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

Percentage Accurate: 99.9% → 99.9%

Time: 8.3s

Alternatives: 12

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. Add Preprocessing

Alternative 2: 85.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-25}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-22}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+146}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.75e+162)
     t_0
     (if (<= z -7.2e-25)
       (+ x z)
       (if (<= z 1.22e-22) (+ x (sin y)) (if (<= z 1.45e+146) (+ x z) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.75e+162) {
		tmp = t_0;
	} else if (z <= -7.2e-25) {
		tmp = x + z;
	} else if (z <= 1.22e-22) {
		tmp = x + sin(y);
	} else if (z <= 1.45e+146) {
		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 <= (-1.75d+162)) then
        tmp = t_0
    else if (z <= (-7.2d-25)) then
        tmp = x + z
    else if (z <= 1.22d-22) then
        tmp = x + sin(y)
    else if (z <= 1.45d+146) 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 <= -1.75e+162) {
		tmp = t_0;
	} else if (z <= -7.2e-25) {
		tmp = x + z;
	} else if (z <= 1.22e-22) {
		tmp = x + Math.sin(y);
	} else if (z <= 1.45e+146) {
		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 <= -1.75e+162:
		tmp = t_0
	elif z <= -7.2e-25:
		tmp = x + z
	elif z <= 1.22e-22:
		tmp = x + math.sin(y)
	elif z <= 1.45e+146:
		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 <= -1.75e+162)
		tmp = t_0;
	elseif (z <= -7.2e-25)
		tmp = Float64(x + z);
	elseif (z <= 1.22e-22)
		tmp = Float64(x + sin(y));
	elseif (z <= 1.45e+146)
		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 <= -1.75e+162)
		tmp = t_0;
	elseif (z <= -7.2e-25)
		tmp = x + z;
	elseif (z <= 1.22e-22)
		tmp = x + sin(y);
	elseif (z <= 1.45e+146)
		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, -1.75e+162], t$95$0, If[LessEqual[z, -7.2e-25], N[(x + z), $MachinePrecision], If[LessEqual[z, 1.22e-22], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+146], N[(x + z), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75000000000000009e162 or 1.4499999999999999e146 < z

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

   6. Taylor expanded in x around 0 88.2%

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

   if -1.75000000000000009e162 < z < -7.1999999999999998e-25 or 1.2200000000000001e-22 < z < 1.4499999999999999e146

   1. Initial program 99.9%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 82.3%

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

      1. +-commutative 82.3%

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

   7. Simplified 82.3%

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

   if -7.1999999999999998e-25 < z < 1.2200000000000001e-22

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 93.7%

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

      1. +-commutative 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-25}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-22}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+146}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+14}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+98}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.6e+14)
   (+ x z)
   (if (<= y 3.1e+18) (+ y (+ x z)) (if (<= y 1.08e+98) (sin y) (+ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e+14) {
		tmp = x + z;
	} else if (y <= 3.1e+18) {
		tmp = y + (x + z);
	} else if (y <= 1.08e+98) {
		tmp = sin(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 (y <= (-5.6d+14)) then
        tmp = x + z
    else if (y <= 3.1d+18) then
        tmp = y + (x + z)
    else if (y <= 1.08d+98) then
        tmp = sin(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 (y <= -5.6e+14) {
		tmp = x + z;
	} else if (y <= 3.1e+18) {
		tmp = y + (x + z);
	} else if (y <= 1.08e+98) {
		tmp = Math.sin(y);
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.6e+14:
		tmp = x + z
	elif y <= 3.1e+18:
		tmp = y + (x + z)
	elif y <= 1.08e+98:
		tmp = math.sin(y)
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.6e+14)
		tmp = Float64(x + z);
	elseif (y <= 3.1e+18)
		tmp = Float64(y + Float64(x + z));
	elseif (y <= 1.08e+98)
		tmp = sin(y);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.6e+14)
		tmp = x + z;
	elseif (y <= 3.1e+18)
		tmp = y + (x + z);
	elseif (y <= 1.08e+98)
		tmp = sin(y);
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.6e+14], N[(x + z), $MachinePrecision], If[LessEqual[y, 3.1e+18], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+98], N[Sin[y], $MachinePrecision], N[(x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6e14 or 1.07999999999999997e98 < y

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 45.0%

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

      1. +-commutative 45.0%

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

   7. Simplified 45.0%

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

   if -5.6e14 < y < 3.1e18

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 96.4%

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

      1. +-commutative 96.4%

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

      2. associate-+l+ 96.4%

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

   7. Simplified 96.4%

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

   if 3.1e18 < y < 1.07999999999999997e98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.8%

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

   4. Taylor expanded in z around 0 58.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+14}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+18}:\\ \;\;\;\;y + \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+98}:\\ \;\;\;\;\sin y\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+30} \lor \neg \left(z \leq 5.6 \cdot 10^{-22}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.75e+30) (not (<= z 5.6e-22)))
   (+ x (* z (cos y)))
   (+ (+ x (sin y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.75e+30) || !(z <= 5.6e-22)) {
		tmp = x + (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 <= (-1.75d+30)) .or. (.not. (z <= 5.6d-22))) then
        tmp = x + (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 <= -1.75e+30) || !(z <= 5.6e-22)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = (x + Math.sin(y)) + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.75e+30) or not (z <= 5.6e-22):
		tmp = x + (z * math.cos(y))
	else:
		tmp = (x + math.sin(y)) + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.75e+30) || !(z <= 5.6e-22))
		tmp = Float64(x + 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 <= -1.75e+30) || ~((z <= 5.6e-22)))
		tmp = x + (z * cos(y));
	else
		tmp = (x + sin(y)) + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.75e+30], N[Not[LessEqual[z, 5.6e-22]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75000000000000011e30 or 5.5999999999999999e-22 < 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 99.0%

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

   if -1.75000000000000011e30 < z < 5.5999999999999999e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+30} \lor \neg \left(z \leq 5.6 \cdot 10^{-22}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + \sin y\right) + z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 6.8 \cdot 10^{-23}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.8e-25) (not (<= z 6.8e-23)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.8e-25) || !(z <= 6.8e-23)) {
		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 <= (-5.8d-25)) .or. (.not. (z <= 6.8d-23))) 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 <= -5.8e-25) || !(z <= 6.8e-23)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.8e-25) or not (z <= 6.8e-23):
		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 <= -5.8e-25) || !(z <= 6.8e-23))
		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 <= -5.8e-25) || ~((z <= 6.8e-23)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.8e-25], N[Not[LessEqual[z, 6.8e-23]], $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 < -5.8000000000000001e-25 or 6.8000000000000001e-23 < 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 98.9%

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

   if -5.8000000000000001e-25 < z < 6.8000000000000001e-23

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around 0 93.7%

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

      1. +-commutative 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 6.8 \cdot 10^{-23}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.58 \cdot 10^{-18} \lor \neg \left(x \leq 1.12 \cdot 10^{-94}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.58e-18) (not (<= x 1.12e-94))) (+ x z) (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.58e-18) || !(x <= 1.12e-94)) {
		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 <= (-1.58d-18)) .or. (.not. (x <= 1.12d-94))) 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 <= -1.58e-18) || !(x <= 1.12e-94)) {
		tmp = x + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.58e-18) or not (x <= 1.12e-94):
		tmp = x + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.58e-18) || !(x <= 1.12e-94))
		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 <= -1.58e-18) || ~((x <= 1.12e-94)))
		tmp = x + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.58e-18], N[Not[LessEqual[x, 1.12e-94]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5800000000000001e-18 or 1.12e-94 < x

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 84.3%

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

      1. +-commutative 84.3%

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

   7. Simplified 84.3%

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

   if -1.5800000000000001e-18 < x < 1.12e-94

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 62.8%

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

   6. Taylor expanded in x around 0 61.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.58 \cdot 10^{-18} \lor \neg \left(x \leq 1.12 \cdot 10^{-94}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.7% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+14} \lor \neg \left(y \leq 2.4 \cdot 10^{+32}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+14) (not (<= y 2.4e+32))) (+ x z) (+ y (+ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+14) || !(y <= 2.4e+32)) {
		tmp = x + z;
	} else {
		tmp = y + (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 ((y <= (-3d+14)) .or. (.not. (y <= 2.4d+32))) then
        tmp = x + z
    else
        tmp = y + (x + z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+14) || !(y <= 2.4e+32)) {
		tmp = x + z;
	} else {
		tmp = y + (x + z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+14) or not (y <= 2.4e+32):
		tmp = x + z
	else:
		tmp = y + (x + z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+14) || !(y <= 2.4e+32))
		tmp = Float64(x + z);
	else
		tmp = Float64(y + Float64(x + z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e+14) || ~((y <= 2.4e+32)))
		tmp = x + z;
	else
		tmp = y + (x + z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+14], N[Not[LessEqual[y, 2.4e+32]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + N[(x + z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e14 or 2.39999999999999991e32 < y

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 42.6%

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

      1. +-commutative 42.6%

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

   7. Simplified 42.6%

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

   if -3e14 < y < 2.39999999999999991e32

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. associate-+l+ 95.2%

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

   7. Simplified 95.2%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+14} \lor \neg \left(y \leq 2.4 \cdot 10^{+32}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.5% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-92} \lor \neg \left(x \leq 1.4 \cdot 10^{-124}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e-92) (not (<= x 1.4e-124))) (+ x z) (+ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-92) || !(x <= 1.4e-124)) {
		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 <= (-4.3d-92)) .or. (.not. (x <= 1.4d-124))) 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 <= -4.3e-92) || !(x <= 1.4e-124)) {
		tmp = x + z;
	} else {
		tmp = y + z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e-92) or not (x <= 1.4e-124):
		tmp = x + z
	else:
		tmp = y + z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e-92) || !(x <= 1.4e-124))
		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 <= -4.3e-92) || ~((x <= 1.4e-124)))
		tmp = x + z;
	else
		tmp = y + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e-92], N[Not[LessEqual[x, 1.4e-124]], $MachinePrecision]], N[(x + z), $MachinePrecision], N[(y + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.30000000000000014e-92 or 1.39999999999999999e-124 < x

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 82.5%

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

      1. +-commutative 82.5%

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

   7. Simplified 82.5%

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

   if -4.30000000000000014e-92 < x < 1.39999999999999999e-124

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.0%

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

   4. Taylor expanded in y around 0 52.6%

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

      1. +-commutative 52.6%

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

   6. Simplified 52.6%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-92} \lor \neg \left(x \leq 1.4 \cdot 10^{-124}\right):\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y + z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.85:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e-22) x (if (<= x 1.85) z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-22) {
		tmp = x;
	} else if (x <= 1.85) {
		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 <= (-1.8d-22)) then
        tmp = x
    else if (x <= 1.85d0) 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 <= -1.8e-22) {
		tmp = x;
	} else if (x <= 1.85) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.8e-22:
		tmp = x
	elif x <= 1.85:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e-22)
		tmp = x;
	elseif (x <= 1.85)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.8e-22)
		tmp = x;
	elseif (x <= 1.85)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e-22], x, If[LessEqual[x, 1.85], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7999999999999999e-22 or 1.8500000000000001 < x

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 80.1%

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

   if -1.7999999999999999e-22 < x < 1.8500000000000001

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 56.2%

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

      1. +-commutative 56.2%

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

      2. associate-+l+ 56.2%

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

   7. Simplified 56.2%

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

   8. Taylor expanded in z around inf 43.3%

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

Alternative 10: 45.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-116}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e-123) x (if (<= x 5.2e-116) y x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-123) {
		tmp = x;
	} else if (x <= 5.2e-116) {
		tmp = y;
	} 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 <= (-1.5d-123)) then
        tmp = x
    else if (x <= 5.2d-116) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e-123) {
		tmp = x;
	} else if (x <= 5.2e-116) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e-123:
		tmp = x
	elif x <= 5.2e-116:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e-123)
		tmp = x;
	elseif (x <= 5.2e-116)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e-123)
		tmp = x;
	elseif (x <= 5.2e-116)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e-123], x, If[LessEqual[x, 5.2e-116], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999992e-123 or 5.2000000000000001e-116 < x

   1. Initial program 100.0%

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

      1. log1p-expm1-u 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 61.0%

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

   if -1.49999999999999992e-123 < x < 5.2000000000000001e-116

   1. Initial program 99.9%

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

      1. log1p-expm1-u 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. +-commutative 56.9%

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

      2. associate-+l+ 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in y around inf 16.1%

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

Alternative 11: 66.9% 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. Step-by-step derivation

   1. log1p-expm1-u 99.9%

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in y around 0 68.0%

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

   1. +-commutative 68.0%

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

7. Simplified 68.0%

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

8. Final simplification 68.0%

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

Alternative 12: 43.0% 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. log1p-expm1-u 99.9%

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

4. Applied egg-rr 99.9%

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

5. Taylor expanded in x around inf 43.1%

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

Reproduce

herbie shell --seed 2024170 
(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))))