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

Percentage Accurate: 99.9% → 99.9%

Time: 10.4s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

2. Final simplification 99.9%

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

Alternative 3: 82.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \cos y\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-84}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-81}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (cos y))))
   (if (<= z -1.8e+71)
     t_0
     (if (<= z -4.9e-84)
       (+ y (+ z x))
       (if (<= z 3.5e-81) (+ (sin y) x) (if (<= z 2.55e+95) (+ z x) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * cos(y);
	double tmp;
	if (z <= -1.8e+71) {
		tmp = t_0;
	} else if (z <= -4.9e-84) {
		tmp = y + (z + x);
	} else if (z <= 3.5e-81) {
		tmp = sin(y) + x;
	} else if (z <= 2.55e+95) {
		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 <= (-1.8d+71)) then
        tmp = t_0
    else if (z <= (-4.9d-84)) then
        tmp = y + (z + x)
    else if (z <= 3.5d-81) then
        tmp = sin(y) + x
    else if (z <= 2.55d+95) 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 <= -1.8e+71) {
		tmp = t_0;
	} else if (z <= -4.9e-84) {
		tmp = y + (z + x);
	} else if (z <= 3.5e-81) {
		tmp = Math.sin(y) + x;
	} else if (z <= 2.55e+95) {
		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 <= -1.8e+71:
		tmp = t_0
	elif z <= -4.9e-84:
		tmp = y + (z + x)
	elif z <= 3.5e-81:
		tmp = math.sin(y) + x
	elif z <= 2.55e+95:
		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 <= -1.8e+71)
		tmp = t_0;
	elseif (z <= -4.9e-84)
		tmp = Float64(y + Float64(z + x));
	elseif (z <= 3.5e-81)
		tmp = Float64(sin(y) + x);
	elseif (z <= 2.55e+95)
		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 <= -1.8e+71)
		tmp = t_0;
	elseif (z <= -4.9e-84)
		tmp = y + (z + x);
	elseif (z <= 3.5e-81)
		tmp = sin(y) + x;
	elseif (z <= 2.55e+95)
		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, -1.8e+71], t$95$0, If[LessEqual[z, -4.9e-84], N[(y + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-81], N[(N[Sin[y], $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.55e+95], N[(z + x), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8e71 or 2.55000000000000001e95 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-+r+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. flip-+ 26.5%

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

      6. clear-num 26.5%

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

      7. *-un-lft-identity 26.5%

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

      8. associate-/l* 26.5%

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

      9. flip-+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. fma-udef 99.6%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

   6. Taylor expanded in z around inf 92.8%

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

   if -1.8e71 < z < -4.8999999999999998e-84

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 84.9%

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

      1. +-commutative 84.9%

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

   6. Simplified 84.9%

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

      1. *-un-lft-identity 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-+r+ 85.0%

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

      4. +-commutative 85.0%

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

      5. +-commutative 85.0%

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

   8. Applied egg-rr 85.0%

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

   if -4.8999999999999998e-84 < z < 3.49999999999999986e-81

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 96.1%

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

   if 3.49999999999999986e-81 < z < 2.55000000000000001e95

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. flip-+ 68.8%

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

      6. clear-num 68.7%

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

      7. *-un-lft-identity 68.7%

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

      8. associate-/l* 68.7%

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

      9. flip-+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. fma-udef 99.4%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

   5. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

   6. Taylor expanded in y around 0 85.4%

      \[\leadsto \color{blue}{x + z} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+71}:\\ \;\;\;\;z \cdot \cos y\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{-84}:\\ \;\;\;\;y + \left(z + x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-81}:\\ \;\;\;\;\sin y + x\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+95}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]

Alternative 4: 89.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+71} \lor \neg \left(z \leq 1.56 \cdot 10^{+96}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + \left(z + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e+71) (not (<= z 1.56e+96)))
   (* z (cos y))
   (+ (sin y) (+ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e+71) || !(z <= 1.56e+96)) {
		tmp = z * cos(y);
	} else {
		tmp = sin(y) + (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 ((z <= (-2.6d+71)) .or. (.not. (z <= 1.56d+96))) then
        tmp = z * cos(y)
    else
        tmp = sin(y) + (z + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e+71) || !(z <= 1.56e+96)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = Math.sin(y) + (z + x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.6e+71) or not (z <= 1.56e+96):
		tmp = z * math.cos(y)
	else:
		tmp = math.sin(y) + (z + x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.6e+71) || !(z <= 1.56e+96))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(sin(y) + Float64(z + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.6e+71) || ~((z <= 1.56e+96)))
		tmp = z * cos(y);
	else
		tmp = sin(y) + (z + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.6e+71], N[Not[LessEqual[z, 1.56e+96]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[Sin[y], $MachinePrecision] + N[(z + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999991e71 or 1.5599999999999999e96 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-+r+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. flip-+ 26.5%

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

      6. clear-num 26.5%

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

      7. *-un-lft-identity 26.5%

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

      8. associate-/l* 26.5%

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

      9. flip-+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. fma-udef 99.6%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

   6. Taylor expanded in z around inf 92.8%

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

   if -2.59999999999999991e71 < z < 1.5599999999999999e96

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 95.6%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+71} \lor \neg \left(z \leq 1.56 \cdot 10^{+96}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;\sin y + \left(z + x\right)\\ \end{array} \]

Alternative 5: 73.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+71} \lor \neg \left(z \leq 2.15 \cdot 10^{+97}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8.5e+71) (not (<= z 2.15e+97))) (* z (cos y)) (+ z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8.5e+71) || !(z <= 2.15e+97)) {
		tmp = z * cos(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 ((z <= (-8.5d+71)) .or. (.not. (z <= 2.15d+97))) then
        tmp = z * cos(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 ((z <= -8.5e+71) || !(z <= 2.15e+97)) {
		tmp = z * Math.cos(y);
	} else {
		tmp = z + x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8.5e+71) or not (z <= 2.15e+97):
		tmp = z * math.cos(y)
	else:
		tmp = z + x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8.5e+71) || !(z <= 2.15e+97))
		tmp = Float64(z * cos(y));
	else
		tmp = Float64(z + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -8.5e+71) || ~((z <= 2.15e+97)))
		tmp = z * cos(y);
	else
		tmp = z + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8.5e+71], N[Not[LessEqual[z, 2.15e+97]], $MachinePrecision]], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e71 or 2.1499999999999999e97 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. associate-+r+ 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-+l+ 99.8%

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

      5. flip-+ 26.5%

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

      6. clear-num 26.5%

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

      7. *-un-lft-identity 26.5%

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

      8. associate-/l* 26.5%

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

      9. flip-+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. fma-udef 99.6%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

   6. Taylor expanded in z around inf 92.8%

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

   if -8.4999999999999996e71 < z < 2.1499999999999999e97

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. flip-+ 72.7%

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

      6. clear-num 72.3%

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

      7. *-un-lft-identity 72.3%

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

      8. associate-/l* 72.4%

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

      9. flip-+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. fma-udef 99.6%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

   6. Taylor expanded in y around 0 76.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+71} \lor \neg \left(z \leq 2.15 \cdot 10^{+97}\right):\\ \;\;\;\;z \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 6: 52.0% accurate, 40.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5e+33) z (if (<= z 3.1e+106) x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+33) {
		tmp = z;
	} else if (z <= 3.1e+106) {
		tmp = x;
	} else {
		tmp = 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 <= (-5.5d+33)) then
        tmp = z
    else if (z <= 3.1d+106) then
        tmp = x
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+33) {
		tmp = z;
	} else if (z <= 3.1e+106) {
		tmp = x;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5e+33:
		tmp = z
	elif z <= 3.1e+106:
		tmp = x
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5e+33)
		tmp = z;
	elseif (z <= 3.1e+106)
		tmp = x;
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.5e+33)
		tmp = z;
	elseif (z <= 3.1e+106)
		tmp = x;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5e+33], z, If[LessEqual[z, 3.1e+106], x, z]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000006e33 or 3.0999999999999999e106 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 65.4%

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

      1. +-commutative 65.4%

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

   6. Simplified 65.4%

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

   7. Taylor expanded in z around inf 57.1%

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

   if -5.5000000000000006e33 < z < 3.0999999999999999e106

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+r+ 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

      5. flip-+ 72.9%

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

      6. clear-num 72.6%

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

      7. *-un-lft-identity 72.6%

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

      8. associate-/l* 72.6%

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

      9. flip-+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. fma-udef 99.6%

          \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

   6. Taylor expanded in x around inf 63.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+33}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 66.4% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

   1. fma-udef 99.9%

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

   2. associate-+r+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. flip-+ 57.9%

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

   6. clear-num 57.7%

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

   7. *-un-lft-identity 57.7%

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

   8. associate-/l* 57.7%

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

   9. flip-+ 99.6%

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

   10. +-commutative 99.6%

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

   11. associate-+r+ 99.6%

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

   12. fma-udef 99.6%

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

5. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

6. Taylor expanded in y around 0 72.7%

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

7. Final simplification 72.7%

   \[\leadsto z + x \]

Alternative 8: 42.0% 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. Step-by-step derivation

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. fma-def 99.9%

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

3. Simplified 99.9%

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

   1. fma-udef 99.9%

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

   2. associate-+r+ 99.9%

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

   3. +-commutative 99.9%

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

   4. associate-+l+ 99.9%

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

   5. flip-+ 57.9%

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

   6. clear-num 57.7%

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

   7. *-un-lft-identity 57.7%

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

   8. associate-/l* 57.7%

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

   9. flip-+ 99.6%

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

   10. +-commutative 99.6%

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

   11. associate-+r+ 99.6%

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

   12. fma-udef 99.6%

       \[\leadsto \frac{1}{\frac{1}{\color{blue}{\mathsf{fma}\left(z, \cos y, x\right)} + \sin y}} \]

5. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\frac{1}{\frac{1}{\mathsf{fma}\left(z, \cos y, x\right) + \sin y}}} \]

6. Taylor expanded in x around inf 45.4%

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

7. Final simplification 45.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023301 
(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))))