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

Percentage Accurate: 99.9% → 99.9%

Time: 7.6s

Alternatives: 10

Speedup: 1.0×

• 26.3% 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. Final simplification 100.0%

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

Alternative 2: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+116} \lor \neg \left(z \leq 6.6 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e+116) (not (<= z 6.6e+164)))
   (/ z (* t -2.0))
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+116) || !(z <= 6.6e+164)) {
		tmp = z / (t * -2.0);
	} else {
		tmp = 0.5 * ((x + y) / 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 ((z <= (-2.9d+116)) .or. (.not. (z <= 6.6d+164))) then
        tmp = z / (t * (-2.0d0))
    else
        tmp = 0.5d0 * ((x + y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.9e+116) || !(z <= 6.6e+164)) {
		tmp = z / (t * -2.0);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.9e+116) or not (z <= 6.6e+164):
		tmp = z / (t * -2.0)
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.9e+116) || !(z <= 6.6e+164))
		tmp = Float64(z / Float64(t * -2.0));
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.9e+116) || ~((z <= 6.6e+164)))
		tmp = z / (t * -2.0);
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.9e+116], N[Not[LessEqual[z, 6.6e+164]], $MachinePrecision]], N[(z / N[(t * -2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9000000000000001e116 or 6.59999999999999991e164 < z

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. times-frac 99.9%

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

      4. neg-mul-1 99.9%

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

      5. sub-neg 99.9%

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

      6. +-commutative 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. remove-double-neg 99.9%

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

      9. sub-neg 99.9%

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

      10. +-commutative 99.9%

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

      11. associate--r+ 99.9%

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

      12. neg-mul-1 99.9%

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

      13. distribute-rgt-neg-in 99.9%

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

      14. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.2%

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

   if -2.9000000000000001e116 < z < 6.59999999999999991e164

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 86.0%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+116} \lor \neg \left(z \leq 6.6 \cdot 10^{+164}\right):\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-172}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.22e-172)
   (* 0.5 (/ x t))
   (if (<= y 2e+52) (* z (/ -0.5 t)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-172) {
		tmp = 0.5 * (x / t);
	} else if (y <= 2e+52) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 * (y / 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 <= (-1.22d-172)) then
        tmp = 0.5d0 * (x / t)
    else if (y <= 2d+52) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-172) {
		tmp = 0.5 * (x / t);
	} else if (y <= 2e+52) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.22e-172:
		tmp = 0.5 * (x / t)
	elif y <= 2e+52:
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.22e-172)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (y <= 2e+52)
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.22e-172)
		tmp = 0.5 * (x / t);
	elseif (y <= 2e+52)
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.22e-172], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+52], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22e-172

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 32.6%

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

   if -1.22e-172 < y < 2e52

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 49.0%

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

   if 2e52 < y

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. times-frac 99.9%

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

      4. *-commutative 99.9%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 69.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-172}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-179}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+52}:\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e-179)
   (* 0.5 (/ x t))
   (if (<= y 1.95e+52) (/ z (* t -2.0)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e-179) {
		tmp = 0.5 * (x / t);
	} else if (y <= 1.95e+52) {
		tmp = z / (t * -2.0);
	} else {
		tmp = 0.5 * (y / 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 <= (-1.5d-179)) then
        tmp = 0.5d0 * (x / t)
    else if (y <= 1.95d+52) then
        tmp = z / (t * (-2.0d0))
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e-179) {
		tmp = 0.5 * (x / t);
	} else if (y <= 1.95e+52) {
		tmp = z / (t * -2.0);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e-179:
		tmp = 0.5 * (x / t)
	elif y <= 1.95e+52:
		tmp = z / (t * -2.0)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e-179)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (y <= 1.95e+52)
		tmp = Float64(z / Float64(t * -2.0));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e-179)
		tmp = 0.5 * (x / t);
	elseif (y <= 1.95e+52)
		tmp = z / (t * -2.0);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e-179], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+52], N[(z / N[(t * -2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.50000000000000003e-179

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 32.6%

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

   if -1.50000000000000003e-179 < y < 1.95e52

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 49.0%

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

   if 1.95e52 < y

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. times-frac 99.9%

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

      4. *-commutative 99.9%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 69.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-179}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+52}:\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-241}:\\ \;\;\;\;\frac{z - x}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -2e-241) (/ (- z x) (* t -2.0)) (* (- z y) (/ -0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -2e-241) {
		tmp = (z - x) / (t * -2.0);
	} else {
		tmp = (z - 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-241)) then
        tmp = (z - x) / (t * (-2.0d0))
    else
        tmp = (z - 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-241) {
		tmp = (z - x) / (t * -2.0);
	} else {
		tmp = (z - y) * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -2e-241:
		tmp = (z - x) / (t * -2.0)
	else:
		tmp = (z - y) * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -2e-241)
		tmp = Float64(Float64(z - x) / Float64(t * -2.0));
	else
		tmp = Float64(Float64(z - 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-241)
		tmp = (z - x) / (t * -2.0);
	else
		tmp = (z - y) * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e-241], N[(N[(z - x), $MachinePrecision] / N[(t * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.9999999999999999e-241

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 62.9%

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

   if -1.9999999999999999e-241 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. associate-*l/ 67.1%

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

      3. *-commutative 67.1%

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

   7. Simplified 67.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-241}:\\ \;\;\;\;\frac{z - x}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{-0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-192}:\\ \;\;\;\;\frac{z - x}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{t \cdot -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -5e-192) (/ (- z x) (* t -2.0)) (/ (- z y) (* t -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -5e-192) {
		tmp = (z - x) / (t * -2.0);
	} else {
		tmp = (z - 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) <= (-5d-192)) then
        tmp = (z - x) / (t * (-2.0d0))
    else
        tmp = (z - 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) <= -5e-192) {
		tmp = (z - x) / (t * -2.0);
	} else {
		tmp = (z - y) / (t * -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -5e-192:
		tmp = (z - x) / (t * -2.0)
	else:
		tmp = (z - y) / (t * -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -5e-192)
		tmp = Float64(Float64(z - x) / Float64(t * -2.0));
	else
		tmp = Float64(Float64(z - y) / Float64(t * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -5e-192)
		tmp = (z - x) / (t * -2.0);
	else
		tmp = (z - y) / (t * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-192], N[(N[(z - x), $MachinePrecision] / N[(t * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] / N[(t * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000001e-192

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 62.2%

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

   if -5.0000000000000001e-192 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. neg-mul-1 100.0%

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

      5. sub-neg 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. associate--r+ 100.0%

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

      12. neg-mul-1 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 67.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-192}:\\ \;\;\;\;\frac{z - x}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{t \cdot -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+19}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.5e+19) (* 0.5 (/ (+ x y) t)) (* (- z y) (/ -0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.5e+19) {
		tmp = 0.5 * ((x + y) / t);
	} else {
		tmp = (z - 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 <= (-5.5d+19)) then
        tmp = 0.5d0 * ((x + y) / t)
    else
        tmp = (z - 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 <= -5.5e+19) {
		tmp = 0.5 * ((x + y) / t);
	} else {
		tmp = (z - y) * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.5e+19:
		tmp = 0.5 * ((x + y) / t)
	else:
		tmp = (z - y) * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.5e+19)
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	else
		tmp = Float64(Float64(z - y) * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.5e+19)
		tmp = 0.5 * ((x + y) / t);
	else
		tmp = (z - y) * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.5e+19], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e19

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 87.0%

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

   if -5.5e19 < x

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 74.5%

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

      1. associate-*r/ 74.9%

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

      2. associate-*l/ 74.7%

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

      3. *-commutative 74.7%

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

   7. Simplified 74.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+19}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{-0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+33}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.6e+33) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.6e+33) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / 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 <= 2.6d+33) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.6e+33) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.6e+33:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.6e+33)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.6e+33)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.6e+33], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5999999999999997e33

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. times-frac 100.0%

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

      4. *-commutative 100.0%

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

      5. times-frac 99.7%

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

      6. remove-double-neg 99.7%

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

      7. sub0-neg 99.7%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.7%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.7%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.7%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.7%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.7%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.7%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.7%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.7%

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

      17. +-commutative 99.7%

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

      18. sub-neg 99.7%

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

      19. +-commutative 99.7%

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

      20. associate--r+ 99.7%

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

      21. *-commutative 99.7%

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

      22. associate-/r* 99.7%

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

      23. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 40.9%

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

   if 2.5999999999999997e33 < y

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. times-frac 99.9%

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

      4. *-commutative 99.9%

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

      5. times-frac 99.6%

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

      6. remove-double-neg 99.6%

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

      7. sub0-neg 99.6%

         \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

      8. div-sub 99.6%

         \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

      9. metadata-eval 99.6%

         \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      10. neg-mul-1 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      11. *-commutative 99.6%

          \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

      12. associate-/l* 99.6%

          \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

      13. metadata-eval 99.6%

          \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

      14. /-rgt-identity 99.6%

          \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

      15. associate--r- 99.6%

          \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

      16. neg-sub0 99.6%

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

      17. +-commutative 99.6%

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

      18. sub-neg 99.6%

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

      19. +-commutative 99.6%

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

      20. associate--r+ 99.6%

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

      21. *-commutative 99.6%

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

      22. associate-/r* 99.6%

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

      23. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 68.5%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+33}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z - y), $MachinePrecision] - x), $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. *-lft-identity 100.0%

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

   2. metadata-eval 100.0%

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

   3. times-frac 100.0%

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

   4. *-commutative 100.0%

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

   5. times-frac 99.7%

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

   6. remove-double-neg 99.7%

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

   7. sub0-neg 99.7%

      \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

   8. div-sub 99.7%

      \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

   9. metadata-eval 99.7%

      \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   10. neg-mul-1 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   11. *-commutative 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   12. associate-/l* 99.7%

       \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

   13. metadata-eval 99.7%

       \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

   14. /-rgt-identity 99.7%

       \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

   15. associate--r- 99.7%

       \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

   16. neg-sub0 99.7%

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

   17. +-commutative 99.7%

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

   18. sub-neg 99.7%

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

   19. +-commutative 99.7%

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

   20. associate--r+ 99.7%

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

   21. *-commutative 99.7%

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

   22. associate-/r* 99.7%

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

   23. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 10: 36.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-lft-identity 100.0%

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

   2. metadata-eval 100.0%

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

   3. times-frac 100.0%

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

   4. *-commutative 100.0%

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

   5. times-frac 99.7%

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

   6. remove-double-neg 99.7%

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

   7. sub0-neg 99.7%

      \[\leadsto \frac{\color{blue}{0 - \left(-\left(\left(x + y\right) - z\right)\right)}}{-1} \cdot \frac{-1}{t \cdot 2} \]

   8. div-sub 99.7%

      \[\leadsto \color{blue}{\left(\frac{0}{-1} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right)} \cdot \frac{-1}{t \cdot 2} \]

   9. metadata-eval 99.7%

      \[\leadsto \left(\color{blue}{0} - \frac{-\left(\left(x + y\right) - z\right)}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   10. neg-mul-1 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{-1 \cdot \left(\left(x + y\right) - z\right)}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   11. *-commutative 99.7%

       \[\leadsto \left(0 - \frac{\color{blue}{\left(\left(x + y\right) - z\right) \cdot -1}}{-1}\right) \cdot \frac{-1}{t \cdot 2} \]

   12. associate-/l* 99.7%

       \[\leadsto \left(0 - \color{blue}{\frac{\left(x + y\right) - z}{\frac{-1}{-1}}}\right) \cdot \frac{-1}{t \cdot 2} \]

   13. metadata-eval 99.7%

       \[\leadsto \left(0 - \frac{\left(x + y\right) - z}{\color{blue}{1}}\right) \cdot \frac{-1}{t \cdot 2} \]

   14. /-rgt-identity 99.7%

       \[\leadsto \left(0 - \color{blue}{\left(\left(x + y\right) - z\right)}\right) \cdot \frac{-1}{t \cdot 2} \]

   15. associate--r- 99.7%

       \[\leadsto \color{blue}{\left(\left(0 - \left(x + y\right)\right) + z\right)} \cdot \frac{-1}{t \cdot 2} \]

   16. neg-sub0 99.7%

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

   17. +-commutative 99.7%

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

   18. sub-neg 99.7%

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

   19. +-commutative 99.7%

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

   20. associate--r+ 99.7%

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

   21. *-commutative 99.7%

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

   22. associate-/r* 99.7%

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

   23. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in x around inf 35.8%

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

6. Final simplification 35.8%

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

Reproduce

herbie shell --seed 2024020 
(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)))