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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

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: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-5} \lor \neg \left(x \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.6e-5) (not (<= x 1.15e+22)))
   (+ x z)
   (+ (sin y) (* z (cos y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e-5) || !(x <= 1.15e+22)) {
		tmp = x + z;
	} else {
		tmp = sin(y) + (z * cos(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7.6d-5)) .or. (.not. (x <= 1.15d+22))) then
        tmp = x + z
    else
        tmp = sin(y) + (z * cos(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.6e-5) || !(x <= 1.15e+22)) {
		tmp = x + z;
	} else {
		tmp = Math.sin(y) + (z * Math.cos(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.6e-5) or not (x <= 1.15e+22):
		tmp = x + z
	else:
		tmp = math.sin(y) + (z * math.cos(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.6e-5) || !(x <= 1.15e+22))
		tmp = Float64(x + z);
	else
		tmp = Float64(sin(y) + Float64(z * cos(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.6e-5) || ~((x <= 1.15e+22)))
		tmp = x + z;
	else
		tmp = sin(y) + (z * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.6e-5], N[Not[LessEqual[x, 1.15e+22]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000004e-5 or 1.1500000000000001e22 < 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 88.9%

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

      1. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -7.6000000000000004e-5 < x < 1.1500000000000001e22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.8%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{-5} \lor \neg \left(x \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;\sin y + z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;x \leq -0.0142:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-296}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= x -0.0142)
     (+ x z)
     (if (<= x 5.2e-296)
       t_0
       (if (<= x 1.55e-214) (+ z (+ x y)) (if (<= x 1.32e+22) t_0 (+ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (x <= -0.0142) {
		tmp = x + z;
	} else if (x <= 5.2e-296) {
		tmp = t_0;
	} else if (x <= 1.55e-214) {
		tmp = z + (x + y);
	} else if (x <= 1.32e+22) {
		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 (x <= (-0.0142d0)) then
        tmp = x + z
    else if (x <= 5.2d-296) then
        tmp = t_0
    else if (x <= 1.55d-214) then
        tmp = z + (x + y)
    else if (x <= 1.32d+22) 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 (x <= -0.0142) {
		tmp = x + z;
	} else if (x <= 5.2e-296) {
		tmp = t_0;
	} else if (x <= 1.55e-214) {
		tmp = z + (x + y);
	} else if (x <= 1.32e+22) {
		tmp = t_0;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if x <= -0.0142:
		tmp = x + z
	elif x <= 5.2e-296:
		tmp = t_0
	elif x <= 1.55e-214:
		tmp = z + (x + y)
	elif x <= 1.32e+22:
		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 (x <= -0.0142)
		tmp = Float64(x + z);
	elseif (x <= 5.2e-296)
		tmp = t_0;
	elseif (x <= 1.55e-214)
		tmp = Float64(z + Float64(x + y));
	elseif (x <= 1.32e+22)
		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 (x <= -0.0142)
		tmp = x + z;
	elseif (x <= 5.2e-296)
		tmp = t_0;
	elseif (x <= 1.55e-214)
		tmp = z + (x + y);
	elseif (x <= 1.32e+22)
		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[x, -0.0142], N[(x + z), $MachinePrecision], If[LessEqual[x, 5.2e-296], t$95$0, If[LessEqual[x, 1.55e-214], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e+22], t$95$0, N[(x + z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.014200000000000001 or 1.32e22 < 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 88.9%

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

      1. +-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -0.014200000000000001 < x < 5.2000000000000001e-296 or 1.55000000000000002e-214 < x < 1.32e22

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 67.3%

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

   if 5.2000000000000001e-296 < x < 1.55000000000000002e-214

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.5%

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

      1. +-commutative 79.5%

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

      2. +-commutative 79.5%

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

      3. associate-+l+ 79.5%

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

   5. Simplified 79.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0142:\\ \;\;\;\;x + z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-296}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-214}:\\ \;\;\;\;z + \left(x + y\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{+128}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-40}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 5.05 \cdot 10^{-64}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+197}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -2.45e+128)
     t_0
     (if (<= z -2.75e-40)
       (+ x z)
       (if (<= z 5.05e-64) (+ x (sin y)) (if (<= z 2.35e+197) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -2.45e+128) {
		tmp = t_0;
	} else if (z <= -2.75e-40) {
		tmp = x + z;
	} else if (z <= 5.05e-64) {
		tmp = x + sin(y);
	} else if (z <= 2.35e+197) {
		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 <= (-2.45d+128)) then
        tmp = t_0
    else if (z <= (-2.75d-40)) then
        tmp = x + z
    else if (z <= 5.05d-64) then
        tmp = x + sin(y)
    else if (z <= 2.35d+197) 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 <= -2.45e+128) {
		tmp = t_0;
	} else if (z <= -2.75e-40) {
		tmp = x + z;
	} else if (z <= 5.05e-64) {
		tmp = x + Math.sin(y);
	} else if (z <= 2.35e+197) {
		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 <= -2.45e+128:
		tmp = t_0
	elif z <= -2.75e-40:
		tmp = x + z
	elif z <= 5.05e-64:
		tmp = x + math.sin(y)
	elif z <= 2.35e+197:
		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 <= -2.45e+128)
		tmp = t_0;
	elseif (z <= -2.75e-40)
		tmp = Float64(x + z);
	elseif (z <= 5.05e-64)
		tmp = Float64(x + sin(y));
	elseif (z <= 2.35e+197)
		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 <= -2.45e+128)
		tmp = t_0;
	elseif (z <= -2.75e-40)
		tmp = x + z;
	elseif (z <= 5.05e-64)
		tmp = x + sin(y);
	elseif (z <= 2.35e+197)
		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, -2.45e+128], t$95$0, If[LessEqual[z, -2.75e-40], N[(x + z), $MachinePrecision], If[LessEqual[z, 5.05e-64], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.35e+197], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000009e128 or 2.35e197 < 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 82.7%

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

   if -2.45000000000000009e128 < z < -2.75000000000000001e-40 or 5.05000000000000009e-64 < z < 2.35e197

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.1%

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

      1. +-commutative 78.1%

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

   5. Simplified 78.1%

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

   if -2.75000000000000001e-40 < z < 5.05000000000000009e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 95.0%

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

      1. +-commutative 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+128}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-40}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 5.05 \cdot 10^{-64}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+197}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.7% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+32} \lor \neg \left(y \leq 7.5 \cdot 10^{+23}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4e+32) (not (<= y 7.5e+23))) (+ x z) (+ z (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+32) || !(y <= 7.5e+23)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4d+32)) .or. (.not. (y <= 7.5d+23))) then
        tmp = x + z
    else
        tmp = z + (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4e+32) || !(y <= 7.5e+23)) {
		tmp = x + z;
	} else {
		tmp = z + (x + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4e+32) or not (y <= 7.5e+23):
		tmp = x + z
	else:
		tmp = z + (x + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4e+32) || !(y <= 7.5e+23))
		tmp = Float64(x + z);
	else
		tmp = Float64(z + Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4e+32) || ~((y <= 7.5e+23)))
		tmp = x + z;
	else
		tmp = z + (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4e+32], N[Not[LessEqual[y, 7.5e+23]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z + N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.00000000000000021e32 or 7.49999999999999987e23 < 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 49.5%

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

      1. +-commutative 49.5%

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

   5. Simplified 49.5%

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

   if -4.00000000000000021e32 < y < 7.49999999999999987e23

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. +-commutative 93.3%

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

      3. associate-+l+ 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+32} \lor \neg \left(y \leq 7.5 \cdot 10^{+23}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.4% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.000175:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.000175) x (if (<= x 1.2e+22) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.000175) {
		tmp = x;
	} else if (x <= 1.2e+22) {
		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 <= (-0.000175d0)) then
        tmp = x
    else if (x <= 1.2d+22) 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 <= -0.000175) {
		tmp = x;
	} else if (x <= 1.2e+22) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.000175:
		tmp = x
	elif x <= 1.2e+22:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.000175)
		tmp = x;
	elseif (x <= 1.2e+22)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.000175)
		tmp = x;
	elseif (x <= 1.2e+22)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.000175], x, If[LessEqual[x, 1.2e+22], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.74999999999999998e-4 or 1.2e22 < 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 81.0%

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

   if -1.74999999999999998e-4 < x < 1.2e22

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 65.4%

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

   4. Taylor expanded in y around 0 41.7%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.000175:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.5% 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 68.6%

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

   1. +-commutative 68.6%

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

5. Simplified 68.6%

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

6. Final simplification 68.6%

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

Alternative 8: 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 45.2%

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

4. Final simplification 45.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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))))