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

Percentage Accurate: 99.9% → 99.9%

Time: 9.5s

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. Final simplification 99.9%

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

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \sin y\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{-16} \lor \neg \left(x \leq 2.65 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;\cos y - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (sin y))))
   (if (or (<= x -3.7e-16) (not (<= x 2.65e-6)))
     (- (+ 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 <= -3.7e-16) || !(x <= 2.65e-6)) {
		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 <= (-3.7d-16)) .or. (.not. (x <= 2.65d-6))) 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 <= -3.7e-16) || !(x <= 2.65e-6)) {
		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 <= -3.7e-16) or not (x <= 2.65e-6):
		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 <= -3.7e-16) || !(x <= 2.65e-6))
		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 <= -3.7e-16) || ~((x <= 2.65e-6)))
		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, -3.7e-16], N[Not[LessEqual[x, 2.65e-6]], $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 < -3.7e-16 or 2.65e-6 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. +-commutative 98.7%

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

   4. Simplified 98.7%

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

   if -3.7e-16 < x < 2.65e-6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-16} \lor \neg \left(x \leq 2.65 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;\cos y - z \cdot \sin y\\ \end{array} \]

Alternative 3: 83.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - z \cdot \sin y\\ \mathbf{if}\;z \leq -6 \cdot 10^{+57}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+149}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+220} \lor \neg \left(z \leq 1.45 \cdot 10^{+249}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- 1.0 (* z (sin y)))))
   (if (<= z -6e+57)
     t_0
     (if (<= z 1.2e+29)
       (+ x (cos y))
       (if (<= z 2.4e+73)
         t_0
         (if (<= z 3.95e+149)
           (+ x 1.0)
           (if (or (<= z 2.4e+220) (not (<= z 1.45e+249)))
             t_0
             (+ x (- 1.0 (* y z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 - (z * sin(y));
	double tmp;
	if (z <= -6e+57) {
		tmp = t_0;
	} else if (z <= 1.2e+29) {
		tmp = x + cos(y);
	} else if (z <= 2.4e+73) {
		tmp = t_0;
	} else if (z <= 3.95e+149) {
		tmp = x + 1.0;
	} else if ((z <= 2.4e+220) || !(z <= 1.45e+249)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (z * sin(y))
    if (z <= (-6d+57)) then
        tmp = t_0
    else if (z <= 1.2d+29) then
        tmp = x + cos(y)
    else if (z <= 2.4d+73) then
        tmp = t_0
    else if (z <= 3.95d+149) then
        tmp = x + 1.0d0
    else if ((z <= 2.4d+220) .or. (.not. (z <= 1.45d+249))) then
        tmp = t_0
    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 t_0 = 1.0 - (z * Math.sin(y));
	double tmp;
	if (z <= -6e+57) {
		tmp = t_0;
	} else if (z <= 1.2e+29) {
		tmp = x + Math.cos(y);
	} else if (z <= 2.4e+73) {
		tmp = t_0;
	} else if (z <= 3.95e+149) {
		tmp = x + 1.0;
	} else if ((z <= 2.4e+220) || !(z <= 1.45e+249)) {
		tmp = t_0;
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 - (z * math.sin(y))
	tmp = 0
	if z <= -6e+57:
		tmp = t_0
	elif z <= 1.2e+29:
		tmp = x + math.cos(y)
	elif z <= 2.4e+73:
		tmp = t_0
	elif z <= 3.95e+149:
		tmp = x + 1.0
	elif (z <= 2.4e+220) or not (z <= 1.45e+249):
		tmp = t_0
	else:
		tmp = x + (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 - Float64(z * sin(y)))
	tmp = 0.0
	if (z <= -6e+57)
		tmp = t_0;
	elseif (z <= 1.2e+29)
		tmp = Float64(x + cos(y));
	elseif (z <= 2.4e+73)
		tmp = t_0;
	elseif (z <= 3.95e+149)
		tmp = Float64(x + 1.0);
	elseif ((z <= 2.4e+220) || !(z <= 1.45e+249))
		tmp = t_0;
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 - (z * sin(y));
	tmp = 0.0;
	if (z <= -6e+57)
		tmp = t_0;
	elseif (z <= 1.2e+29)
		tmp = x + cos(y);
	elseif (z <= 2.4e+73)
		tmp = t_0;
	elseif (z <= 3.95e+149)
		tmp = x + 1.0;
	elseif ((z <= 2.4e+220) || ~((z <= 1.45e+249)))
		tmp = t_0;
	else
		tmp = x + (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+57], t$95$0, If[LessEqual[z, 1.2e+29], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+73], t$95$0, If[LessEqual[z, 3.95e+149], N[(x + 1.0), $MachinePrecision], If[Or[LessEqual[z, 2.4e+220], N[Not[LessEqual[z, 1.45e+249]], $MachinePrecision]], t$95$0, N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.9999999999999999e57 or 1.2e29 < z < 2.40000000000000002e73 or 3.94999999999999982e149 < z < 2.3999999999999998e220 or 1.45000000000000008e249 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around 0 80.4%

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

   if -5.9999999999999999e57 < z < 1.2e29

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. flip-+ 76.2%

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

      3. pow1 76.2%

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

      4. pow1 76.2%

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

      5. pow-prod-up 76.2%

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

      6. metadata-eval 76.2%

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

   3. Applied egg-rr 76.2%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\cos y - z \cdot \sin y\right)}^{2}}{x - \left(\cos y - z \cdot \sin y\right)}} \]
   4. Step-by-step derivation

      1. clear-num 76.0%

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

      2. inv-pow 76.0%

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

      3. clear-num 76.0%

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

      4. unpow2 76.0%

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

      5. flip-+ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 97.0%

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

   if 2.40000000000000002e73 < z < 3.94999999999999982e149

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{1 + x} \]
   6. Step-by-step derivation

      1. +-commutative 74.5%

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

   7. Simplified 74.5%

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

   if 2.3999999999999998e220 < z < 1.45000000000000008e249

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.5%

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

      1. associate-+r+ 91.5%

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

      2. +-commutative 91.5%

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

      3. mul-1-neg 91.5%

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

      4. unsub-neg 91.5%

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

   4. Simplified 91.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+57}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+73}:\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+149}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+220} \lor \neg \left(z \leq 1.45 \cdot 10^{+249}\right):\\ \;\;\;\;1 - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 4: 81.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+69} \lor \neg \left(z \leq 3.8 \cdot 10^{+150}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (sin y) (- z))))
   (if (<= z -2.5e+116)
     t_0
     (if (<= z 2.8e+30)
       (+ x (cos y))
       (if (or (<= z 4.4e+69) (not (<= z 3.8e+150))) t_0 (+ x 1.0))))))

C

double code(double x, double y, double z) {
	double t_0 = sin(y) * -z;
	double tmp;
	if (z <= -2.5e+116) {
		tmp = t_0;
	} else if (z <= 2.8e+30) {
		tmp = x + cos(y);
	} else if ((z <= 4.4e+69) || !(z <= 3.8e+150)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = sin(y) * -z
    if (z <= (-2.5d+116)) then
        tmp = t_0
    else if (z <= 2.8d+30) then
        tmp = x + cos(y)
    else if ((z <= 4.4d+69) .or. (.not. (z <= 3.8d+150))) then
        tmp = t_0
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.sin(y) * -z;
	double tmp;
	if (z <= -2.5e+116) {
		tmp = t_0;
	} else if (z <= 2.8e+30) {
		tmp = x + Math.cos(y);
	} else if ((z <= 4.4e+69) || !(z <= 3.8e+150)) {
		tmp = t_0;
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.sin(y) * -z
	tmp = 0
	if z <= -2.5e+116:
		tmp = t_0
	elif z <= 2.8e+30:
		tmp = x + math.cos(y)
	elif (z <= 4.4e+69) or not (z <= 3.8e+150):
		tmp = t_0
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(sin(y) * Float64(-z))
	tmp = 0.0
	if (z <= -2.5e+116)
		tmp = t_0;
	elseif (z <= 2.8e+30)
		tmp = Float64(x + cos(y));
	elseif ((z <= 4.4e+69) || !(z <= 3.8e+150))
		tmp = t_0;
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = sin(y) * -z;
	tmp = 0.0;
	if (z <= -2.5e+116)
		tmp = t_0;
	elseif (z <= 2.8e+30)
		tmp = x + cos(y);
	elseif ((z <= 4.4e+69) || ~((z <= 3.8e+150)))
		tmp = t_0;
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Sin[y], $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -2.5e+116], t$95$0, If[LessEqual[z, 2.8e+30], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.4e+69], N[Not[LessEqual[z, 3.8e+150]], $MachinePrecision]], t$95$0, N[(x + 1.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000013e116 or 2.79999999999999983e30 < z < 4.4000000000000003e69 or 3.79999999999999989e150 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. neg-mul-1 70.6%

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

      3. *-commutative 70.6%

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

   4. Simplified 70.6%

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

   if -2.50000000000000013e116 < z < 2.79999999999999983e30

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. flip-+ 77.2%

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

      3. pow1 77.2%

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

      4. pow1 77.2%

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

      5. pow-prod-up 77.2%

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

      6. metadata-eval 77.2%

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

   3. Applied egg-rr 77.2%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\cos y - z \cdot \sin y\right)}^{2}}{x - \left(\cos y - z \cdot \sin y\right)}} \]
   4. Step-by-step derivation

      1. clear-num 76.9%

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

      2. inv-pow 76.9%

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

      3. clear-num 77.0%

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

      4. unpow2 77.0%

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

      5. flip-+ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 95.8%

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

   if 4.4000000000000003e69 < z < 3.79999999999999989e150

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 74.5%

      \[\leadsto \color{blue}{1 + x} \]
   6. Step-by-step derivation

      1. +-commutative 74.5%

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

   7. Simplified 74.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+116}:\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+69} \lor \neg \left(z \leq 3.8 \cdot 10^{+150}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 5: 99.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22.5 \lor \neg \left(z \leq 6 \cdot 10^{-26}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -22.5) (not (<= z 6e-26)))
   (- (+ x 1.0) (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -22.5) || !(z <= 6e-26)) {
		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 <= (-22.5d0)) .or. (.not. (z <= 6d-26))) 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 <= -22.5) || !(z <= 6e-26)) {
		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 <= -22.5) or not (z <= 6e-26):
		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 <= -22.5) || !(z <= 6e-26))
		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 <= -22.5) || ~((z <= 6e-26)))
		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, -22.5], N[Not[LessEqual[z, 6e-26]], $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 < -22.5 or 6.00000000000000023e-26 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 98.0%

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

      1. +-commutative 98.0%

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

   4. Simplified 98.0%

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

   if -22.5 < z < 6.00000000000000023e-26

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. flip-+ 78.8%

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

      3. pow1 78.8%

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

      4. pow1 78.8%

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

      5. pow-prod-up 78.8%

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

      6. metadata-eval 78.8%

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

   3. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\cos y - z \cdot \sin y\right)}^{2}}{x - \left(\cos y - z \cdot \sin y\right)}} \]
   4. Step-by-step derivation

      1. clear-num 78.5%

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

      2. inv-pow 78.5%

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

      3. clear-num 78.6%

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

      4. unpow2 78.6%

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

      5. flip-+ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 99.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22.5 \lor \neg \left(z \leq 6 \cdot 10^{-26}\right):\\ \;\;\;\;\left(x + 1\right) - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 6: 93.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1400000000 \lor \neg \left(z \leq 8 \cdot 10^{+29}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1400000000.0) (not (<= z 8e+29)))
   (- x (* z (sin y)))
   (+ x (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1400000000.0) || !(z <= 8e+29)) {
		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 <= (-1400000000.0d0)) .or. (.not. (z <= 8d+29))) 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 <= -1400000000.0) || !(z <= 8e+29)) {
		tmp = x - (z * Math.sin(y));
	} else {
		tmp = x + Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1400000000.0) or not (z <= 8e+29):
		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 <= -1400000000.0) || !(z <= 8e+29))
		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 <= -1400000000.0) || ~((z <= 8e+29)))
		tmp = x - (z * sin(y));
	else
		tmp = x + cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1400000000.0], N[Not[LessEqual[z, 8e+29]], $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 < -1.4e9 or 7.99999999999999931e29 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 89.9%

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

   if -1.4e9 < z < 7.99999999999999931e29

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

      2. flip-+ 78.8%

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

      3. pow1 78.8%

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

      4. pow1 78.8%

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

      5. pow-prod-up 78.8%

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

      6. metadata-eval 78.8%

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

   3. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\cos y - z \cdot \sin y\right)}^{2}}{x - \left(\cos y - z \cdot \sin y\right)}} \]
   4. Step-by-step derivation

      1. clear-num 78.5%

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

      2. inv-pow 78.5%

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

      3. clear-num 78.6%

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

      4. unpow2 78.6%

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

      5. flip-+ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around 0 97.6%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400000000 \lor \neg \left(z \leq 8 \cdot 10^{+29}\right):\\ \;\;\;\;x - z \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 7: 80.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23} \lor \neg \left(y \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+23) (not (<= y 7.8e-16)))
   (+ x (cos y))
   (+ x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+23) || !(y <= 7.8e-16)) {
		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 <= (-4.5d+23)) .or. (.not. (y <= 7.8d-16))) 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 <= -4.5e+23) || !(y <= 7.8e-16)) {
		tmp = x + Math.cos(y);
	} else {
		tmp = x + (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+23) or not (y <= 7.8e-16):
		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 <= -4.5e+23) || !(y <= 7.8e-16))
		tmp = Float64(x + cos(y));
	else
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.5e+23) || ~((y <= 7.8e-16)))
		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, -4.5e+23], N[Not[LessEqual[y, 7.8e-16]], $MachinePrecision]], N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999979e23 or 7.79999999999999954e-16 < y

   1. Initial program 99.8%

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

      1. associate--l+ 99.8%

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

      2. flip-+ 58.1%

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

      3. pow1 58.1%

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

      4. pow1 58.1%

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

      5. pow-prod-up 58.1%

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

      6. metadata-eval 58.1%

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

   3. Applied egg-rr 58.1%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\cos y - z \cdot \sin y\right)}^{2}}{x - \left(\cos y - z \cdot \sin y\right)}} \]
   4. Step-by-step derivation

      1. clear-num 57.8%

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

      2. inv-pow 57.8%

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

      3. clear-num 57.8%

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

      4. unpow2 57.8%

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

      5. flip-+ 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in z around 0 62.7%

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

   if -4.49999999999999979e23 < y < 7.79999999999999954e-16

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.1%

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

      1. associate-+r+ 96.1%

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

      2. +-commutative 96.1%

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

      3. mul-1-neg 96.1%

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

      4. unsub-neg 96.1%

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

   4. Simplified 96.1%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+23} \lor \neg \left(y \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 8: 70.4% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+77}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.15e+60)
   (+ x 1.0)
   (if (<= y 1.16e+77) (+ x (- 1.0 (* y z))) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+60) {
		tmp = x + 1.0;
	} else if (y <= 1.16e+77) {
		tmp = x + (1.0 - (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 (y <= (-2.15d+60)) then
        tmp = x + 1.0d0
    else if (y <= 1.16d+77) then
        tmp = x + (1.0d0 - (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 (y <= -2.15e+60) {
		tmp = x + 1.0;
	} else if (y <= 1.16e+77) {
		tmp = x + (1.0 - (y * z));
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.15e+60:
		tmp = x + 1.0
	elif y <= 1.16e+77:
		tmp = x + (1.0 - (y * z))
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.15e+60)
		tmp = Float64(x + 1.0);
	elseif (y <= 1.16e+77)
		tmp = Float64(x + Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.15e+60)
		tmp = x + 1.0;
	elseif (y <= 1.16e+77)
		tmp = x + (1.0 - (y * z));
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.15e+60], N[(x + 1.0), $MachinePrecision], If[LessEqual[y, 1.16e+77], N[(x + N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.14999999999999986e60 or 1.1600000000000001e77 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 71.3%

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

      1. +-commutative 71.3%

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

   4. Simplified 71.3%

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

   5. Taylor expanded in z around 0 34.3%

      \[\leadsto \color{blue}{1 + x} \]
   6. Step-by-step derivation

      1. +-commutative 34.3%

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

   7. Simplified 34.3%

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

   if -2.14999999999999986e60 < y < 1.1600000000000001e77

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.9%

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

      1. associate-+r+ 86.9%

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

      2. +-commutative 86.9%

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

      3. mul-1-neg 86.9%

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

      4. unsub-neg 86.9%

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

   4. Simplified 86.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+60}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+77}:\\ \;\;\;\;x + \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9: 66.1% accurate, 22.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+126} \lor \neg \left(z \leq 7.2 \cdot 10^{+191}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.7e+126) (not (<= z 7.2e+191))) (- x (* y z)) (+ x 1.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+126) || !(z <= 7.2e+191)) {
		tmp = x - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.7d+126)) .or. (.not. (z <= 7.2d+191))) then
        tmp = x - (y * z)
    else
        tmp = x + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.7e+126) || !(z <= 7.2e+191)) {
		tmp = x - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.7e+126) or not (z <= 7.2e+191):
		tmp = x - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.7e+126) || !(z <= 7.2e+191))
		tmp = Float64(x - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.7e+126) || ~((z <= 7.2e+191)))
		tmp = x - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.7e+126], N[Not[LessEqual[z, 7.2e+191]], $MachinePrecision]], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999998e126 or 7.1999999999999999e191 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 53.4%

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

   3. Taylor expanded in x around inf 47.3%

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

   if -3.6999999999999998e126 < z < 7.1999999999999999e191

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.9%

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

      1. +-commutative 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in z around 0 67.7%

      \[\leadsto \color{blue}{1 + x} \]
   6. Step-by-step derivation

      1. +-commutative 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+126} \lor \neg \left(z \leq 7.2 \cdot 10^{+191}\right):\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 10: 67.7% accurate, 22.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-39}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.7e-16) (+ x 1.0) (if (<= x 1.1e-39) (- 1.0 (* y z)) (+ x 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.7e-16) {
		tmp = x + 1.0;
	} else if (x <= 1.1e-39) {
		tmp = 1.0 - (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 (x <= (-3.7d-16)) then
        tmp = x + 1.0d0
    else if (x <= 1.1d-39) then
        tmp = 1.0d0 - (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 (x <= -3.7e-16) {
		tmp = x + 1.0;
	} else if (x <= 1.1e-39) {
		tmp = 1.0 - (y * z);
	} else {
		tmp = x + 1.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.7e-16:
		tmp = x + 1.0
	elif x <= 1.1e-39:
		tmp = 1.0 - (y * z)
	else:
		tmp = x + 1.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.7e-16)
		tmp = Float64(x + 1.0);
	elseif (x <= 1.1e-39)
		tmp = Float64(1.0 - Float64(y * z));
	else
		tmp = Float64(x + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.7e-16)
		tmp = x + 1.0;
	elseif (x <= 1.1e-39)
		tmp = 1.0 - (y * z);
	else
		tmp = x + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.7e-16], N[(x + 1.0), $MachinePrecision], If[LessEqual[x, 1.1e-39], N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + 1.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7e-16 or 1.1e-39 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 97.5%

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

      1. +-commutative 97.5%

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

   4. Simplified 97.5%

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

   5. Taylor expanded in z around 0 72.1%

      \[\leadsto \color{blue}{1 + x} \]
   6. Step-by-step derivation

      1. +-commutative 72.1%

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

   7. Simplified 72.1%

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

   if -3.7e-16 < x < 1.1e-39

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 74.0%

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

      1. +-commutative 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in x around 0 74.0%

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

   6. Taylor expanded in y around 0 52.6%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-16}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-39}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 11: 62.4% 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. Taylor expanded in y around 0 85.4%

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

   1. +-commutative 85.4%

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

4. Simplified 85.4%

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

5. Taylor expanded in z around 0 56.5%

   \[\leadsto \color{blue}{1 + x} \]
6. Step-by-step derivation

   1. +-commutative 56.5%

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

7. Simplified 56.5%

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

8. Final simplification 56.5%

   \[\leadsto x + 1 \]

Alternative 12: 43.0% accurate, 207.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. associate--l+ 99.9%

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

   2. flip-+ 65.1%

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

   3. pow1 65.1%

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

   4. pow1 65.1%

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

   5. pow-prod-up 65.1%

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

   6. metadata-eval 65.1%

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

3. Applied egg-rr 65.1%

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

4. Taylor expanded in z around inf 99.9%

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

5. Taylor expanded in x around inf 35.1%

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

6. Final simplification 35.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(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))))