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

Percentage Accurate: 99.9% → 99.9%

Time: 17.9s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * 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 = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * 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 = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * 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 = (x + cos(y)) - (z * sin(y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.85\right):\\ \;\;\;\;x - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -1.0) (not (<= x 0.85))) (- x t_0) (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -1.0) || !(x <= 0.85)) {
		tmp = x - t_0;
	} else {
		tmp = cos(y) - 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 * sin(y)
    if ((x <= (-1.0d0)) .or. (.not. (x <= 0.85d0))) then
        tmp = x - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -1.0) || !(x <= 0.85)) {
		tmp = x - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -1.0) or not (x <= 0.85):
		tmp = x - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.85))
		tmp = Float64(x - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 0.85)))
		tmp = x - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.85]], $MachinePrecision]], N[(x - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.849999999999999978 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 97.4%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   if -1 < x < 0.849999999999999978

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 98.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.85\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+89}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+193} \lor \neg \left(z \leq 6.5 \cdot 10^{+252}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= z -1.16e+117)
     t_0
     (if (<= z 1.25e+89)
       (+ x (cos y))
       (if (or (<= z 8.5e+193) (not (<= z 6.5e+252)))
         t_0
         (+ 1.0 (- x (* y z))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (z <= -1.16e+117) {
		tmp = t_0;
	} else if (z <= 1.25e+89) {
		tmp = x + cos(y);
	} else if ((z <= 8.5e+193) || !(z <= 6.5e+252)) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (x - (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) :: t_0
    real(8) :: tmp
    t_0 = z * -sin(y)
    if (z <= (-1.16d+117)) then
        tmp = t_0
    else if (z <= 1.25d+89) then
        tmp = x + cos(y)
    else if ((z <= 8.5d+193) .or. (.not. (z <= 6.5d+252))) then
        tmp = t_0
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -Math.sin(y);
	double tmp;
	if (z <= -1.16e+117) {
		tmp = t_0;
	} else if (z <= 1.25e+89) {
		tmp = x + Math.cos(y);
	} else if ((z <= 8.5e+193) || !(z <= 6.5e+252)) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	tmp = 0
	if z <= -1.16e+117:
		tmp = t_0
	elif z <= 1.25e+89:
		tmp = x + math.cos(y)
	elif (z <= 8.5e+193) or not (z <= 6.5e+252):
		tmp = t_0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (z <= -1.16e+117)
		tmp = t_0;
	elseif (z <= 1.25e+89)
		tmp = Float64(x + cos(y));
	elseif ((z <= 8.5e+193) || !(z <= 6.5e+252))
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	tmp = 0.0;
	if (z <= -1.16e+117)
		tmp = t_0;
	elseif (z <= 1.25e+89)
		tmp = x + cos(y);
	elseif ((z <= 8.5e+193) || ~((z <= 6.5e+252)))
		tmp = t_0;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -1.16e+117], t$95$0, If[LessEqual[z, 1.25e+89], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 8.5e+193], N[Not[LessEqual[z, 6.5e+252]], $MachinePrecision]], t$95$0, N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1600000000000001e117 or 1.24999999999999996e89 < z < 8.5000000000000003e193 or 6.5e252 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 78.6%

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

      1. associate-*r* 78.6%

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

      2. neg-mul-1 78.6%

         \[\leadsto \color{blue}{\left(-z\right)} \cdot \sin y \]

      3. *-commutative 78.6%

         \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   5. Simplified 78.6%

      \[\leadsto \color{blue}{\sin y \cdot \left(-z\right)} \]

   if -1.1600000000000001e117 < z < 1.24999999999999996e89

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 90.4%

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

      1. +-commutative 90.4%

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

   5. Simplified 90.4%

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

   if 8.5000000000000003e193 < z < 6.5e252

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.3%

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

      1. mul-1-neg 82.3%

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

      2. unsub-neg 82.3%

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

   5. Simplified 82.3%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+89}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+193} \lor \neg \left(z \leq 6.5 \cdot 10^{+252}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+43} \lor \neg \left(z \leq 18\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e+43) (not (<= z 18.0)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+43) || !(z <= 18.0)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x + 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 ((z <= (-2.15d+43)) .or. (.not. (z <= 18.0d0))) then
        tmp = x - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e+43) || !(z <= 18.0)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.15e+43) or not (z <= 18.0):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e+43) || !(z <= 18.0))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.15e+43) || ~((z <= 18.0)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e+43], N[Not[LessEqual[z, 18.0]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15e43 or 18 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 89.0%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   if -2.15e43 < z < 18

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. +-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+43} \lor \neg \left(z \leq 18\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21.5 \lor \neg \left(y \leq 1600000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -21.5) (not (<= y 1600000.0)))
   (+ x (cos y))
   (+ 1.0 (+ x (* y (- (* y (- (* (* y z) 0.16666666666666666) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -21.5) || !(y <= 1600000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - 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 <= (-21.5d0)) .or. (.not. (y <= 1600000.0d0))) then
        tmp = x + cos(y)
    else
        tmp = 1.0d0 + (x + (y * ((y * (((y * z) * 0.16666666666666666d0) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -21.5) || !(y <= 1600000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -21.5) or not (y <= 1600000.0):
		tmp = x + math.cos(y)
	else:
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -21.5) || !(y <= 1600000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(y * z) * 0.16666666666666666) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -21.5) || ~((y <= 1600000.0)))
		tmp = x + cos(y);
	else
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -21.5], N[Not[LessEqual[y, 1600000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -21.5 or 1.6e6 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -21.5 < y < 1.6e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21.5 \lor \neg \left(y \leq 1600000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.2% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1000 \lor \neg \left(y \leq 1600000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1000.0) (not (<= y 1600000.0)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y (- (* (* y z) 0.16666666666666666) 0.5)) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1000.0) || !(y <= 1600000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - 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 <= (-1000.0d0)) .or. (.not. (y <= 1600000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * (((y * z) * 0.16666666666666666d0) - 0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1000.0) || !(y <= 1600000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1000.0) or not (y <= 1600000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1000.0) || !(y <= 1600000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * Float64(Float64(Float64(y * z) * 0.16666666666666666) - 0.5)) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1000.0) || ~((y <= 1600000.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * (((y * z) * 0.16666666666666666) - 0.5)) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1000.0], N[Not[LessEqual[y, 1600000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * N[(N[(N[(y * z), $MachinePrecision] * 0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e3 or 1.6e6 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

      2. pow3 98.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

      3. associate--l+ 98.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 47.0%

      \[\leadsto \color{blue}{1 + x} \]

   if -1e3 < y < 1.6e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1000 \lor \neg \left(y \leq 1600000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.0% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+14} \lor \neg \left(y \leq 1550000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+14) (not (<= y 1550000.0)))
   (+ x 1.0)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+14) || !(y <= 1550000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (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 <= (-4.5d+14)) .or. (.not. (y <= 1550000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+14) || !(y <= 1550000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+14) or not (y <= 1550000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e+14) || !(y <= 1550000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.5e+14) || ~((y <= 1550000.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+14], N[Not[LessEqual[y, 1550000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e14 or 1.55e6 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

      2. pow3 98.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

      3. associate--l+ 98.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 46.1%

      \[\leadsto \color{blue}{1 + x} \]

   if -4.5e14 < y < 1.55e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. unsub-neg 98.9%

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

   5. Simplified 98.9%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+14} \lor \neg \left(y \leq 1550000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+175} \lor \neg \left(z \leq 1.05 \cdot 10^{+147}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.5e+175) (not (<= z 1.05e+147))) (- x (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+175) || !(z <= 1.05e+147)) {
		tmp = x - (y * z);
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if ((z <= (-7.5d+175)) .or. (.not. (z <= 1.05d+147))) then
        tmp = x - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.5e+175) || !(z <= 1.05e+147)) {
		tmp = x - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.5e+175) or not (z <= 1.05e+147):
		tmp = x - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.5e+175) || !(z <= 1.05e+147))
		tmp = Float64(x - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.5e+175) || ~((z <= 1.05e+147)))
		tmp = x - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.5e+175], N[Not[LessEqual[z, 1.05e+147]], $MachinePrecision]], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000001e175 or 1.05000000000000003e147 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.8%

      \[\leadsto \color{blue}{x} - z \cdot \sin y \]

   4. Taylor expanded in y around 0 58.6%

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

      1. mul-1-neg 58.6%

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

      2. unsub-neg 58.6%

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

      3. *-commutative 58.6%

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

   6. Simplified 58.6%

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

   if -7.5000000000000001e175 < z < 1.05000000000000003e147

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

      2. pow3 98.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

      3. associate--l+ 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 73.6%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+175} \lor \neg \left(z \leq 1.05 \cdot 10^{+147}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.3% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+229} \lor \neg \left(z \leq 5.5 \cdot 10^{+208}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e+229) (not (<= z 5.5e+208))) (* z (- y)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e+229) || !(z <= 5.5e+208)) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	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) :: tmp
    if ((z <= (-3.5d+229)) .or. (.not. (z <= 5.5d+208))) then
        tmp = z * -y
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e+229) || !(z <= 5.5e+208)) {
		tmp = z * -y;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e+229) or not (z <= 5.5e+208):
		tmp = z * -y
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e+229) || !(z <= 5.5e+208))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e+229) || ~((z <= 5.5e+208)))
		tmp = z * -y;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e+229], N[Not[LessEqual[z, 5.5e+208]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e229 or 5.4999999999999997e208 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

      2. pow3 98.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

      3. associate--l+ 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around inf 53.0%

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

      1. associate-*r* 53.0%

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

      2. mul-1-neg 53.0%

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

   10. Simplified 53.0%

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

   if -3.5000000000000002e229 < z < 5.4999999999999997e208

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

      2. pow3 98.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

      3. associate--l+ 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

   4. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

   5. Taylor expanded in y around 0 70.5%

      \[\leadsto \color{blue}{1 + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+229} \lor \neg \left(z \leq 5.5 \cdot 10^{+208}\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.8% accurate, 69.0× speedup

Math

\[\begin{array}{l} \\ x + 1 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x 1.0))

C

double code(double x, double y, double z) {
	return x + 1.0;
}

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 + 1.0d0
end function

Java

public static double code(double x, double y, double z) {
	return x + 1.0;
}

Python

def code(x, y, z):
	return x + 1.0

Julia

function code(x, y, z)
	return Float64(x + 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x + 1.0), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 98.3%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y} \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right) \cdot \sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}} \]

   2. pow3 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x + \cos y\right) - z \cdot \sin y}\right)}^{3}} \]

   3. associate--l+ 98.3%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x + \left(\cos y - z \cdot \sin y\right)}}\right)}^{3} \]

4. Applied egg-rr 98.3%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\cos y - z \cdot \sin y\right)}\right)}^{3}} \]

5. Taylor expanded in y around 0 63.1%

   \[\leadsto \color{blue}{1 + x} \]

6. Final simplification 63.1%

   \[\leadsto x + 1 \]
7. Add Preprocessing

Alternative 11: 42.1% 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%

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

   1. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. add-cube-cbrt 99.5%

      \[\leadsto \left(-\color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}}\right) + \left(x + \cos y\right) \]

   4. distribute-rgt-neg-in 99.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \left(-\sqrt[3]{z \cdot \sin y}\right)} + \left(x + \cos y\right) \]

   5. fma-define 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

   6. pow2 99.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right) \]

4. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{z \cdot \sin y}\right)}^{2}, -\sqrt[3]{z \cdot \sin y}, x + \cos y\right)} \]

5. Taylor expanded in x around inf 45.4%

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

6. Final simplification 45.4%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))