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

Percentage Accurate: 99.9% → 99.9%

Time: 9.5s

Alternatives: 11

Speedup: 1.0×

• 26.2% 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: 99.9% 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: 99.9% 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: 36.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x + y\right) - z}{t \cdot 2} \leq -2 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- (+ x y) z) (* t 2.0)) -2e-245) (/ (* x 0.5) t) (/ (* y 0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x + y) - z) / (t * 2.0)) <= -2e-245) {
		tmp = (x * 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) - z) / (t * 2.0d0)) <= (-2d-245)) then
        tmp = (x * 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) - z) / (t * 2.0)) <= -2e-245) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x + y) - z) / (t * 2.0)) <= -2e-245:
		tmp = (x * 0.5) / t
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0)) <= -2e-245)
		tmp = Float64(Float64(x * 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) - z) / (t * 2.0)) <= -2e-245)
		tmp = (x * 0.5) / t;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], -2e-245], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64))) < -1.9999999999999999e-245

   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. /-lowering-/.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. *-lowering-*.f64 39.1

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

   5. Simplified 39.1%

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

   if -1.9999999999999999e-245 < (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64)))

   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. /-lowering-/.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. *-lowering-*.f64 34.9

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

   5. Simplified 34.9%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x + y\right) - z}{t \cdot 2} \leq -2 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -4e+18)
   (/ (* x 0.5) t)
   (if (<= (+ x y) 2e+75) (/ (* 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+18) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 2e+75) {
		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+18)) then
        tmp = (x * 0.5d0) / t
    else if ((x + y) <= 2d+75) 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+18) {
		tmp = (x * 0.5) / t;
	} else if ((x + y) <= 2e+75) {
		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+18:
		tmp = (x * 0.5) / t
	elif (x + y) <= 2e+75:
		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+18)
		tmp = Float64(Float64(x * 0.5) / t);
	elseif (Float64(x + y) <= 2e+75)
		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) <= -4e+18)
		tmp = (x * 0.5) / t;
	elseif ((x + y) <= 2e+75)
		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+18], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 2e+75], 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) < -4e18

   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. /-lowering-/.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. *-lowering-*.f64 40.4

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

   5. Simplified 40.4%

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

   if -4e18 < (+.f64 x y) < 1.99999999999999985e75

   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. /-lowering-/.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. *-lowering-*.f64 72.8

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

   5. Simplified 72.8%

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

   if 1.99999999999999985e75 < (+.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. /-lowering-/.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. *-lowering-*.f64 40.7

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

   5. Simplified 40.7%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+18}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= z -3e+92) t_1 (if (<= z 5.2e+85) (* (+ 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 <= -3e+92) {
		tmp = t_1;
	} else if (z <= 5.2e+85) {
		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 <= (-3d+92)) then
        tmp = t_1
    else if (z <= 5.2d+85) 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 <= -3e+92) {
		tmp = t_1;
	} else if (z <= 5.2e+85) {
		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 <= -3e+92:
		tmp = t_1
	elif z <= 5.2e+85:
		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 <= -3e+92)
		tmp = t_1;
	elseif (z <= 5.2e+85)
		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 <= -3e+92)
		tmp = t_1;
	elseif (z <= 5.2e+85)
		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, -3e+92], t$95$1, If[LessEqual[z, 5.2e+85], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000013e92 or 5.20000000000000021e85 < 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. /-lowering-/.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. *-lowering-*.f64 75.4

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

   5. Simplified 75.4%

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

   if -3.00000000000000013e92 < z < 5.20000000000000021e85

   1. Initial program 100.0%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. /-lowering-/.f64 N/A

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

      7. metadata-eval N/A

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

      8. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.7

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

   4. Applied egg-rr 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. +-lowering-+.f64 89.2

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

   7. Simplified 89.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+92}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+85}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-121}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-121) (/ (- 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) <= -5e-121) {
		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) <= (-5d-121)) 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) <= -5e-121) {
		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) <= -5e-121:
		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) <= -5e-121)
		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) <= -5e-121)
		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], -5e-121], 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) < -4.99999999999999989e-121

   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. --lowering--.f64 66.0

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

   5. Simplified 66.0%

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

   if -4.99999999999999989e-121 < (+.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. --lowering--.f64 63.9

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

   5. Simplified 63.9%

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

Alternative 6: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+75) (/ (- 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) <= 2e+75) {
		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) <= 2d+75) 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) <= 2e+75) {
		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) <= 2e+75:
		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) <= 2e+75)
		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) <= 2e+75)
		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], 2e+75], 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) < 1.99999999999999985e75

   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. --lowering--.f64 72.4

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

   5. Simplified 72.4%

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

   if 1.99999999999999985e75 < (+.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. +-lowering-+.f64 95.1

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

   5. Simplified 95.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+75) (* (/ 0.5 t) (- x z)) (/ (+ x y) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+75) {
		tmp = (0.5 / t) * (x - z);
	} 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) <= 2d+75) then
        tmp = (0.5d0 / t) * (x - z)
    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) <= 2e+75) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (x + y) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e+75:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (x + y) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e+75)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	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) <= 2e+75)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (x + y) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e+75], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $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) < 1.99999999999999985e75

   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. --lowering--.f64 72.4

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

   5. Simplified 72.4%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. metadata-eval N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 72.2

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

   7. Applied egg-rr 72.2%

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

   if 1.99999999999999985e75 < (+.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. +-lowering-+.f64 95.1

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

   5. Simplified 95.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+75) (* (/ 0.5 t) (- x z)) (* (+ x y) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+75) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (x + 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) <= 2d+75) then
        tmp = (0.5d0 / t) * (x - z)
    else
        tmp = (x + 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) <= 2e+75) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (x + y) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e+75:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (x + y) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e+75)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2e+75)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (x + y) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e+75], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 1.99999999999999985e75

   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. --lowering--.f64 72.4

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

   5. Simplified 72.4%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. metadata-eval N/A

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

      6. *-lowering-*.f64 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. --lowering--.f64 72.2

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

   7. Applied egg-rr 72.2%

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

   if 1.99999999999999985e75 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. /-lowering-/.f64 N/A

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

      7. metadata-eval N/A

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

      8. associate--l+ N/A

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

      9. +-lowering-+.f64 N/A

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

      10. --lowering--.f64 99.7

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

   4. Applied egg-rr 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. +-lowering-+.f64 94.8

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

   7. Simplified 94.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+75}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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. clear-num N/A

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

   2. associate-/r/ N/A

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

   3. *-lowering-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/r* N/A

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

   6. /-lowering-/.f64 N/A

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

   7. metadata-eval N/A

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

   8. associate--l+ N/A

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

   9. +-lowering-+.f64 N/A

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

   10. --lowering--.f64 99.7

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

4. Applied egg-rr 99.7%

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

Alternative 10: 37.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * 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 = (x * 0.5d0) / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. /-lowering-/.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. *-lowering-*.f64 39.8

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

5. Simplified 39.8%

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

6. Final simplification 39.8%

   \[\leadsto \frac{x \cdot 0.5}{t} \]
7. Add Preprocessing

Alternative 11: 37.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x * (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 = x * (0.5d0 / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x * 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 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. /-lowering-/.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. *-lowering-*.f64 39.8

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

5. Simplified 39.8%

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

   1. associate-*l/ N/A

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

   2. *-lowering-*.f64 N/A

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

   3. /-lowering-/.f64 39.7

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

7. Applied egg-rr 39.7%

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

8. Final simplification 39.7%

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

Reproduce

herbie shell --seed 2024198 
(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)))