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

Percentage Accurate: 99.9% → 99.9%

Time: 7.9s

Alternatives: 11

Speedup: 1.0×

• 26.4% 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

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

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(x + Float64(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[(x + N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

Alternative 2: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e+148)
   (/ (+ x y) (* t 2.0))
   (if (<= x -2e-36) (/ (- x z) (* t 2.0)) (* (- y z) (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e+148) {
		tmp = (x + y) / (t * 2.0);
	} else if (x <= -2e-36) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) * (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 <= (-5.8d+148)) then
        tmp = (x + y) / (t * 2.0d0)
    else if (x <= (-2d-36)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) * (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 <= -5.8e+148) {
		tmp = (x + y) / (t * 2.0);
	} else if (x <= -2e-36) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e+148:
		tmp = (x + y) / (t * 2.0)
	elif x <= -2e-36:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e+148)
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	elseif (x <= -2e-36)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e+148)
		tmp = (x + y) / (t * 2.0);
	elseif (x <= -2e-36)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e+148], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2e-36], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7999999999999999e148

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 97.3%

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

      1. associate-*r/ 97.3%

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

      2. *-commutative 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-/l* 97.3%

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

      5. *-rgt-identity 97.3%

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

      6. rem-square-sqrt 18.9%

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

      7. associate-/l* 18.9%

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

      8. associate-*l/ 18.9%

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

      9. *-commutative 18.9%

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

      10. associate-*l/ 18.9%

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

      11. associate-*r/ 18.9%

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

      12. associate-/r* 18.9%

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

      13. associate-*r/ 18.9%

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

      14. rem-square-sqrt 97.3%

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

      15. +-commutative 97.3%

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

   7. Simplified 97.3%

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

   if -5.7999999999999999e148 < x < -1.9999999999999999e-36

   1. Initial program 100.0%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 79.3%

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

   if -1.9999999999999999e-36 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 80.7%

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

      3. associate-*r/ 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e+148)
   (/ (+ x y) (* t 2.0))
   (if (<= x -2.1e-36) (* (/ 0.5 t) (- x z)) (* (- y z) (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e+148) {
		tmp = (x + y) / (t * 2.0);
	} else if (x <= -2.1e-36) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (y - z) * (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 <= (-5.8d+148)) then
        tmp = (x + y) / (t * 2.0d0)
    else if (x <= (-2.1d-36)) then
        tmp = (0.5d0 / t) * (x - z)
    else
        tmp = (y - z) * (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 <= -5.8e+148) {
		tmp = (x + y) / (t * 2.0);
	} else if (x <= -2.1e-36) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e+148:
		tmp = (x + y) / (t * 2.0)
	elif x <= -2.1e-36:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e+148)
		tmp = Float64(Float64(x + y) / Float64(t * 2.0));
	elseif (x <= -2.1e-36)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e+148)
		tmp = (x + y) / (t * 2.0);
	elseif (x <= -2.1e-36)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e+148], N[(N[(x + y), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-36], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.7999999999999999e148

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 97.3%

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

      1. associate-*r/ 97.3%

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

      2. *-commutative 97.3%

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

      3. metadata-eval 97.3%

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

      4. associate-/l* 97.3%

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

      5. *-rgt-identity 97.3%

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

      6. rem-square-sqrt 18.9%

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

      7. associate-/l* 18.9%

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

      8. associate-*l/ 18.9%

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

      9. *-commutative 18.9%

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

      10. associate-*l/ 18.9%

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

      11. associate-*r/ 18.9%

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

      12. associate-/r* 18.9%

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

      13. associate-*r/ 18.9%

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

      14. rem-square-sqrt 97.3%

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

      15. +-commutative 97.3%

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

   7. Simplified 97.3%

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

   if -5.7999999999999999e148 < x < -2.09999999999999991e-36

   1. Initial program 100.0%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 79.3%

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

      1. clear-num 79.1%

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

      2. associate-/r/ 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-/r* 79.0%

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

      5. metadata-eval 79.0%

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

   7. Applied egg-rr 79.0%

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

   if -2.09999999999999991e-36 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 80.7%

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

      3. associate-*r/ 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{x + y}{t \cdot 2}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+146}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e+146)
   (* (/ 0.5 t) (+ x y))
   (if (<= x -2.1e-36) (* (/ 0.5 t) (- x z)) (* (- y z) (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e+146) {
		tmp = (0.5 / t) * (x + y);
	} else if (x <= -2.1e-36) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (y - z) * (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 <= (-6d+146)) then
        tmp = (0.5d0 / t) * (x + y)
    else if (x <= (-2.1d-36)) then
        tmp = (0.5d0 / t) * (x - z)
    else
        tmp = (y - z) * (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 <= -6e+146) {
		tmp = (0.5 / t) * (x + y);
	} else if (x <= -2.1e-36) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e+146:
		tmp = (0.5 / t) * (x + y)
	elif x <= -2.1e-36:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e+146)
		tmp = Float64(Float64(0.5 / t) * Float64(x + y));
	elseif (x <= -2.1e-36)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6e+146)
		tmp = (0.5 / t) * (x + y);
	elseif (x <= -2.1e-36)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e+146], N[(N[(0.5 / t), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e-36], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.00000000000000005e146

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 97.3%

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

      1. associate-*r/ 97.3%

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

      2. associate-*l/ 97.2%

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

      3. +-commutative 97.2%

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

   7. Simplified 97.2%

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

   if -6.00000000000000005e146 < x < -2.09999999999999991e-36

   1. Initial program 100.0%

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

      1. associate--l+ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 79.3%

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

      1. clear-num 79.1%

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

      2. associate-/r/ 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-/r* 79.0%

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

      5. metadata-eval 79.0%

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

   7. Applied egg-rr 79.0%

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

   if -2.09999999999999991e-36 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.7%

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

      1. *-commutative 80.7%

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

      2. associate-*l/ 80.7%

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

      3. associate-*r/ 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+146}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x + y\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.4e+53)
   (/ x (* t 2.0))
   (if (<= x -8.5e-243) (* (/ z t) -0.5) (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.4e+53) {
		tmp = x / (t * 2.0);
	} else if (x <= -8.5e-243) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = 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 <= (-4.4d+53)) then
        tmp = x / (t * 2.0d0)
    else if (x <= (-8.5d-243)) then
        tmp = (z / t) * (-0.5d0)
    else
        tmp = 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 <= -4.4e+53) {
		tmp = x / (t * 2.0);
	} else if (x <= -8.5e-243) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.4e+53:
		tmp = x / (t * 2.0)
	elif x <= -8.5e-243:
		tmp = (z / t) * -0.5
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.4e+53)
		tmp = Float64(x / Float64(t * 2.0));
	elseif (x <= -8.5e-243)
		tmp = Float64(Float64(z / t) * -0.5);
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.4e+53)
		tmp = x / (t * 2.0);
	elseif (x <= -8.5e-243)
		tmp = (z / t) * -0.5;
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.4e+53], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.5e-243], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.39999999999999997e53

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 70.5%

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

   if -4.39999999999999997e53 < x < -8.5000000000000002e-243

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

   7. Simplified 53.6%

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

   if -8.5000000000000002e-243 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 47.4%

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

Alternative 6: 46.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.7e+53)
   (/ x (* t 2.0))
   (if (<= x -4.3e-243) (* (/ z t) -0.5) (* y (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.7e+53) {
		tmp = x / (t * 2.0);
	} else if (x <= -4.3e-243) {
		tmp = (z / t) * -0.5;
	} 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 <= (-5.7d+53)) then
        tmp = x / (t * 2.0d0)
    else if (x <= (-4.3d-243)) then
        tmp = (z / t) * (-0.5d0)
    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 <= -5.7e+53) {
		tmp = x / (t * 2.0);
	} else if (x <= -4.3e-243) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.7e+53:
		tmp = x / (t * 2.0)
	elif x <= -4.3e-243:
		tmp = (z / t) * -0.5
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.7e+53)
		tmp = Float64(x / Float64(t * 2.0));
	elseif (x <= -4.3e-243)
		tmp = Float64(Float64(z / t) * -0.5);
	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 <= -5.7e+53)
		tmp = x / (t * 2.0);
	elseif (x <= -4.3e-243)
		tmp = (z / t) * -0.5;
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.7e+53], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e-243], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.70000000000000017e53

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 70.5%

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

   if -5.70000000000000017e53 < x < -4.3e-243

   1. Initial program 99.9%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

   7. Simplified 53.6%

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

   if -4.3e-243 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. associate-*l/ 71.4%

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

      3. +-commutative 71.4%

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

   7. Simplified 71.4%

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

   8. Taylor expanded in y around inf 47.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-243}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.4e+53) (* (/ 0.5 t) (+ x y)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.4e+53) {
		tmp = (0.5 / t) * (x + y);
	} else {
		tmp = (y - z) * (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 <= (-3.4d+53)) then
        tmp = (0.5d0 / t) * (x + y)
    else
        tmp = (y - z) * (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 <= -3.4e+53) {
		tmp = (0.5 / t) * (x + y);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.4e+53:
		tmp = (0.5 / t) * (x + y)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.4e+53)
		tmp = Float64(Float64(0.5 / t) * Float64(x + y));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.4e+53)
		tmp = (0.5 / t) * (x + y);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.4e+53], N[(N[(0.5 / t), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999998e53

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 86.7%

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

      1. associate-*r/ 86.7%

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

      2. associate-*l/ 86.5%

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

      3. +-commutative 86.5%

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

   7. Simplified 86.5%

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

   if -3.39999999999999998e53 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.8%

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

      1. *-commutative 80.8%

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

      2. associate-*l/ 80.8%

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

      3. associate-*r/ 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+53}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.5e+60) (/ x (* t 2.0)) (* (- y z) (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e+60) {
		tmp = x / (t * 2.0);
	} else {
		tmp = (y - z) * (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 <= (-6.5d+60)) then
        tmp = x / (t * 2.0d0)
    else
        tmp = (y - z) * (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 <= -6.5e+60) {
		tmp = x / (t * 2.0);
	} else {
		tmp = (y - z) * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.5e+60:
		tmp = x / (t * 2.0)
	else:
		tmp = (y - z) * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.5e+60)
		tmp = Float64(x / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.5e+60)
		tmp = x / (t * 2.0);
	else
		tmp = (y - z) * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.5e+60], N[(x / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999931e60

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 71.6%

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

   if -6.49999999999999931e60 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*l/ 80.9%

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

      3. associate-*r/ 80.6%

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

   7. Simplified 80.6%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 47.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 6.2e+56) (* (/ z t) -0.5) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 6.2e+56) {
		tmp = (z / t) * -0.5;
	} 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 (y <= 6.2d+56) then
        tmp = (z / t) * (-0.5d0)
    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 (y <= 6.2e+56) {
		tmp = (z / t) * -0.5;
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 6.2e+56:
		tmp = (z / t) * -0.5
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 6.2e+56)
		tmp = Float64(Float64(z / t) * -0.5);
	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 (y <= 6.2e+56)
		tmp = (z / t) * -0.5;
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 6.2e+56], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.20000000000000009e56

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 44.6%

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

      1. *-commutative 44.6%

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

   7. Simplified 44.6%

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

   if 6.20000000000000009e56 < y

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. associate-*l/ 82.6%

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

      3. +-commutative 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in y around inf 73.4%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

   1. clear-num 99.4%

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

   2. associate-/r/ 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/r* 99.7%

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

   5. metadata-eval 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 11: 37.2% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in z around 0 71.2%

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

   1. associate-*r/ 71.2%

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

   2. associate-*l/ 71.0%

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

   3. +-commutative 71.0%

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

7. Simplified 71.0%

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

8. Taylor expanded in y around inf 39.7%

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

9. Final simplification 39.7%

   \[\leadsto y \cdot \frac{0.5}{t} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024157 
(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)))