Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B

Percentage Accurate: 100.0% → 100.0%

Time: 9.0s

Alternatives: 11

Speedup: 1.0×

• 26.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 48.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1.5e+54)
   (/ (* x 0.5) t)
   (if (<= (+ x y) 4e-81) (/ (* z -0.5) t) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1.5e+54) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 4e-81) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1.5d+54)) then
        tmp = (x * 0.5d0) / t
    else if ((x + y) <= 4d-81) then
        tmp = (z * (-0.5d0)) / t
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1.5e+54) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 4e-81) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1.5e+54:
		tmp = (x * 0.5) / t
	elif (x + y) <= 4e-81:
		tmp = (z * -0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1.5e+54)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (Float64(x + y) <= 4e-81)
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1.5e+54)
		tmp = (x * 0.5) / t;
	elseif ((x + y) <= 4e-81)
		tmp = (z * -0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1.5e+54], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e-81], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.4999999999999999e54

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot x}}{t} \]

      5. lower-*.f64 40.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot x}}{t} \]

   5. Applied rewrites 40.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -1.4999999999999999e54 < (+.f64 x y) < 3.9999999999999998e-81

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. lower-*.f64 73.0

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if 3.9999999999999998e-81 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. lower-*.f64 44.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot y}}{t} \]

   5. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1.5e+54)
   (/ (* x 0.5) t)
   (if (<= (+ x y) 4e-81) (* z (/ -0.5 t)) (/ (* y 0.5) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1.5e+54) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 4e-81) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1.5d+54)) then
        tmp = (x * 0.5d0) / t
    else if ((x + y) <= 4d-81) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1.5e+54) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 4e-81) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1.5e+54:
		tmp = (x * 0.5) / t
	elif (x + y) <= 4e-81:
		tmp = z * (-0.5 / t)
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1.5e+54)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (Float64(x + y) <= 4e-81)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1.5e+54)
		tmp = (x * 0.5) / t;
	elseif ((x + y) <= 4e-81)
		tmp = z * (-0.5 / t);
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1.5e+54], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e-81], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.4999999999999999e54

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot x}}{t} \]

      5. lower-*.f64 40.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot x}}{t} \]

   5. Applied rewrites 40.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -1.4999999999999999e54 < (+.f64 x y) < 3.9999999999999998e-81

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. lower-*.f64 73.0

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

      4. lower-/.f64 72.8

         \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   7. Applied rewrites 72.8%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 3.9999999999999998e-81 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. lower-*.f64 44.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot y}}{t} \]

   5. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1.5e+54)
   (/ (* x 0.5) t)
   (if (<= (+ x y) 4e-81) (* z (/ -0.5 t)) (* y (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1.5e+54) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 4e-81) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1.5d+54)) then
        tmp = (x * 0.5d0) / t
    else if ((x + y) <= 4d-81) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = y * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1.5e+54) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 4e-81) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1.5e+54:
		tmp = (x * 0.5) / t
	elif (x + y) <= 4e-81:
		tmp = z * (-0.5 / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1.5e+54)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (Float64(x + y) <= 4e-81)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1.5e+54)
		tmp = (x * 0.5) / t;
	elseif ((x + y) <= 4e-81)
		tmp = z * (-0.5 / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1.5e+54], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 4e-81], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -1.4999999999999999e54

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot x}}{t} \]

      5. lower-*.f64 40.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot x}}{t} \]

   5. Applied rewrites 40.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} \]

   if -1.4999999999999999e54 < (+.f64 x y) < 3.9999999999999998e-81

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. lower-*.f64 73.0

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

   5. Applied rewrites 73.0%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

      4. lower-/.f64 72.8

         \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   7. Applied rewrites 72.8%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 3.9999999999999998e-81 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. lower-*.f64 44.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot y}}{t} \]

   5. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
   6. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{t} \cdot y} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{t}} \cdot y \]

      3. lower-*.f64 44.3

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot y} \]

   7. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+113}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= z -2.5e+94) t_1 (if (<= z 3e+113) (/ (+ x y) (* t 2.0)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -2.5e+94) {
		tmp = t_1;
	} else if (z <= 3e+113) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    if (z <= (-2.5d+94)) then
        tmp = t_1
    else if (z <= 3d+113) then
        tmp = (x + y) / (t * 2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -2.5e+94) {
		tmp = t_1;
	} else if (z <= 3e+113) {
		tmp = (x + y) / (t * 2.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	tmp = 0
	if z <= -2.5e+94:
		tmp = t_1
	elif z <= 3e+113:
		tmp = (x + y) / (t * 2.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (z <= -2.5e+94)
		tmp = t_1;
	elseif (z <= 3e+113)
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	tmp = 0.0;
	if (z <= -2.5e+94)
		tmp = t_1;
	elseif (z <= 3e+113)
		tmp = (x + y) / (t * 2.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.5e+94], t$95$1, If[LessEqual[z, 3e+113], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000005e94 or 3e113 < z

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. lower-*.f64 80.0

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

   5. Applied rewrites 80.0%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if -2.50000000000000005e94 < z < 3e113

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{x + y}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

      2. lower-+.f64 89.9

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

   5. Applied rewrites 89.9%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+113}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+113}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= z -2.5e+94) t_1 (if (<= z 3e+113) (* (+ x y) (/ 0.5 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -2.5e+94) {
		tmp = t_1;
	} else if (z <= 3e+113) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    if (z <= (-2.5d+94)) then
        tmp = t_1
    else if (z <= 3d+113) then
        tmp = (x + y) * (0.5d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (z <= -2.5e+94) {
		tmp = t_1;
	} else if (z <= 3e+113) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	tmp = 0
	if z <= -2.5e+94:
		tmp = t_1
	elif z <= 3e+113:
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (z <= -2.5e+94)
		tmp = t_1;
	elseif (z <= 3e+113)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	tmp = 0.0;
	if (z <= -2.5e+94)
		tmp = t_1;
	elseif (z <= 3e+113)
		tmp = (x + y) * (0.5 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.5e+94], t$95$1, If[LessEqual[z, 3e+113], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000005e94 or 3e113 < z

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. lower-*.f64 80.0

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

   5. Applied rewrites 80.0%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if -2.50000000000000005e94 < z < 3e113

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. div-inv N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. lower-/.f64 N/A

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

      11. metadata-eval 99.7

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

      12. lift--.f64 N/A

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

      13. lift-+.f64 N/A

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

      14. associate--l+ N/A

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

      15. lower-+.f64 N/A

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

      16. lower--.f64 99.7

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

   4. Applied rewrites 99.7%

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

   5. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{1}{2}}{t} \cdot \color{blue}{\left(x + y\right)} \]
   6. Step-by-step derivation

      1. lower-+.f64 89.7

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

   7. Applied rewrites 89.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+113}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-150}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e-150) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-150) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d-150)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e-150) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e-150:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e-150)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e-150)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-150], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.00000000000000001e-150

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. lower--.f64 64.9

         \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   5. Applied rewrites 64.9%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -1.00000000000000001e-150 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. lower--.f64 66.9

         \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]

   5. Applied rewrites 66.9%

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 4e-81) (/ (- x z) (* t 2.0)) (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 4e-81) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 4d-81) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (x + y) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 4e-81) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 4e-81:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 4e-81)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 4e-81)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 4e-81], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 3.9999999999999998e-81

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. lower--.f64 69.8

         \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   5. Applied rewrites 69.8%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if 3.9999999999999998e-81 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{x + y}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

      2. lower-+.f64 82.0

         \[\leadsto \frac{\color{blue}{y + x}}{t \cdot 2} \]

   5. Applied rewrites 82.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 4e-81) (* z (/ -0.5 t)) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 4e-81) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 4d-81) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = y * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 4e-81) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 4e-81:
		tmp = z * (-0.5 / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 4e-81)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 4e-81)
		tmp = z * (-0.5 / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 4e-81], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 3.9999999999999998e-81

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      2. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

      4. lower-*.f64 42.7

         \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

   5. Applied rewrites 42.7%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

      4. lower-/.f64 42.6

         \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   7. Applied rewrites 42.6%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 3.9999999999999998e-81 < (+.f64 x y)

   1. Initial program 100.0%

      \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{y}{t} \cdot \frac{1}{2}} \]

      2. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      3. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \frac{1}{2}}{t}} \]

      4. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\frac{1}{2} \cdot y}}{t} \]

      5. lower-*.f64 44.5

         \[\leadsto \frac{\color{blue}{0.5 \cdot y}}{t} \]

   5. Applied rewrites 44.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
   6. Step-by-step derivation

      1. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{t} \cdot y} \]

      2. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{2}}{t}} \cdot y \]

      3. lower-*.f64 44.3

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot y} \]

   7. Applied rewrites 44.3%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ 0.5 t) (+ x (- y z))))

C

double code(double x, double y, double z, double t) {
	return (0.5 / t) * (x + (y - z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (0.5d0 / t) * (x + (y - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (0.5 / t) * (x + (y - z));
}

Python

def code(x, y, z, t):
	return (0.5 / t) * (x + (y - z))

Julia

function code(x, y, z, t)
	return Float64(Float64(0.5 / t) * Float64(x + Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (0.5 / t) * (x + (y - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(0.5 / t), $MachinePrecision] * N[(x + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. div-inv N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. associate-/r* N/A

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

   10. lower-/.f64 N/A

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

   11. metadata-eval 99.7

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

   12. lift--.f64 N/A

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

   13. lift-+.f64 N/A

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

   14. associate--l+ N/A

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

   15. lower-+.f64 N/A

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

   16. lower--.f64 99.7

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

4. Applied rewrites 99.7%

   \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right)} \]
5. Add Preprocessing

Alternative 11: 38.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ z \cdot \frac{-0.5}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* z (/ -0.5 t)))

C

double code(double x, double y, double z, double t) {
	return z * (-0.5 / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = z * ((-0.5d0) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return z * (-0.5 / t);
}

Python

def code(x, y, z, t):
	return z * (-0.5 / t)

Julia

function code(x, y, z, t)
	return Float64(z * Float64(-0.5 / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = z * (-0.5 / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

   2. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot z}{t}} \]

   3. *-commutative N/A

      \[\leadsto \frac{\color{blue}{z \cdot \frac{-1}{2}}}{t} \]

   4. lower-*.f64 33.8

      \[\leadsto \frac{\color{blue}{z \cdot -0.5}}{t} \]

5. Applied rewrites 33.8%

   \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]
6. Step-by-step derivation

   1. associate-/l* N/A

      \[\leadsto \color{blue}{z \cdot \frac{\frac{-1}{2}}{t}} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{\frac{-1}{2}}{t} \cdot z} \]

   4. lower-/.f64 33.7

      \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

7. Applied rewrites 33.7%

   \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

8. Final simplification 33.7%

   \[\leadsto z \cdot \frac{-0.5}{t} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024216 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))