} \lor \neg \left(x \leq 14500000\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+50} \lor \neg \left(y \leq 3.2\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.65e+50) (not (<= y 3.2))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e+50) || !(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 <= (-2.65d+50)) .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 <= -2.65e+50) || !(y <= 3.2)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.65e+50) 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 <= -2.65e+50) || !(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 <= -2.65e+50) || ~((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, -2.65e+50], 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 < -2.6500000000000001e50 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 43.5%

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

      1. +-commutative 43.5%

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

   5. Simplified 43.5%

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

   if -2.6500000000000001e50 < 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 91.7%

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

      1. +-commutative 91.7%

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

      2. +-commutative 91.7%

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

      3. associate-+l+ 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+50} \lor \neg \left(y \leq 3.2\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% 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 67.6%

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

   1. +-commutative 67.6%

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

5. Simplified 67.6%

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

6. Final simplification 67.6%

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

Alternative 9: 42.4% 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 41.3%

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

4. Final simplification 41.3%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024040 
(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))))