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

Percentage Accurate: 99.9% → 99.9%

Time: 7.4s

Alternatives: 10

Speedup: 1.0×

• 26.0% 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. Final simplification 100.0%

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

Alternative 2: 44.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ t_2 := \frac{x \cdot 0.5}{t}\\ \mathbf{if}\;y \leq 5.5 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+33} \lor \neg \left(y \leq 4.4 \cdot 10^{+47}\right) \land \left(y \leq 4.9 \cdot 10^{+151} \lor \neg \left(y \leq 1.02 \cdot 10^{+192}\right)\right):\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)) (t_2 (/ (* x 0.5) t)))
   (if (<= y 5.5e-293)
     t_2
     (if (<= y 5.6e-132)
       t_1
       (if (<= y 5.8e-86)
         t_2
         (if (<= y 4.4e-13)
           (* z (/ -0.5 t))
           (if (or (<= y 6.5e+33)
                   (and (not (<= y 4.4e+47))
                        (or (<= y 4.9e+151) (not (<= y 1.02e+192)))))
             (/ (* y 0.5) t)
             t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= 5.5e-293) {
		tmp = t_2;
	} else if (y <= 5.6e-132) {
		tmp = t_1;
	} else if (y <= 5.8e-86) {
		tmp = t_2;
	} else if (y <= 4.4e-13) {
		tmp = z * (-0.5 / t);
	} else if ((y <= 6.5e+33) || (!(y <= 4.4e+47) && ((y <= 4.9e+151) || !(y <= 1.02e+192)))) {
		tmp = (y * 0.5) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    t_2 = (x * 0.5d0) / t
    if (y <= 5.5d-293) then
        tmp = t_2
    else if (y <= 5.6d-132) then
        tmp = t_1
    else if (y <= 5.8d-86) then
        tmp = t_2
    else if (y <= 4.4d-13) then
        tmp = z * ((-0.5d0) / t)
    else if ((y <= 6.5d+33) .or. (.not. (y <= 4.4d+47)) .and. (y <= 4.9d+151) .or. (.not. (y <= 1.02d+192))) then
        tmp = (y * 0.5d0) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double t_2 = (x * 0.5) / t;
	double tmp;
	if (y <= 5.5e-293) {
		tmp = t_2;
	} else if (y <= 5.6e-132) {
		tmp = t_1;
	} else if (y <= 5.8e-86) {
		tmp = t_2;
	} else if (y <= 4.4e-13) {
		tmp = z * (-0.5 / t);
	} else if ((y <= 6.5e+33) || (!(y <= 4.4e+47) && ((y <= 4.9e+151) || !(y <= 1.02e+192)))) {
		tmp = (y * 0.5) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	t_2 = (x * 0.5) / t
	tmp = 0
	if y <= 5.5e-293:
		tmp = t_2
	elif y <= 5.6e-132:
		tmp = t_1
	elif y <= 5.8e-86:
		tmp = t_2
	elif y <= 4.4e-13:
		tmp = z * (-0.5 / t)
	elif (y <= 6.5e+33) or (not (y <= 4.4e+47) and ((y <= 4.9e+151) or not (y <= 1.02e+192))):
		tmp = (y * 0.5) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	t_2 = Float64(Float64(x * 0.5) / t)
	tmp = 0.0
	if (y <= 5.5e-293)
		tmp = t_2;
	elseif (y <= 5.6e-132)
		tmp = t_1;
	elseif (y <= 5.8e-86)
		tmp = t_2;
	elseif (y <= 4.4e-13)
		tmp = Float64(z * Float64(-0.5 / t));
	elseif ((y <= 6.5e+33) || (!(y <= 4.4e+47) && ((y <= 4.9e+151) || !(y <= 1.02e+192))))
		tmp = Float64(Float64(y * 0.5) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	t_2 = (x * 0.5) / t;
	tmp = 0.0;
	if (y <= 5.5e-293)
		tmp = t_2;
	elseif (y <= 5.6e-132)
		tmp = t_1;
	elseif (y <= 5.8e-86)
		tmp = t_2;
	elseif (y <= 4.4e-13)
		tmp = z * (-0.5 / t);
	elseif ((y <= 6.5e+33) || (~((y <= 4.4e+47)) && ((y <= 4.9e+151) || ~((y <= 1.02e+192)))))
		tmp = (y * 0.5) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, 5.5e-293], t$95$2, If[LessEqual[y, 5.6e-132], t$95$1, If[LessEqual[y, 5.8e-86], t$95$2, If[LessEqual[y, 4.4e-13], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 6.5e+33], And[N[Not[LessEqual[y, 4.4e+47]], $MachinePrecision], Or[LessEqual[y, 4.9e+151], N[Not[LessEqual[y, 1.02e+192]], $MachinePrecision]]]], N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < 5.50000000000000028e-293 or 5.60000000000000005e-132 < y < 5.7999999999999998e-86

   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. Taylor expanded in x around inf 41.6%

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

      1. associate-*r/ 41.6%

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

   6. Simplified 41.6%

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

   if 5.50000000000000028e-293 < y < 5.60000000000000005e-132 or 6.49999999999999993e33 < y < 4.3999999999999999e47 or 4.8999999999999999e151 < y < 1.01999999999999996e192

   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. Taylor expanded in z around inf 57.3%

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

      1. associate-*r/ 57.3%

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

   6. Simplified 57.3%

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

   if 5.7999999999999998e-86 < y < 4.39999999999999993e-13

   1. Initial program 99.7%

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

      1. *-lft-identity 99.7%

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

      2. metadata-eval 99.7%

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

      3. times-frac 99.7%

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

      4. *-commutative 99.7%

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

      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. Step-by-step derivation

      1. associate-*r/ 99.7%

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

      2. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{\left(\left(z - y\right) - x\right) \cdot -0.5}}} \]

      3. associate--l- 99.7%

         \[\leadsto \frac{1}{\frac{t}{\color{blue}{\left(z - \left(y + x\right)\right)} \cdot -0.5}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{\left(z - \left(y + x\right)\right) \cdot -0.5}}} \]

   6. Taylor expanded in z around inf 60.8%

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

      1. associate-*r/ 60.8%

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

      2. associate-/l* 60.5%

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

   8. Simplified 60.5%

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

      1. associate-/r/ 60.8%

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

   10. Applied egg-rr 60.8%

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

   if 4.39999999999999993e-13 < y < 6.49999999999999993e33 or 4.3999999999999999e47 < y < 4.8999999999999999e151 or 1.01999999999999996e192 < 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 99.9%

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

      6. remove-double-neg 99.9%

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

      7. sub0-neg 99.9%

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

      8. div-sub 99.9%

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

      9. metadata-eval 99.9%

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

      10. neg-mul-1 99.9%

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

      11. *-commutative 99.9%

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

      12. associate-/l* 99.9%

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

      13. metadata-eval 99.9%

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

      14. /-rgt-identity 99.9%

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

      15. associate--r- 99.9%

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

      16. neg-sub0 99.9%

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

      17. +-commutative 99.9%

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

      18. sub-neg 99.9%

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

      19. +-commutative 99.9%

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

      20. associate--r+ 99.9%

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

      21. *-commutative 99.9%

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

      22. associate-/r* 99.9%

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

      23. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. associate-*r/ 77.3%

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

   6. Simplified 77.3%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.5 \cdot 10^{-293}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-132}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+33} \lor \neg \left(y \leq 4.4 \cdot 10^{+47}\right) \land \left(y \leq 4.9 \cdot 10^{+151} \lor \neg \left(y \leq 1.02 \cdot 10^{+192}\right)\right):\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]

Alternative 3: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+157} \lor \neg \left(x \leq -5.9 \cdot 10^{+85}\right) \land x \leq -4.8:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e+157) (and (not (<= x -5.9e+85)) (<= x -4.8)))
   (/ (* x 0.5) t)
   (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e+157) || (!(x <= -5.9e+85) && (x <= -4.8))) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = -0.5 * ((z - 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 <= (-7.2d+157)) .or. (.not. (x <= (-5.9d+85))) .and. (x <= (-4.8d0))) then
        tmp = (x * 0.5d0) / t
    else
        tmp = (-0.5d0) * ((z - 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 <= -7.2e+157) || (!(x <= -5.9e+85) && (x <= -4.8))) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e+157) or (not (x <= -5.9e+85) and (x <= -4.8)):
		tmp = (x * 0.5) / t
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e+157) || (!(x <= -5.9e+85) && (x <= -4.8)))
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(-0.5 * Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e+157) || (~((x <= -5.9e+85)) && (x <= -4.8)))
		tmp = (x * 0.5) / t;
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e+157], And[N[Not[LessEqual[x, -5.9e+85]], $MachinePrecision], LessEqual[x, -4.8]]], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000049e157 or -5.9e85 < x < -4.79999999999999982

   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. Taylor expanded in x around inf 67.1%

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

      1. associate-*r/ 67.1%

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

   6. Simplified 67.1%

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

   if -7.20000000000000049e157 < x < -5.9e85 or -4.79999999999999982 < x

   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. Taylor expanded in x around 0 75.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+157} \lor \neg \left(x \leq -5.9 \cdot 10^{+85}\right) \land x \leq -4.8:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 4: 69.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-155}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -2e-155) (/ -0.5 (/ t (- z x))) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -2e-155) {
		tmp = -0.5 / (t / (z - x));
	} else {
		tmp = -0.5 * ((z - 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 + y) <= (-2d-155)) then
        tmp = (-0.5d0) / (t / (z - x))
    else
        tmp = (-0.5d0) * ((z - 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 + y) <= -2e-155) {
		tmp = -0.5 / (t / (z - x));
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -2e-155:
		tmp = -0.5 / (t / (z - x))
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -2e-155)
		tmp = Float64(-0.5 / Float64(t / Float64(z - x)));
	else
		tmp = Float64(-0.5 * Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -2e-155)
		tmp = -0.5 / (t / (z - x));
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e-155], N[(-0.5 / N[(t / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2.00000000000000003e-155

   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. Taylor expanded in y around 0 66.3%

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

      1. associate-*r/ 66.3%

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

      2. associate-/l* 66.1%

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

   6. Simplified 66.1%

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

   if -2.00000000000000003e-155 < (+.f64 x 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 99.8%

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

      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. Taylor expanded in x around 0 70.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-155}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 5: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.2e-6) (* (+ x y) (/ 0.5 t)) (* -0.5 (/ (- z y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.2e-6) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = -0.5 * ((z - 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 <= (-7.2d-6)) then
        tmp = (x + y) * (0.5d0 / t)
    else
        tmp = (-0.5d0) * ((z - 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 <= -7.2e-6) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = -0.5 * ((z - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.2e-6:
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = -0.5 * ((z - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.2e-6)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = Float64(-0.5 * Float64(Float64(z - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.2e-6)
		tmp = (x + y) * (0.5 / t);
	else
		tmp = -0.5 * ((z - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.2e-6], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.19999999999999967e-6

   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. Taylor expanded in z around 0 80.1%

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

      1. associate-*r/ 80.1%

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

   6. Simplified 80.1%

      \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x + y\right)}{t}} \]
   7. Step-by-step derivation

      1. associate-/l* 79.9%

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

      2. +-commutative 79.9%

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

      3. associate-/r/ 79.9%

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

   8. Applied egg-rr 79.9%

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

   if -7.19999999999999967e-6 < x

   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. Taylor expanded in x around 0 76.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-6}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{z - y}{t}\\ \end{array} \]

Alternative 6: 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. Final simplification 99.7%

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

Alternative 7: 46.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-6) (* x (/ 0.5 t)) (* z (/ -0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-6) {
		tmp = x * (0.5 / t);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.4d-6)) then
        tmp = x * (0.5d0 / t)
    else
        tmp = z * ((-0.5d0) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-6) {
		tmp = x * (0.5 / t);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-6:
		tmp = x * (0.5 / t)
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-6)
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.4e-6)
		tmp = x * (0.5 / t);
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-6], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3999999999999999e-6

   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. Taylor expanded in x around inf 60.5%

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

      1. associate-*r/ 60.5%

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

      2. metadata-eval 60.5%

         \[\leadsto \frac{\color{blue}{\left(-0.5 \cdot -1\right)} \cdot x}{t} \]

      3. associate-*r* 60.5%

         \[\leadsto \frac{\color{blue}{-0.5 \cdot \left(-1 \cdot x\right)}}{t} \]

      4. neg-mul-1 60.5%

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

      5. *-commutative 60.5%

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

      6. associate-*r/ 60.3%

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

      7. distribute-lft-neg-in 60.3%

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

      8. distribute-rgt-neg-in 60.3%

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

      9. distribute-neg-frac 60.3%

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

      10. metadata-eval 60.3%

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

   6. Simplified 60.3%

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

   if -2.3999999999999999e-6 < x

   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. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{\left(\left(z - y\right) - x\right) \cdot -0.5}}} \]

      3. associate--l- 99.7%

         \[\leadsto \frac{1}{\frac{t}{\color{blue}{\left(z - \left(y + x\right)\right)} \cdot -0.5}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{\left(z - \left(y + x\right)\right) \cdot -0.5}}} \]

   6. Taylor expanded in z around inf 39.4%

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

      1. associate-*r/ 39.4%

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

      2. associate-/l* 39.3%

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

   8. Simplified 39.3%

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

      1. associate-/r/ 39.3%

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

   10. Applied egg-rr 39.3%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]

Alternative 8: 46.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-6) (* x (/ 0.5 t)) (/ (* z -0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-6) {
		tmp = x * (0.5 / t);
	} else {
		tmp = (z * -0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.6d-6)) then
        tmp = x * (0.5d0 / t)
    else
        tmp = (z * (-0.5d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-6) {
		tmp = x * (0.5 / t);
	} else {
		tmp = (z * -0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-6:
		tmp = x * (0.5 / t)
	else:
		tmp = (z * -0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-6)
		tmp = Float64(x * Float64(0.5 / t));
	else
		tmp = Float64(Float64(z * -0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-6)
		tmp = x * (0.5 / t);
	else
		tmp = (z * -0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-6], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000009e-6

   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. Taylor expanded in x around inf 60.5%

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

      1. associate-*r/ 60.5%

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

      2. metadata-eval 60.5%

         \[\leadsto \frac{\color{blue}{\left(-0.5 \cdot -1\right)} \cdot x}{t} \]

      3. associate-*r* 60.5%

         \[\leadsto \frac{\color{blue}{-0.5 \cdot \left(-1 \cdot x\right)}}{t} \]

      4. neg-mul-1 60.5%

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

      5. *-commutative 60.5%

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

      6. associate-*r/ 60.3%

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

      7. distribute-lft-neg-in 60.3%

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

      8. distribute-rgt-neg-in 60.3%

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

      9. distribute-neg-frac 60.3%

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

      10. metadata-eval 60.3%

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

   6. Simplified 60.3%

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

   if -2.60000000000000009e-6 < x

   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. Taylor expanded in z around inf 39.4%

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

      1. associate-*r/ 39.4%

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

   6. Simplified 39.4%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]

Alternative 9: 46.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.5e-6) (/ (* x 0.5) t) (/ (* z -0.5) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e-6) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = (z * -0.5) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.5d-6)) then
        tmp = (x * 0.5d0) / t
    else
        tmp = (z * (-0.5d0)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e-6) {
		tmp = (x * 0.5) / t;
	} else {
		tmp = (z * -0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.5e-6:
		tmp = (x * 0.5) / t
	else:
		tmp = (z * -0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.5e-6)
		tmp = Float64(Float64(x * 0.5) / t);
	else
		tmp = Float64(Float64(z * -0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.5e-6)
		tmp = (x * 0.5) / t;
	else
		tmp = (z * -0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.5e-6], N[(N[(x * 0.5), $MachinePrecision] / t), $MachinePrecision], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4999999999999996e-6

   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. Taylor expanded in x around inf 60.5%

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

      1. associate-*r/ 60.5%

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

   6. Simplified 60.5%

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

   if -6.4999999999999996e-6 < x

   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. Taylor expanded in z around inf 39.4%

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

      1. associate-*r/ 39.4%

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

   6. Simplified 39.4%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot 0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \end{array} \]

Alternative 10: 36.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
2. 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. Taylor expanded in x around inf 36.6%

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

   1. associate-*r/ 36.6%

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

   2. metadata-eval 36.6%

      \[\leadsto \frac{\color{blue}{\left(-0.5 \cdot -1\right)} \cdot x}{t} \]

   3. associate-*r* 36.6%

      \[\leadsto \frac{\color{blue}{-0.5 \cdot \left(-1 \cdot x\right)}}{t} \]

   4. neg-mul-1 36.6%

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

   5. *-commutative 36.6%

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

   6. associate-*r/ 36.5%

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

   7. distribute-lft-neg-in 36.5%

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

   8. distribute-rgt-neg-in 36.5%

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

   9. distribute-neg-frac 36.5%

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

   10. metadata-eval 36.5%

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

6. Simplified 36.5%

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

7. Final simplification 36.5%

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

Reproduce

herbie shell --seed 2023322 
(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)))