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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 9

Speedup: 1.0×

• 26.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 82.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+132} \lor \neg \left(z \leq 5.5 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.8e+132) (not (<= z 5.5e+123)))
   (/ z (* t -2.0))
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e+132) || !(z <= 5.5e+123)) {
		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 <= (-6.8d+132)) .or. (.not. (z <= 5.5d+123))) 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 <= -6.8e+132) || !(z <= 5.5e+123)) {
		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 <= -6.8e+132) or not (z <= 5.5e+123):
		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 <= -6.8e+132) || !(z <= 5.5e+123))
		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 <= -6.8e+132) || ~((z <= 5.5e+123)))
		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, -6.8e+132], N[Not[LessEqual[z, 5.5e+123]], $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 < -6.80000000000000051e132 or 5.5000000000000002e123 < z

   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%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. associate--r+ 100.0%

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

      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 82.5%

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

   if -6.80000000000000051e132 < z < 5.5000000000000002e123

   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 85.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+132} \lor \neg \left(z \leq 5.5 \cdot 10^{+123}\right):\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -4e+75) (* 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 + y) <= -4e+75) {
		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 + y) <= (-4d+75)) 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 + y) <= -4e+75) {
		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 + y) <= -4e+75:
		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 (Float64(x + y) <= -4e+75)
		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 + y) <= -4e+75)
		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[N[(x + y), $MachinePrecision], -4e+75], 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 (+.f64 x y) < -3.99999999999999971e75

   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 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

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

      8. div-sub 99.8%

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

      9. metadata-eval 99.8%

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

      10. neg-mul-1 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 99.8%

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

      13. metadata-eval 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. associate--r- 99.8%

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

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 82.2%

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

   if -3.99999999999999971e75 < (+.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 72.8%

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

      1. associate-*r/ 72.8%

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

      2. associate-*l/ 72.6%

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

      3. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 75.7%

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

Alternative 4: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{-166}:\\ \;\;\;\;\frac{z - x}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e-166) (/ (- 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-166) {
		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-166) 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-166) {
		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-166:
		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-166)
		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-166)
		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-166], 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) < 2.00000000000000008e-166

   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%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. associate--r+ 100.0%

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

      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 71.3%

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

   if 2.00000000000000008e-166 < (+.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 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

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

      8. div-sub 99.8%

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

      9. metadata-eval 99.8%

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

      10. neg-mul-1 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 99.8%

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

      13. metadata-eval 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. associate--r- 99.8%

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

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 68.2%

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

      1. associate-*r/ 68.2%

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

      2. associate-*l/ 68.1%

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

      3. *-commutative 68.1%

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

   7. Simplified 68.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{-166}:\\ \;\;\;\;\frac{z - x}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{-0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-167}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.95e-167)
   (* 0.5 (/ x t))
   (if (<= y 7.3e+56) (/ -0.5 (/ t z)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.95e-167) {
		tmp = 0.5 * (x / t);
	} else if (y <= 7.3e+56) {
		tmp = -0.5 / (t / z);
	} 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 <= (-1.95d-167)) then
        tmp = 0.5d0 * (x / t)
    else if (y <= 7.3d+56) then
        tmp = (-0.5d0) / (t / z)
    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 <= -1.95e-167) {
		tmp = 0.5 * (x / t);
	} else if (y <= 7.3e+56) {
		tmp = -0.5 / (t / z);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.95e-167:
		tmp = 0.5 * (x / t)
	elif y <= 7.3e+56:
		tmp = -0.5 / (t / z)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.95e-167)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (y <= 7.3e+56)
		tmp = Float64(-0.5 / Float64(t / z));
	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 <= -1.95e-167)
		tmp = 0.5 * (x / t);
	elseif (y <= 7.3e+56)
		tmp = -0.5 / (t / z);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.95e-167], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.3e+56], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.94999999999999992e-167

   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 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

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

      8. div-sub 99.8%

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

      9. metadata-eval 99.8%

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

      10. neg-mul-1 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 99.8%

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

      13. metadata-eval 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. associate--r- 99.8%

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

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 33.9%

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

   if -1.94999999999999992e-167 < y < 7.3e56

   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 52.8%

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

      1. associate-*r/ 52.8%

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

      2. associate-/l* 52.5%

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

   7. Simplified 52.5%

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

   if 7.3e56 < 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 99.7%

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

      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 y around inf 63.1%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-167}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 7.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-169}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.7e-169)
   (* 0.5 (/ x t))
   (if (<= y 2.75e+57) (/ z (* t -2.0)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.7e-169) {
		tmp = 0.5 * (x / t);
	} else if (y <= 2.75e+57) {
		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 <= (-4.7d-169)) then
        tmp = 0.5d0 * (x / t)
    else if (y <= 2.75d+57) 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 <= -4.7e-169) {
		tmp = 0.5 * (x / t);
	} else if (y <= 2.75e+57) {
		tmp = z / (t * -2.0);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.7e-169:
		tmp = 0.5 * (x / t)
	elif y <= 2.75e+57:
		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 <= -4.7e-169)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (y <= 2.75e+57)
		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 <= -4.7e-169)
		tmp = 0.5 * (x / t);
	elseif (y <= 2.75e+57)
		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, -4.7e-169], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e+57], 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 < -4.6999999999999999e-169

   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 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

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

      8. div-sub 99.8%

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

      9. metadata-eval 99.8%

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

      10. neg-mul-1 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 99.8%

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

      13. metadata-eval 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. associate--r- 99.8%

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

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 33.9%

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

   if -4.6999999999999999e-169 < y < 2.7500000000000001e57

   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%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. neg-mul-1 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. associate--r+ 100.0%

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

      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 52.8%

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

   if 2.7500000000000001e57 < 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 99.7%

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

      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 y around inf 63.1%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-169}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{t \cdot -2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 45.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.9e-69) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.9e-69) {
		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 (x <= (-3.9d-69)) 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 (x <= -3.9e-69) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.9e-69:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.9e-69)
		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 (x <= -3.9e-69)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.9e-69], 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 x < -3.89999999999999981e-69

   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 54.8%

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

   if -3.89999999999999981e-69 < 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 99.8%

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

      6. remove-double-neg 99.8%

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

      7. sub0-neg 99.8%

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

      8. div-sub 99.8%

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

      9. metadata-eval 99.8%

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

      10. neg-mul-1 99.8%

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

      11. *-commutative 99.8%

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

      12. associate-/l* 99.8%

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

      13. metadata-eval 99.8%

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

      14. /-rgt-identity 99.8%

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

      15. associate--r- 99.8%

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

      16. neg-sub0 99.8%

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

      17. +-commutative 99.8%

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

      18. sub-neg 99.8%

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

      19. +-commutative 99.8%

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

      20. associate--r+ 99.8%

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

      21. *-commutative 99.8%

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

      22. associate-/r* 99.8%

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

      23. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 44.6%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.2% 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 36.6%

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

6. Final simplification 36.6%

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

Reproduce

herbie shell --seed 2024010 
(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)))