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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

Alternatives: 12

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: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.95 \cdot 10^{-20}\right):\\ \;\;\;\;x - t\_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -1.0) (not (<= x 1.95e-20))) (- x t_0) (- (cos y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * sin(y);
	double tmp;
	if ((x <= -1.0) || !(x <= 1.95e-20)) {
		tmp = x - t_0;
	} else {
		tmp = cos(y) - t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * sin(y)
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.95d-20))) then
        tmp = x - t_0
    else
        tmp = cos(y) - t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * Math.sin(y);
	double tmp;
	if ((x <= -1.0) || !(x <= 1.95e-20)) {
		tmp = x - t_0;
	} else {
		tmp = Math.cos(y) - t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * math.sin(y)
	tmp = 0
	if (x <= -1.0) or not (x <= 1.95e-20):
		tmp = x - t_0
	else:
		tmp = math.cos(y) - t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * sin(y))
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.95e-20))
		tmp = Float64(x - t_0);
	else
		tmp = Float64(cos(y) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * sin(y);
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.95e-20)))
		tmp = x - t_0;
	else
		tmp = cos(y) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.95e-20]], $MachinePrecision]], N[(x - t$95$0), $MachinePrecision], N[(N[Cos[y], $MachinePrecision] - t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.95000000000000004e-20 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 98.7%

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

   if -1 < x < 1.95000000000000004e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.95 \cdot 10^{-20}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-\sin y\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+98} \lor \neg \left(z \leq 4.9 \cdot 10^{+218}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- (sin y)))))
   (if (<= z -3e+171)
     t_0
     (if (<= z -5.4e+158)
       x
       (if (or (<= z -9.5e+98) (not (<= z 4.9e+218))) t_0 (+ x (cos y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -sin(y);
	double tmp;
	if (z <= -3e+171) {
		tmp = t_0;
	} else if (z <= -5.4e+158) {
		tmp = x;
	} else if ((z <= -9.5e+98) || !(z <= 4.9e+218)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = z * -sin(y)
    if (z <= (-3d+171)) then
        tmp = t_0
    else if (z <= (-5.4d+158)) then
        tmp = x
    else if ((z <= (-9.5d+98)) .or. (.not. (z <= 4.9d+218))) then
        tmp = t_0
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -Math.sin(y);
	double tmp;
	if (z <= -3e+171) {
		tmp = t_0;
	} else if (z <= -5.4e+158) {
		tmp = x;
	} else if ((z <= -9.5e+98) || !(z <= 4.9e+218)) {
		tmp = t_0;
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -math.sin(y)
	tmp = 0
	if z <= -3e+171:
		tmp = t_0
	elif z <= -5.4e+158:
		tmp = x
	elif (z <= -9.5e+98) or not (z <= 4.9e+218):
		tmp = t_0
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-sin(y)))
	tmp = 0.0
	if (z <= -3e+171)
		tmp = t_0;
	elseif (z <= -5.4e+158)
		tmp = x;
	elseif ((z <= -9.5e+98) || !(z <= 4.9e+218))
		tmp = t_0;
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -sin(y);
	tmp = 0.0;
	if (z <= -3e+171)
		tmp = t_0;
	elseif (z <= -5.4e+158)
		tmp = x;
	elseif ((z <= -9.5e+98) || ~((z <= 4.9e+218)))
		tmp = t_0;
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-N[Sin[y], $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -3e+171], t$95$0, If[LessEqual[z, -5.4e+158], x, If[Or[LessEqual[z, -9.5e+98], N[Not[LessEqual[z, 4.9e+218]], $MachinePrecision]], t$95$0, N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.0000000000000001e171 or -5.39999999999999957e158 < z < -9.5000000000000001e98 or 4.8999999999999997e218 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 77.1%

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

      1. associate-*r* 77.1%

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

      2. neg-mul-1 77.1%

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

      3. *-commutative 77.1%

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

   5. Simplified 77.1%

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

   if -3.0000000000000001e171 < z < -5.39999999999999957e158

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. add-cube-cbrt 100.0%

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

      5. associate-*r* 100.0%

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

      6. fma-def 100.0%

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

      7. pow2 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around inf 81.8%

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

   if -9.5000000000000001e98 < z < 4.8999999999999997e218

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.5%

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

      1. +-commutative 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{+158}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+98} \lor \neg \left(z \leq 4.9 \cdot 10^{+218}\right):\\ \;\;\;\;z \cdot \left(-\sin y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -47000000000000 \lor \neg \left(z \leq 3.6 \cdot 10^{+211}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -47000000000000.0) (not (<= z 3.6e+211)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -47000000000000.0) || !(z <= 3.6e+211)) {
		tmp = x - (z * sin(y));
	} else {
		tmp = x + cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-47000000000000.0d0)) .or. (.not. (z <= 3.6d+211))) then
        tmp = x - (z * sin(y))
    else
        tmp = x + cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -47000000000000.0) || !(z <= 3.6e+211)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -47000000000000.0) or not (z <= 3.6e+211):
		tmp = x - (z * math.sin(y))
	else:
		tmp = x + math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -47000000000000.0) || !(z <= 3.6e+211))
		tmp = Float64(x - Float64(z * sin(y)));
	else
		tmp = Float64(x + cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -47000000000000.0) || ~((z <= 3.6e+211)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -47000000000000.0], N[Not[LessEqual[z, 3.6e+211]], $MachinePrecision]], N[(x - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7e13 or 3.60000000000000003e211 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 91.6%

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

   if -4.7e13 < z < 3.60000000000000003e211

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 94.0%

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

      1. +-commutative 94.0%

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

   5. Simplified 94.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -47000000000000 \lor \neg \left(z \leq 3.6 \cdot 10^{+211}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+40} \lor \neg \left(y \leq 1050000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.2e+40) (not (<= y 1050000000.0)))
   (+ x (cos y))
   (- (+ x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.2e+40) || !(y <= 1050000000.0)) {
		tmp = x + cos(y);
	} else {
		tmp = (x + 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 ((y <= (-8.2d+40)) .or. (.not. (y <= 1050000000.0d0))) then
        tmp = x + cos(y)
    else
        tmp = (x + 1.0d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.2e+40) || !(y <= 1050000000.0)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = (x + 1.0) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.2e+40) or not (y <= 1050000000.0):
		tmp = x + math.cos(y)
	else:
		tmp = (x + 1.0) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.2e+40) || !(y <= 1050000000.0))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.2e+40) || ~((y <= 1050000000.0)))
		tmp = x + cos(y);
	else
		tmp = (x + 1.0) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.2e+40], N[Not[LessEqual[y, 1050000000.0]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000003e40 or 1.05e9 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 67.2%

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

      1. +-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -8.2000000000000003e40 < y < 1.05e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.2%

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

      1. associate-+r+ 96.2%

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

      2. +-commutative 96.2%

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

      3. mul-1-neg 96.2%

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

   5. Simplified 96.2%

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

      1. unsub-neg 96.2%

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

   7. Applied egg-rr 96.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+40} \lor \neg \left(y \leq 1050000000\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-188}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-20}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.06e-188)
   (- (+ x 1.0) (* y z))
   (if (<= x 1.95e-20) (cos y) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e-188) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 1.95e-20) {
		tmp = cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.06d-188)) then
        tmp = (x + 1.0d0) - (y * z)
    else if (x <= 1.95d-20) then
        tmp = cos(y)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.06e-188) {
		tmp = (x + 1.0) - (y * z);
	} else if (x <= 1.95e-20) {
		tmp = Math.cos(y);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.06e-188:
		tmp = (x + 1.0) - (y * z)
	elif x <= 1.95e-20:
		tmp = math.cos(y)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.06e-188)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	elseif (x <= 1.95e-20)
		tmp = cos(y);
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.06e-188)
		tmp = (x + 1.0) - (y * z);
	elseif (x <= 1.95e-20)
		tmp = cos(y);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.06e-188], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e-20], N[Cos[y], $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.06e-188

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 79.0%

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

      1. associate-+r+ 79.0%

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

      2. +-commutative 79.0%

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

      3. mul-1-neg 79.0%

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

   5. Simplified 79.0%

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

      1. unsub-neg 79.0%

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

   7. Applied egg-rr 79.0%

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

   if -1.06e-188 < x < 1.95000000000000004e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in z around 0 61.3%

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

   if 1.95000000000000004e-20 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.7%

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

      5. associate-*r* 99.7%

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

      6. fma-def 99.7%

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

      7. pow2 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0 82.2%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.06 \cdot 10^{-188}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-20}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-19} \lor \neg \left(x \leq 0.0048\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e-19) (not (<= x 0.0048))) (+ x 1.0) (- 1.0 (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e-19) || !(x <= 0.0048)) {
		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 <= (-5d-19)) .or. (.not. (x <= 0.0048d0))) 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 <= -5e-19) || !(x <= 0.0048)) {
		tmp = x + 1.0;
	} else {
		tmp = 1.0 - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e-19) or not (x <= 0.0048):
		tmp = x + 1.0
	else:
		tmp = 1.0 - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e-19) || !(x <= 0.0048))
		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 <= -5e-19) || ~((x <= 0.0048)))
		tmp = x + 1.0;
	else
		tmp = 1.0 - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e-19], N[Not[LessEqual[x, 0.0048]], $MachinePrecision]], N[(x + 1.0), $MachinePrecision], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000004e-19 or 0.00479999999999999958 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.7%

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

      5. associate-*r* 99.8%

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

      6. fma-def 99.8%

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

      7. pow2 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 83.9%

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

   if -5.0000000000000004e-19 < x < 0.00479999999999999958

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 58.3%

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

      1. associate-+r+ 58.3%

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

      2. +-commutative 58.3%

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

      3. mul-1-neg 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in x around 0 58.3%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-19} \lor \neg \left(x \leq 0.0048\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.8% accurate, 14.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+174} \lor \neg \left(z \leq 2.2 \cdot 10^{+223}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.05e+174) (not (<= z 2.2e+223))) (* y (- z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.05e+174) || !(z <= 2.2e+223)) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.05d+174)) .or. (.not. (z <= 2.2d+223))) then
        tmp = y * -z
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.05e+174) || !(z <= 2.2e+223)) {
		tmp = y * -z;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.05e+174) or not (z <= 2.2e+223):
		tmp = y * -z
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.05e+174) || !(z <= 2.2e+223))
		tmp = Float64(y * Float64(-z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.05e+174) || ~((z <= 2.2e+223)))
		tmp = y * -z;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.05e+174], N[Not[LessEqual[z, 2.2e+223]], $MachinePrecision]], N[(y * (-z)), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.05e174 or 2.2e223 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 58.3%

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

      1. associate-+r+ 58.3%

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

      2. +-commutative 58.3%

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

      3. mul-1-neg 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in y around inf 37.2%

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

      1. associate-*r* 37.2%

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

      2. neg-mul-1 37.2%

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

   8. Simplified 37.2%

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

   if -3.05e174 < z < 2.2e223

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. add-cube-cbrt 99.8%

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

      5. associate-*r* 99.8%

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

      6. fma-def 99.8%

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

      7. pow2 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 75.9%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+174} \lor \neg \left(z \leq 2.2 \cdot 10^{+223}\right):\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.4% accurate, 17.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{+64}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 8.8e+64) (- (+ x 1.0) (* y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.8e+64) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 8.8d+64) then
        tmp = (x + 1.0d0) - (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 8.8e+64) {
		tmp = (x + 1.0) - (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 8.8e+64:
		tmp = (x + 1.0) - (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 8.8e+64)
		tmp = Float64(Float64(x + 1.0) - Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 8.8e+64)
		tmp = (x + 1.0) - (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 8.8e+64], N[(N[(x + 1.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < 8.80000000000000007e64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.8%

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

      1. associate-+r+ 67.8%

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

      2. +-commutative 67.8%

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

      3. mul-1-neg 67.8%

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

   5. Simplified 67.8%

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

      1. unsub-neg 67.8%

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

   7. Applied egg-rr 67.8%

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

   if 8.80000000000000007e64 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.7%

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

      5. associate-*r* 99.7%

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

      6. fma-def 99.7%

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

      7. pow2 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 84.2%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8.8 \cdot 10^{+64}:\\ \;\;\;\;\left(x + 1\right) - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-42}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.9e-14) x (if (<= x 1.55e-42) 1.0 x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.9e-14) {
		tmp = x;
	} else if (x <= 1.55e-42) {
		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 <= (-4.9d-14)) then
        tmp = x
    else if (x <= 1.55d-42) 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 <= -4.9e-14) {
		tmp = x;
	} else if (x <= 1.55e-42) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.9e-14:
		tmp = x
	elif x <= 1.55e-42:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.9e-14)
		tmp = x;
	elseif (x <= 1.55e-42)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.9e-14)
		tmp = x;
	elseif (x <= 1.55e-42)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.9e-14], x, If[LessEqual[x, 1.55e-42], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.89999999999999995e-14 or 1.5500000000000001e-42 < x

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-lft-neg-in 99.9%

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

      4. add-cube-cbrt 99.7%

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

      5. associate-*r* 99.7%

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

      6. fma-def 99.7%

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

      7. pow2 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 81.6%

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

   if -4.89999999999999995e-14 < x < 1.5500000000000001e-42

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

   4. Taylor expanded in y around 0 42.6%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-42}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.9% 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. sub-neg 99.9%

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

   2. +-commutative 99.9%

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

   3. distribute-lft-neg-in 99.9%

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

   4. add-cube-cbrt 99.5%

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

   5. associate-*r* 99.5%

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

   6. fma-def 99.5%

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

   7. pow2 99.5%

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

4. Applied egg-rr 99.5%

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

5. Taylor expanded in y around 0 64.2%

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

6. Final simplification 64.2%

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

Alternative 12: 21.5% 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 56.3%

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

4. Taylor expanded in y around 0 21.3%

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

5. Final simplification 21.3%

   \[\leadsto 1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024027 
(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))))