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

Percentage Accurate: 99.9% → 99.9%

Time: 8.0s

Alternatives: 11

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(z * N[Cos[y], $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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(z, \cos y, x + \sin y\right) \]

Alternative 2: 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. Final simplification 99.9%

   \[\leadsto \left(x + \sin y\right) + z \cdot \cos y \]

Alternative 3: 69.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{+164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+97}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq -66000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+19}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= y -8.2e+164)
     t_0
     (if (<= y -9.5e+97)
       (+ z x)
       (if (<= y -66000.0) t_0 (if (<= y 3.3e+19) (+ y (+ z x)) (+ z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (y <= -8.2e+164) {
		tmp = t_0;
	} else if (y <= -9.5e+97) {
		tmp = z + x;
	} else if (y <= -66000.0) {
		tmp = t_0;
	} else if (y <= 3.3e+19) {
		tmp = y + (z + x);
	} else {
		tmp = z + 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) :: t_0
    real(8) :: tmp
    t_0 = z * cos(y)
    if (y <= (-8.2d+164)) then
        tmp = t_0
    else if (y <= (-9.5d+97)) then
        tmp = z + x
    else if (y <= (-66000.0d0)) then
        tmp = t_0
    else if (y <= 3.3d+19) then
        tmp = y + (z + x)
    else
        tmp = z + x
    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 (y <= -8.2e+164) {
		tmp = t_0;
	} else if (y <= -9.5e+97) {
		tmp = z + x;
	} else if (y <= -66000.0) {
		tmp = t_0;
	} else if (y <= 3.3e+19) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if y <= -8.2e+164:
		tmp = t_0
	elif y <= -9.5e+97:
		tmp = z + x
	elif y <= -66000.0:
		tmp = t_0
	elif y <= 3.3e+19:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (y <= -8.2e+164)
		tmp = t_0;
	elseif (y <= -9.5e+97)
		tmp = Float64(z + x);
	elseif (y <= -66000.0)
		tmp = t_0;
	elseif (y <= 3.3e+19)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * cos(y);
	tmp = 0.0;
	if (y <= -8.2e+164)
		tmp = t_0;
	elseif (y <= -9.5e+97)
		tmp = z + x;
	elseif (y <= -66000.0)
		tmp = t_0;
	elseif (y <= 3.3e+19)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.2e+164], t$95$0, If[LessEqual[y, -9.5e+97], N[(z + x), $MachinePrecision], If[LessEqual[y, -66000.0], t$95$0, If[LessEqual[y, 3.3e+19], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.20000000000000032e164 or -9.49999999999999975e97 < y < -66000

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. add-sqr-sqrt 57.2%

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

      3. associate-*r* 57.2%

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

      4. fma-def 57.2%

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

   3. Applied egg-rr 57.2%

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

   4. Taylor expanded in z around inf 56.8%

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

   if -8.20000000000000032e164 < y < -9.49999999999999975e97 or 3.3e19 < y

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 59.0%

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

   if -66000 < y < 3.3e19

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 97.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+164}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+97}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq -66000:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+19}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 4: 82.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-59}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+215}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -5e-7)
     t_0
     (if (<= z 6.4e-59) (+ x (sin y)) (if (<= z 4.4e+215) (+ z x) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -5e-7) {
		tmp = t_0;
	} else if (z <= 6.4e-59) {
		tmp = x + sin(y);
	} else if (z <= 4.4e+215) {
		tmp = z + x;
	} 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 <= (-5d-7)) then
        tmp = t_0
    else if (z <= 6.4d-59) then
        tmp = x + sin(y)
    else if (z <= 4.4d+215) then
        tmp = z + x
    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 <= -5e-7) {
		tmp = t_0;
	} else if (z <= 6.4e-59) {
		tmp = x + Math.sin(y);
	} else if (z <= 4.4e+215) {
		tmp = z + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.cos(y)
	tmp = 0
	if z <= -5e-7:
		tmp = t_0
	elif z <= 6.4e-59:
		tmp = x + math.sin(y)
	elif z <= 4.4e+215:
		tmp = z + x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * cos(y))
	tmp = 0.0
	if (z <= -5e-7)
		tmp = t_0;
	elseif (z <= 6.4e-59)
		tmp = Float64(x + sin(y));
	elseif (z <= 4.4e+215)
		tmp = Float64(z + x);
	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 <= -5e-7)
		tmp = t_0;
	elseif (z <= 6.4e-59)
		tmp = x + sin(y);
	elseif (z <= 4.4e+215)
		tmp = z + x;
	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, -5e-7], t$95$0, If[LessEqual[z, 6.4e-59], N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+215], N[(z + x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999977e-7 or 4.4000000000000003e215 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 81.0%

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

      3. associate-*r* 81.0%

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

      4. fma-def 81.0%

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

   3. Applied egg-rr 81.0%

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

   4. Taylor expanded in z around inf 86.2%

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

   if -4.99999999999999977e-7 < z < 6.3999999999999998e-59

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. add-cube-cbrt 99.7%

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

      4. associate-*r* 99.7%

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

      5. fma-def 99.7%

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

      6. pow2 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in z around 0 90.2%

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

   if 6.3999999999999998e-59 < z < 4.4000000000000003e215

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 79.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-59}:\\ \;\;\;\;x + \sin y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+215}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 5: 95.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-26} \lor \neg \left(z \leq 4.6 \cdot 10^{-59}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e-26) (not (<= z 4.6e-59)))
   (+ x (* z (cos y)))
   (+ x (sin y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-26) || !(z <= 4.6e-59)) {
		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 <= (-3.5d-26)) .or. (.not. (z <= 4.6d-59))) 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 <= -3.5e-26) || !(z <= 4.6e-59)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = x + Math.sin(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e-26) or not (z <= 4.6e-59):
		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 <= -3.5e-26) || !(z <= 4.6e-59))
		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 <= -3.5e-26) || ~((z <= 4.6e-59)))
		tmp = x + (z * cos(y));
	else
		tmp = x + sin(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-26], N[Not[LessEqual[z, 4.6e-59]], $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 < -3.49999999999999985e-26 or 4.59999999999999959e-59 < z

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 99.1%

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

   if -3.49999999999999985e-26 < z < 4.59999999999999959e-59

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. add-cube-cbrt 99.8%

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

      4. associate-*r* 99.8%

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

      5. fma-def 99.8%

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

      6. pow2 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 90.7%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-26} \lor \neg \left(z \leq 4.6 \cdot 10^{-59}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \sin y\\ \end{array} \]

Alternative 6: 98.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \lor \neg \left(z \leq 7 \cdot 10^{-59}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5) (not (<= z 7e-59)))
   (+ x (* z (cos y)))
   (+ z (+ x (sin y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5) || !(z <= 7e-59)) {
		tmp = x + (z * cos(y));
	} else {
		tmp = z + (x + sin(y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.5d0)) .or. (.not. (z <= 7d-59))) then
        tmp = x + (z * cos(y))
    else
        tmp = z + (x + sin(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5) || !(z <= 7e-59)) {
		tmp = x + (z * Math.cos(y));
	} else {
		tmp = z + (x + Math.sin(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.5) or not (z <= 7e-59):
		tmp = x + (z * math.cos(y))
	else:
		tmp = z + (x + math.sin(y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.5) || !(z <= 7e-59))
		tmp = Float64(x + Float64(z * cos(y)));
	else
		tmp = Float64(z + Float64(x + sin(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.5) || ~((z <= 7e-59)))
		tmp = x + (z * cos(y));
	else
		tmp = z + (x + sin(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.5], N[Not[LessEqual[z, 7e-59]], $MachinePrecision]], N[(x + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(x + N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5 or 7.0000000000000002e-59 < z

   1. Initial program 99.9%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in x around inf 99.0%

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

   if -4.5 < z < 7.0000000000000002e-59

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. 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 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \lor \neg \left(z \leq 7 \cdot 10^{-59}\right):\\ \;\;\;\;x + z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + \left(x + \sin y\right)\\ \end{array} \]

Alternative 7: 70.3% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;y + \left(\left(z + x\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+27)
   (+ z x)
   (if (<= y 0.88) (+ y (+ (+ z x) (* -0.5 (* z (* y y))))) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+27) {
		tmp = z + x;
	} else if (y <= 0.88) {
		tmp = y + ((z + x) + (-0.5 * (z * (y * y))));
	} else {
		tmp = z + 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 (y <= (-5.8d+27)) then
        tmp = z + x
    else if (y <= 0.88d0) then
        tmp = y + ((z + x) + ((-0.5d0) * (z * (y * y))))
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+27) {
		tmp = z + x;
	} else if (y <= 0.88) {
		tmp = y + ((z + x) + (-0.5 * (z * (y * y))));
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+27:
		tmp = z + x
	elif y <= 0.88:
		tmp = y + ((z + x) + (-0.5 * (z * (y * y))))
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+27)
		tmp = Float64(z + x);
	elseif (y <= 0.88)
		tmp = Float64(y + Float64(Float64(z + x) + Float64(-0.5 * Float64(z * Float64(y * y)))));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+27)
		tmp = z + x;
	elseif (y <= 0.88)
		tmp = y + ((z + x) + (-0.5 * (z * (y * y))));
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+27], N[(z + x), $MachinePrecision], If[LessEqual[y, 0.88], N[(y + N[(N[(z + x), $MachinePrecision] + N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000002e27 or 0.880000000000000004 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 46.3%

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

   if -5.8000000000000002e27 < y < 0.880000000000000004

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. add-cube-cbrt 98.9%

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

      4. associate-*r* 98.9%

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

      5. fma-def 98.9%

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

      6. pow2 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in y around 0 97.4%

      \[\leadsto \color{blue}{y + \left(-0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right) + \left({1}^{0.3333333333333333} \cdot z + x\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 97.4%

         \[\leadsto y + \color{blue}{\left(\left({1}^{0.3333333333333333} \cdot z + x\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right)} \]

      2. pow-base-1 97.4%

         \[\leadsto y + \left(\left(\color{blue}{1} \cdot z + x\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      3. *-lft-identity 97.4%

         \[\leadsto y + \left(\left(\color{blue}{z} + x\right) + -0.5 \cdot \left({1}^{0.3333333333333333} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      4. pow-base-1 97.4%

         \[\leadsto y + \left(\left(z + x\right) + -0.5 \cdot \left(\color{blue}{1} \cdot \left({y}^{2} \cdot z\right)\right)\right) \]

      5. *-lft-identity 97.4%

         \[\leadsto y + \left(\left(z + x\right) + -0.5 \cdot \color{blue}{\left({y}^{2} \cdot z\right)}\right) \]

      6. *-commutative 97.4%

         \[\leadsto y + \left(\left(z + x\right) + -0.5 \cdot \color{blue}{\left(z \cdot {y}^{2}\right)}\right) \]

      7. unpow2 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 0.88:\\ \;\;\;\;y + \left(\left(z + x\right) + -0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 8: 70.3% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.1e+18) (+ z x) (if (<= y 1.25e+23) (+ y (+ z x)) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+18) {
		tmp = z + x;
	} else if (y <= 1.25e+23) {
		tmp = y + (z + x);
	} else {
		tmp = z + 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 (y <= (-1.1d+18)) then
        tmp = z + x
    else if (y <= 1.25d+23) then
        tmp = y + (z + x)
    else
        tmp = z + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+18) {
		tmp = z + x;
	} else if (y <= 1.25e+23) {
		tmp = y + (z + x);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.1e+18:
		tmp = z + x
	elif y <= 1.25e+23:
		tmp = y + (z + x)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.1e+18)
		tmp = Float64(z + x);
	elseif (y <= 1.25e+23)
		tmp = Float64(y + Float64(z + x));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.1e+18)
		tmp = z + x;
	elseif (y <= 1.25e+23)
		tmp = y + (z + x);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.1e+18], N[(z + x), $MachinePrecision], If[LessEqual[y, 1.25e+23], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e18 or 1.25e23 < y

   1. Initial program 99.8%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 45.9%

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

   if -1.1e18 < y < 1.25e23

   1. Initial program 100.0%

      \[\left(x + \sin y\right) + z \cdot \cos y \]

   2. Taylor expanded in y around 0 96.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+18}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+23}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 9: 46.2% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e-80) x (if (<= x 4.4e-10) (+ y x) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-80) {
		tmp = x;
	} else if (x <= 4.4e-10) {
		tmp = y + x;
	} 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 <= (-1.4d-80)) then
        tmp = x
    else if (x <= 4.4d-10) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e-80) {
		tmp = x;
	} else if (x <= 4.4e-10) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e-80:
		tmp = x
	elif x <= 4.4e-10:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e-80)
		tmp = x;
	elseif (x <= 4.4e-10)
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.4e-80)
		tmp = x;
	elseif (x <= 4.4e-10)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e-80], x, If[LessEqual[x, 4.4e-10], N[(y + x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999995e-80 or 4.3999999999999998e-10 < x

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 99.5%

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

      4. associate-*r* 99.5%

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

      5. fma-def 99.5%

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

      6. pow2 99.5%

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

   3. Applied egg-rr 99.5%

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

   4. Taylor expanded in x around inf 68.7%

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

   if -1.39999999999999995e-80 < x < 4.3999999999999998e-10

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. add-cube-cbrt 98.6%

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

      4. associate-*r* 98.6%

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

      5. fma-def 98.6%

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

      6. pow2 98.6%

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

   3. Applied egg-rr 98.6%

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

   4. Taylor expanded in z around 0 35.8%

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

   5. Taylor expanded in y around 0 20.3%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-10}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 65.9% accurate, 69.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return z + 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 = z + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x + \sin y\right) + z \cdot \cos y \]

2. Taylor expanded in y around 0 69.3%

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

3. Final simplification 69.3%

   \[\leadsto z + x \]

Alternative 11: 42.3% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. *-commutative 99.9%

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

   3. add-cube-cbrt 99.1%

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

   4. associate-*r* 99.1%

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

   5. fma-def 99.1%

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

   6. pow2 99.1%

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

3. Applied egg-rr 99.1%

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

4. Taylor expanded in x around inf 42.0%

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

5. Final simplification 42.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023181 
(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))))