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

Percentage Accurate: 99.9% → 99.9%

Time: 10.3s

Alternatives: 14

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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -460 \lor \neg \left(x \leq 1.08\right):\\ \;\;\;\;\left(x + -1\right) - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -460.0) (not (<= x 1.08)))
     (- (+ x -1.0) 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 <= -460.0) || !(x <= 1.08)) {
		tmp = (x + -1.0) - 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 <= (-460.0d0)) .or. (.not. (x <= 1.08d0))) then
        tmp = (x + (-1.0d0)) - 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 <= -460.0) || !(x <= 1.08)) {
		tmp = (x + -1.0) - 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 <= -460.0) or not (x <= 1.08):
		tmp = (x + -1.0) - 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 <= -460.0) || !(x <= 1.08))
		tmp = Float64(Float64(x + -1.0) - 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 <= -460.0) || ~((x <= 1.08)))
		tmp = (x + -1.0) - 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, -460.0], N[Not[LessEqual[x, 1.08]], $MachinePrecision]], N[(N[(x + -1.0), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -460 or 1.0800000000000001 < x

   1. Initial program 99.9%

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

      1. expm1-log1p-u 46.2%

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

      2. expm1-undefine 46.2%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(x + \cos y\right)} - 1\right)} - z \cdot \sin y \]

   4. Applied egg-rr 46.2%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(x + \cos y\right)} - 1\right)} - z \cdot \sin y \]
   5. Step-by-step derivation

      1. expm1-define 46.2%

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

      2. +-commutative 46.2%

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

   6. Simplified 46.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y + x\right)\right)} - z \cdot \sin y \]
   7. Step-by-step derivation

      1. expm1-undefine 46.2%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y + x\right)} - 1\right)} - z \cdot \sin y \]

      2. log1p-undefine 46.2%

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

      3. rem-exp-log 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+r+ 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around inf 98.4%

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

   if -460 < x < 1.0800000000000001

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -460 \lor \neg \left(x \leq 1.08\right):\\ \;\;\;\;\left(x + -1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{elif}\;z \leq 36000:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+97} \lor \neg \left(z \leq 1.2 \cdot 10^{+184}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(-y, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.3e+70)
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))
   (if (<= z 36000.0)
     (+ x (cos y))
     (if (or (<= z 3.4e+97) (not (<= z 1.2e+184)))
       (* z (- (sin y)))
       (+ 1.0 (fma (- y) z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.3e+70) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else if (z <= 36000.0) {
		tmp = x + cos(y);
	} else if ((z <= 3.4e+97) || !(z <= 1.2e+184)) {
		tmp = z * -sin(y);
	} else {
		tmp = 1.0 + fma(-y, z, x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.3e+70)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	elseif (z <= 36000.0)
		tmp = Float64(x + cos(y));
	elseif ((z <= 3.4e+97) || !(z <= 1.2e+184))
		tmp = Float64(z * Float64(-sin(y)));
	else
		tmp = Float64(1.0 + fma(Float64(-y), z, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.3e+70], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 36000.0], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.4e+97], N[Not[LessEqual[z, 1.2e+184]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(1.0 + N[((-y) * z + x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.3e70

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 71.9%

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

   if -1.3e70 < z < 36000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.7%

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

      1. +-commutative 97.7%

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

   5. Simplified 97.7%

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

   if 36000 < z < 3.4000000000000001e97 or 1.19999999999999998e184 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 77.4%

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

      1. associate-*r* 77.4%

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

      2. neg-mul-1 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if 3.4000000000000001e97 < z < 1.19999999999999998e184

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. +-commutative 75.8%

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

      2. associate-*r* 75.8%

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

      3. fma-define 75.8%

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

      4. mul-1-neg 75.8%

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

   5. Simplified 75.8%

      \[\leadsto \color{blue}{1 + \mathsf{fma}\left(-y, z, x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+70}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{elif}\;z \leq 36000:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+97} \lor \neg \left(z \leq 1.2 \cdot 10^{+184}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \mathsf{fma}\left(-y, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+70}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{elif}\;z \leq 36000:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+96} \lor \neg \left(z \leq 1.65 \cdot 10^{+182}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e+70)
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))
   (if (<= z 36000.0)
     (+ x (cos y))
     (if (or (<= z 4.15e+96) (not (<= z 1.65e+182)))
       (* z (- (sin y)))
       (+ 1.0 (- x (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+70) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else if (z <= 36000.0) {
		tmp = x + cos(y);
	} else if ((z <= 4.15e+96) || !(z <= 1.65e+182)) {
		tmp = z * -sin(y);
	} 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 (z <= (-1d+70)) then
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - z)))
    else if (z <= 36000.0d0) then
        tmp = x + cos(y)
    else if ((z <= 4.15d+96) .or. (.not. (z <= 1.65d+182))) then
        tmp = z * -sin(y)
    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 (z <= -1e+70) {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	} else if (z <= 36000.0) {
		tmp = x + Math.cos(y);
	} else if ((z <= 4.15e+96) || !(z <= 1.65e+182)) {
		tmp = z * -Math.sin(y);
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e+70:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	elif z <= 36000.0:
		tmp = x + math.cos(y)
	elif (z <= 4.15e+96) or not (z <= 1.65e+182):
		tmp = z * -math.sin(y)
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+70)
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	elseif (z <= 36000.0)
		tmp = Float64(x + cos(y));
	elseif ((z <= 4.15e+96) || !(z <= 1.65e+182))
		tmp = Float64(z * Float64(-sin(y)));
	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 (z <= -1e+70)
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	elseif (z <= 36000.0)
		tmp = x + cos(y);
	elseif ((z <= 4.15e+96) || ~((z <= 1.65e+182)))
		tmp = z * -sin(y);
	else
		tmp = 1.0 + (x - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+70], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 36000.0], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.15e+96], N[Not[LessEqual[z, 1.65e+182]], $MachinePrecision]], N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision], N[(1.0 + N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000007e70

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 71.9%

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

   if -1.00000000000000007e70 < z < 36000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.7%

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

      1. +-commutative 97.7%

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

   5. Simplified 97.7%

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

   if 36000 < z < 4.1499999999999999e96 or 1.65e182 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 77.4%

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

      1. associate-*r* 77.4%

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

      2. neg-mul-1 77.4%

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

      3. *-commutative 77.4%

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

   5. Simplified 77.4%

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

   if 4.1499999999999999e96 < z < 1.65e182

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. unsub-neg 75.8%

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

   5. Simplified 75.8%

      \[\leadsto \color{blue}{1 + \left(x - y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+70}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \mathbf{elif}\;z \leq 36000:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 4.15 \cdot 10^{+96} \lor \neg \left(z \leq 1.65 \cdot 10^{+182}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+135} \lor \neg \left(z \leq 36000\right):\\ \;\;\;\;\left(x + -1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.5e+135) (not (<= z 36000.0)))
   (- (+ x -1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.5e+135) || !(z <= 36000.0)) {
		tmp = (x + -1.0) - (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 <= (-2.5d+135)) .or. (.not. (z <= 36000.0d0))) then
        tmp = (x + (-1.0d0)) - (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 <= -2.5e+135) || !(z <= 36000.0)) {
		tmp = (x + -1.0) - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.5e+135) or not (z <= 36000.0):
		tmp = (x + -1.0) - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.5e+135) || !(z <= 36000.0))
		tmp = Float64(Float64(x + -1.0) - 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 <= -2.5e+135) || ~((z <= 36000.0)))
		tmp = (x + -1.0) - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.5e+135], N[Not[LessEqual[z, 36000.0]], $MachinePrecision]], N[(N[(x + -1.0), $MachinePrecision] - 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 < -2.50000000000000015e135 or 36000 < z

   1. Initial program 99.7%

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

      1. expm1-log1p-u 74.3%

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

      2. expm1-undefine 74.3%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(x + \cos y\right)} - 1\right)} - z \cdot \sin y \]

   4. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(x + \cos y\right)} - 1\right)} - z \cdot \sin y \]
   5. Step-by-step derivation

      1. expm1-define 74.3%

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

      2. +-commutative 74.3%

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

   6. Simplified 74.3%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos y + x\right)\right)} - z \cdot \sin y \]
   7. Step-by-step derivation

      1. expm1-undefine 74.3%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y + x\right)} - 1\right)} - z \cdot \sin y \]

      2. log1p-undefine 74.3%

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

      3. rem-exp-log 99.7%

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

      4. +-commutative 99.7%

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

      5. associate-+r+ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around inf 91.5%

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

   if -2.50000000000000015e135 < z < 36000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+135} \lor \neg \left(z \leq 36000\right):\\ \;\;\;\;\left(x + -1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0005 \lor \neg \left(y \leq 0.08\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0005) (not (<= y 0.08)))
   (+ 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 <= -0.0005) || !(y <= 0.08)) {
		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 <= (-0.0005d0)) .or. (.not. (y <= 0.08d0))) 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 <= -0.0005) || !(y <= 0.08)) {
		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 <= -0.0005) or not (y <= 0.08):
		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 <= -0.0005) || !(y <= 0.08))
		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 <= -0.0005) || ~((y <= 0.08)))
		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, -0.0005], N[Not[LessEqual[y, 0.08]], $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 < -5.0000000000000001e-4 or 0.0800000000000000017 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 65.0%

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

      1. +-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -5.0000000000000001e-4 < y < 0.0800000000000000017

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0005 \lor \neg \left(y \leq 0.08\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-17} \lor \neg \left(x \leq 1.75 \cdot 10^{-7}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e-17) (not (<= x 1.75e-7))) (+ x 1.0) (cos y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-17) || !(x <= 1.75e-7)) {
		tmp = x + 1.0;
	} else {
		tmp = cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.7d-17)) .or. (.not. (x <= 1.75d-7))) then
        tmp = x + 1.0d0
    else
        tmp = cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e-17) || !(x <= 1.75e-7)) {
		tmp = x + 1.0;
	} else {
		tmp = Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e-17) or not (x <= 1.75e-7):
		tmp = x + 1.0
	else:
		tmp = math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e-17) || !(x <= 1.75e-7))
		tmp = Float64(x + 1.0);
	else
		tmp = cos(y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e-17) || ~((x <= 1.75e-7)))
		tmp = x + 1.0;
	else
		tmp = cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e-17], N[Not[LessEqual[x, 1.75e-7]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[Cos[y], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e-17 or 1.74999999999999992e-7 < x

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 51.6%

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

      2. pow2 51.6%

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

      3. associate--l+ 51.6%

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

   4. Applied egg-rr 51.6%

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

   5. Taylor expanded in y around 0 83.7%

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

   if -1.6999999999999999e-17 < x < 1.74999999999999992e-7

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.7%

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

   4. Taylor expanded in z around 0 63.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-17} \lor \neg \left(x \leq 1.75 \cdot 10^{-7}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.1% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+16} \lor \neg \left(y \leq 7200000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e+16) (not (<= y 7200000000.0)))
   (+ 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 <= -3.1e+16) || !(y <= 7200000000.0)) {
		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 <= (-3.1d+16)) .or. (.not. (y <= 7200000000.0d0))) 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 <= -3.1e+16) || !(y <= 7200000000.0)) {
		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 <= -3.1e+16) or not (y <= 7200000000.0):
		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 <= -3.1e+16) || !(y <= 7200000000.0))
		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 <= -3.1e+16) || ~((y <= 7200000000.0)))
		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, -3.1e+16], N[Not[LessEqual[y, 7200000000.0]], $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 < -3.1e16 or 7.2e9 < y

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 49.2%

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

      2. pow2 49.2%

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

      3. associate--l+ 49.2%

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

   4. Applied egg-rr 49.2%

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

   5. Taylor expanded in y around 0 42.4%

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

   if -3.1e16 < y < 7.2e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+16} \lor \neg \left(y \leq 7200000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot \left(\left(y \cdot z\right) \cdot 0.16666666666666666 - 0.5\right) - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 70.0% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+14} \lor \neg \left(y \leq 28000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+14) (not (<= y 28000000000.0)))
   (+ x 1.0)
   (+ 1.0 (+ x (* y (- (* y -0.5) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+14) || !(y <= 28000000000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * -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 <= (-5.5d+14)) .or. (.not. (y <= 28000000000.0d0))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 + (x + (y * ((y * (-0.5d0)) - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+14) || !(y <= 28000000000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+14) or not (y <= 28000000000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+14) || !(y <= 28000000000.0))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 + Float64(x + Float64(y * Float64(Float64(y * -0.5) - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e+14) || ~((y <= 28000000000.0)))
		tmp = x + 1.0;
	else
		tmp = 1.0 + (x + (y * ((y * -0.5) - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+14], N[Not[LessEqual[y, 28000000000.0]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 + N[(x + N[(y * N[(N[(y * -0.5), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e14 or 2.8e10 < y

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 48.3%

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

      2. pow2 48.3%

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

      3. associate--l+ 48.3%

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

   4. Applied egg-rr 48.3%

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

   5. Taylor expanded in y around 0 42.4%

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

   if -5.5e14 < y < 2.8e10

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+14} \lor \neg \left(y \leq 28000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x + y \cdot \left(y \cdot -0.5 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.9% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -52000000000000 \lor \neg \left(y \leq 1950000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -52000000000000.0) (not (<= y 1950000000000.0)))
   (+ x 1.0)
   (+ 1.0 (- x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -52000000000000.0) || !(y <= 1950000000000.0)) {
		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 <= (-52000000000000.0d0)) .or. (.not. (y <= 1950000000000.0d0))) 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 <= -52000000000000.0) || !(y <= 1950000000000.0)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 + (x - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -52000000000000.0) or not (y <= 1950000000000.0):
		tmp = x + 1.0
	else:
		tmp = 1.0 + (x - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -52000000000000.0) || !(y <= 1950000000000.0))
		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 <= -52000000000000.0) || ~((y <= 1950000000000.0)))
		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, -52000000000000.0], N[Not[LessEqual[y, 1950000000000.0]], $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 < -5.2e13 or 1.95e12 < y

   1. Initial program 99.8%

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

      1. add-sqr-sqrt 48.3%

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

      2. pow2 48.3%

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

      3. associate--l+ 48.3%

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

   4. Applied egg-rr 48.3%

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

   5. Taylor expanded in y around 0 42.4%

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

   if -5.2e13 < y < 1.95e12

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

   5. Simplified 96.4%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -52000000000000 \lor \neg \left(y \leq 1950000000000\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.7% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-9} \lor \neg \left(x \leq 1.65 \cdot 10^{-85}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-9) (not (<= x 1.65e-85))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-9) || !(x <= 1.65e-85)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.8d-9)) .or. (.not. (x <= 1.65d-85))) then
        tmp = x + 1.0d0
    else
        tmp = 1.0d0 - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-9) || !(x <= 1.65e-85)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-9) or not (x <= 1.65e-85):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-9) || !(x <= 1.65e-85))
		tmp = Float64(x + 1.0);
	else
		tmp = Float64(1.0 - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e-9) || ~((x <= 1.65e-85)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-9], N[Not[LessEqual[x, 1.65e-85]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999984e-9 or 1.64999999999999986e-85 < x

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 50.4%

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

      2. pow2 50.4%

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

      3. associate--l+ 50.4%

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

   4. Applied egg-rr 50.4%

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

   5. Taylor expanded in y around 0 80.9%

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

   if -2.79999999999999984e-9 < x < 1.64999999999999986e-85

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in y around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. unsub-neg 55.6%

         \[\leadsto \color{blue}{1 - y \cdot z} \]

      3. *-commutative 55.6%

         \[\leadsto 1 - \color{blue}{z \cdot y} \]

   6. Simplified 55.6%

      \[\leadsto \color{blue}{1 - z \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-9} \lor \neg \left(x \leq 1.65 \cdot 10^{-85}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.1% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -1.0) x (if (<= x 1.2) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 1.2) {
		tmp = 1.0;
	} 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 <= (-1.0d0)) then
        tmp = x
    else if (x <= 1.2d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.0) {
		tmp = x;
	} else if (x <= 1.2) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.0:
		tmp = x
	elif x <= 1.2:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 1.2)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x;
	elseif (x <= 1.2)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.0], x, If[LessEqual[x, 1.2], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.19999999999999996 < x

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 48.9%

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

      2. pow2 48.9%

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

      3. associate--l+ 48.9%

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

   4. Applied egg-rr 48.9%

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

   5. Taylor expanded in x around inf 85.5%

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

   if -1 < x < 1.19999999999999996

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 97.9%

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

   4. Taylor expanded in y around 0 41.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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-sqr-sqrt 59.9%

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

   2. pow2 59.9%

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

   3. associate--l+ 59.9%

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

4. Applied egg-rr 59.9%

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

5. Taylor expanded in y around 0 63.4%

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

6. Final simplification 63.4%

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

Alternative 14: 21.0% accurate, 207.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return 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 = 1.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := 1.0

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around 0 58.6%

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

4. Taylor expanded in y around 0 23.3%

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

5. Final simplification 23.3%

   \[\leadsto 1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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))))