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

Percentage Accurate: 93.4% → 99.4%

Time: 9.9s

Alternatives: 13

Speedup: 0.6×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+242}:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{a}{y}}{t - z}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+216}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -4e+242)
     (- x (/ -1.0 (/ (/ a y) (- t z))))
     (if (<= t_1 2e+216) (- x (/ t_1 a)) (+ x (* y (/ (- t z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -4e+242) {
		tmp = x - (-1.0 / ((a / y) / (t - z)));
	} else if (t_1 <= 2e+216) {
		tmp = x - (t_1 / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if (t_1 <= (-4d+242)) then
        tmp = x - ((-1.0d0) / ((a / y) / (t - z)))
    else if (t_1 <= 2d+216) then
        tmp = x - (t_1 / a)
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -4e+242) {
		tmp = x - (-1.0 / ((a / y) / (t - z)));
	} else if (t_1 <= 2e+216) {
		tmp = x - (t_1 / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -4e+242:
		tmp = x - (-1.0 / ((a / y) / (t - z)))
	elif t_1 <= 2e+216:
		tmp = x - (t_1 / a)
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -4e+242)
		tmp = Float64(x - Float64(-1.0 / Float64(Float64(a / y) / Float64(t - z))));
	elseif (t_1 <= 2e+216)
		tmp = Float64(x - Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -4e+242)
		tmp = x - (-1.0 / ((a / y) / (t - z)));
	elseif (t_1 <= 2e+216)
		tmp = x - (t_1 / a);
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+242], N[(x - N[(-1.0 / N[(N[(a / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+216], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -4.0000000000000002e242

   1. Initial program 67.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 67.5%

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

      2. clear-num 67.7%

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

      3. associate-/r* 100.0%

         \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{a}{y}}{z - t}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto x - \color{blue}{\frac{1}{\frac{\frac{a}{y}}{z - t}}} \]

   if -4.0000000000000002e242 < (*.f64 y (-.f64 z t)) < 2e216

   1. Initial program 99.9%

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

   if 2e216 < (*.f64 y (-.f64 z t))

   1. Initial program 89.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -4 \cdot 10^{+242}:\\ \;\;\;\;x - \frac{-1}{\frac{\frac{a}{y}}{t - z}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+216}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 49.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ t_2 := y \cdot \frac{z}{-a}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-181}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.55 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 0.12:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))) (t_2 (* y (/ z (- a)))))
   (if (<= a -8.6e+22)
     x
     (if (<= a -3.3e-49)
       (* t (/ y a))
       (if (<= a -8.5e-73)
         x
         (if (<= a 9.5e-248)
           t_1
           (if (<= a 8.6e-181)
             t_2
             (if (<= a 4.55e-141)
               t_1
               (if (<= a 1.16e-92) t_2 (if (<= a 0.12) t_1 x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = y * (z / -a);
	double tmp;
	if (a <= -8.6e+22) {
		tmp = x;
	} else if (a <= -3.3e-49) {
		tmp = t * (y / a);
	} else if (a <= -8.5e-73) {
		tmp = x;
	} else if (a <= 9.5e-248) {
		tmp = t_1;
	} else if (a <= 8.6e-181) {
		tmp = t_2;
	} else if (a <= 4.55e-141) {
		tmp = t_1;
	} else if (a <= 1.16e-92) {
		tmp = t_2;
	} else if (a <= 0.12) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (a / y)
    t_2 = y * (z / -a)
    if (a <= (-8.6d+22)) then
        tmp = x
    else if (a <= (-3.3d-49)) then
        tmp = t * (y / a)
    else if (a <= (-8.5d-73)) then
        tmp = x
    else if (a <= 9.5d-248) then
        tmp = t_1
    else if (a <= 8.6d-181) then
        tmp = t_2
    else if (a <= 4.55d-141) then
        tmp = t_1
    else if (a <= 1.16d-92) then
        tmp = t_2
    else if (a <= 0.12d0) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = y * (z / -a);
	double tmp;
	if (a <= -8.6e+22) {
		tmp = x;
	} else if (a <= -3.3e-49) {
		tmp = t * (y / a);
	} else if (a <= -8.5e-73) {
		tmp = x;
	} else if (a <= 9.5e-248) {
		tmp = t_1;
	} else if (a <= 8.6e-181) {
		tmp = t_2;
	} else if (a <= 4.55e-141) {
		tmp = t_1;
	} else if (a <= 1.16e-92) {
		tmp = t_2;
	} else if (a <= 0.12) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	t_2 = y * (z / -a)
	tmp = 0
	if a <= -8.6e+22:
		tmp = x
	elif a <= -3.3e-49:
		tmp = t * (y / a)
	elif a <= -8.5e-73:
		tmp = x
	elif a <= 9.5e-248:
		tmp = t_1
	elif a <= 8.6e-181:
		tmp = t_2
	elif a <= 4.55e-141:
		tmp = t_1
	elif a <= 1.16e-92:
		tmp = t_2
	elif a <= 0.12:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	t_2 = Float64(y * Float64(z / Float64(-a)))
	tmp = 0.0
	if (a <= -8.6e+22)
		tmp = x;
	elseif (a <= -3.3e-49)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= -8.5e-73)
		tmp = x;
	elseif (a <= 9.5e-248)
		tmp = t_1;
	elseif (a <= 8.6e-181)
		tmp = t_2;
	elseif (a <= 4.55e-141)
		tmp = t_1;
	elseif (a <= 1.16e-92)
		tmp = t_2;
	elseif (a <= 0.12)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	t_2 = y * (z / -a);
	tmp = 0.0;
	if (a <= -8.6e+22)
		tmp = x;
	elseif (a <= -3.3e-49)
		tmp = t * (y / a);
	elseif (a <= -8.5e-73)
		tmp = x;
	elseif (a <= 9.5e-248)
		tmp = t_1;
	elseif (a <= 8.6e-181)
		tmp = t_2;
	elseif (a <= 4.55e-141)
		tmp = t_1;
	elseif (a <= 1.16e-92)
		tmp = t_2;
	elseif (a <= 0.12)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8.6e+22], x, If[LessEqual[a, -3.3e-49], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-73], x, If[LessEqual[a, 9.5e-248], t$95$1, If[LessEqual[a, 8.6e-181], t$95$2, If[LessEqual[a, 4.55e-141], t$95$1, If[LessEqual[a, 1.16e-92], t$95$2, If[LessEqual[a, 0.12], t$95$1, x]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.6000000000000004e22 or -3.3e-49 < a < -8.4999999999999996e-73 or 0.12 < a

   1. Initial program 91.2%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 86.4%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 86.4%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around inf 68.1%

      \[\leadsto \color{blue}{x} \]

   if -8.6000000000000004e22 < a < -3.3e-49

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-lft-neg-out 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-/l* 70.9%

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

      6. distribute-neg-frac 70.9%

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

      7. distribute-neg-frac2 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 51.9%

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

   10. Simplified 51.9%

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

   if -8.4999999999999996e-73 < a < 9.49999999999999971e-248 or 8.6e-181 < a < 4.55000000000000026e-141 or 1.1599999999999999e-92 < a < 0.12

   1. Initial program 99.8%

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

      1. associate-/l* 87.9%

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

   3. Simplified 87.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 73.8%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 73.8%

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

      2. mul-1-neg 73.8%

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

      3. distribute-lft-neg-out 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-/l* 66.0%

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

      6. distribute-neg-frac 66.0%

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

      7. distribute-neg-frac2 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in x around 0 63.2%

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

      1. *-commutative 63.2%

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

      2. associate-/l* 56.8%

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

   10. Applied egg-rr 56.8%

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

       1. associate-*r/ 63.2%

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

       2. associate-*l/ 64.5%

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

       3. *-commutative 64.5%

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

       4. clear-num 64.5%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       5. un-div-inv 64.6%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   12. Applied egg-rr 64.6%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if 9.49999999999999971e-248 < a < 8.6e-181 or 4.55000000000000026e-141 < a < 1.1599999999999999e-92

   1. Initial program 99.9%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 92.3%

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

      1. associate-/l* 85.0%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 85.0%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around 0 73.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 73.9%

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

      2. associate-*r/ 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. distribute-neg-frac2 66.6%

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

   10. Simplified 66.6%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-181}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;a \leq 4.55 \cdot 10^{-141}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-92}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;a \leq 0.12:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 1.4:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= a -1e+23)
     x
     (if (<= a -4.4e-49)
       (* t (/ y a))
       (if (<= a -1.1e-76)
         x
         (if (<= a 2.4e-247)
           t_1
           (if (<= a 3.6e-83) (* z (/ y (- a))) (if (<= a 1.4) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (a <= -1e+23) {
		tmp = x;
	} else if (a <= -4.4e-49) {
		tmp = t * (y / a);
	} else if (a <= -1.1e-76) {
		tmp = x;
	} else if (a <= 2.4e-247) {
		tmp = t_1;
	} else if (a <= 3.6e-83) {
		tmp = z * (y / -a);
	} else if (a <= 1.4) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / y)
    if (a <= (-1d+23)) then
        tmp = x
    else if (a <= (-4.4d-49)) then
        tmp = t * (y / a)
    else if (a <= (-1.1d-76)) then
        tmp = x
    else if (a <= 2.4d-247) then
        tmp = t_1
    else if (a <= 3.6d-83) then
        tmp = z * (y / -a)
    else if (a <= 1.4d0) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (a <= -1e+23) {
		tmp = x;
	} else if (a <= -4.4e-49) {
		tmp = t * (y / a);
	} else if (a <= -1.1e-76) {
		tmp = x;
	} else if (a <= 2.4e-247) {
		tmp = t_1;
	} else if (a <= 3.6e-83) {
		tmp = z * (y / -a);
	} else if (a <= 1.4) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if a <= -1e+23:
		tmp = x
	elif a <= -4.4e-49:
		tmp = t * (y / a)
	elif a <= -1.1e-76:
		tmp = x
	elif a <= 2.4e-247:
		tmp = t_1
	elif a <= 3.6e-83:
		tmp = z * (y / -a)
	elif a <= 1.4:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (a <= -1e+23)
		tmp = x;
	elseif (a <= -4.4e-49)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= -1.1e-76)
		tmp = x;
	elseif (a <= 2.4e-247)
		tmp = t_1;
	elseif (a <= 3.6e-83)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (a <= 1.4)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (a <= -1e+23)
		tmp = x;
	elseif (a <= -4.4e-49)
		tmp = t * (y / a);
	elseif (a <= -1.1e-76)
		tmp = x;
	elseif (a <= 2.4e-247)
		tmp = t_1;
	elseif (a <= 3.6e-83)
		tmp = z * (y / -a);
	elseif (a <= 1.4)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1e+23], x, If[LessEqual[a, -4.4e-49], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.1e-76], x, If[LessEqual[a, 2.4e-247], t$95$1, If[LessEqual[a, 3.6e-83], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -9.9999999999999992e22 or -4.3999999999999998e-49 < a < -1.1e-76 or 1.3999999999999999 < a

   1. Initial program 91.2%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 86.4%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 86.4%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around inf 68.1%

      \[\leadsto \color{blue}{x} \]

   if -9.9999999999999992e22 < a < -4.3999999999999998e-49

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-lft-neg-out 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-/l* 70.9%

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

      6. distribute-neg-frac 70.9%

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

      7. distribute-neg-frac2 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 51.9%

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

   10. Simplified 51.9%

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

   if -1.1e-76 < a < 2.40000000000000011e-247 or 3.60000000000000012e-83 < a < 1.3999999999999999

   1. Initial program 99.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 74.1%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.1%

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

      2. mul-1-neg 74.1%

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

      3. distribute-lft-neg-out 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-/l* 66.6%

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

      6. distribute-neg-frac 66.6%

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

      7. distribute-neg-frac2 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in x around 0 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 57.6%

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

   10. Applied egg-rr 57.6%

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

       1. associate-*r/ 63.5%

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

       2. associate-*l/ 63.5%

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

       3. *-commutative 63.5%

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

       4. clear-num 63.5%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       5. un-div-inv 63.6%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   12. Applied egg-rr 63.6%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if 2.40000000000000011e-247 < a < 3.60000000000000012e-83

   1. Initial program 99.9%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 70.6%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 70.6%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around 0 65.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 59.9%

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

      2. associate-*r* 59.9%

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

      3. *-commutative 59.9%

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

      4. associate-*r/ 59.9%

         \[\leadsto z \cdot \color{blue}{\frac{-1 \cdot y}{a}} \]

      5. neg-mul-1 59.9%

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

   10. Simplified 59.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-49}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-247}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-83}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 1.4:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{elif}\;a \leq 0.36:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= a -3.4e+23)
     x
     (if (<= a -1.6e-48)
       (* t (/ y a))
       (if (<= a -8.5e-73)
         x
         (if (<= a 9.5e-248)
           t_1
           (if (<= a 2.95e-89) (/ (* y z) (- a)) (if (<= a 0.36) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (a <= -3.4e+23) {
		tmp = x;
	} else if (a <= -1.6e-48) {
		tmp = t * (y / a);
	} else if (a <= -8.5e-73) {
		tmp = x;
	} else if (a <= 9.5e-248) {
		tmp = t_1;
	} else if (a <= 2.95e-89) {
		tmp = (y * z) / -a;
	} else if (a <= 0.36) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / y)
    if (a <= (-3.4d+23)) then
        tmp = x
    else if (a <= (-1.6d-48)) then
        tmp = t * (y / a)
    else if (a <= (-8.5d-73)) then
        tmp = x
    else if (a <= 9.5d-248) then
        tmp = t_1
    else if (a <= 2.95d-89) then
        tmp = (y * z) / -a
    else if (a <= 0.36d0) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (a <= -3.4e+23) {
		tmp = x;
	} else if (a <= -1.6e-48) {
		tmp = t * (y / a);
	} else if (a <= -8.5e-73) {
		tmp = x;
	} else if (a <= 9.5e-248) {
		tmp = t_1;
	} else if (a <= 2.95e-89) {
		tmp = (y * z) / -a;
	} else if (a <= 0.36) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if a <= -3.4e+23:
		tmp = x
	elif a <= -1.6e-48:
		tmp = t * (y / a)
	elif a <= -8.5e-73:
		tmp = x
	elif a <= 9.5e-248:
		tmp = t_1
	elif a <= 2.95e-89:
		tmp = (y * z) / -a
	elif a <= 0.36:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (a <= -3.4e+23)
		tmp = x;
	elseif (a <= -1.6e-48)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= -8.5e-73)
		tmp = x;
	elseif (a <= 9.5e-248)
		tmp = t_1;
	elseif (a <= 2.95e-89)
		tmp = Float64(Float64(y * z) / Float64(-a));
	elseif (a <= 0.36)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (a <= -3.4e+23)
		tmp = x;
	elseif (a <= -1.6e-48)
		tmp = t * (y / a);
	elseif (a <= -8.5e-73)
		tmp = x;
	elseif (a <= 9.5e-248)
		tmp = t_1;
	elseif (a <= 2.95e-89)
		tmp = (y * z) / -a;
	elseif (a <= 0.36)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+23], x, If[LessEqual[a, -1.6e-48], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.5e-73], x, If[LessEqual[a, 9.5e-248], t$95$1, If[LessEqual[a, 2.95e-89], N[(N[(y * z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[a, 0.36], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.39999999999999992e23 or -1.5999999999999999e-48 < a < -8.4999999999999996e-73 or 0.35999999999999999 < a

   1. Initial program 91.2%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 86.4%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 86.4%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around inf 68.1%

      \[\leadsto \color{blue}{x} \]

   if -3.39999999999999992e23 < a < -1.5999999999999999e-48

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-lft-neg-out 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-/l* 70.9%

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

      6. distribute-neg-frac 70.9%

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

      7. distribute-neg-frac2 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 51.9%

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

   10. Simplified 51.9%

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

   if -8.4999999999999996e-73 < a < 9.49999999999999971e-248 or 2.9500000000000001e-89 < a < 0.35999999999999999

   1. Initial program 99.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 74.1%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 74.1%

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

      2. mul-1-neg 74.1%

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

      3. distribute-lft-neg-out 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-/l* 66.6%

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

      6. distribute-neg-frac 66.6%

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

      7. distribute-neg-frac2 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in x around 0 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 57.6%

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

   10. Applied egg-rr 57.6%

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

       1. associate-*r/ 63.5%

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

       2. associate-*l/ 63.5%

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

       3. *-commutative 63.5%

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

       4. clear-num 63.5%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       5. un-div-inv 63.6%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   12. Applied egg-rr 63.6%

       \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   if 9.49999999999999971e-248 < a < 2.9500000000000001e-89

   1. Initial program 99.9%

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

      1. associate-/l* 81.6%

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

   3. Simplified 81.6%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.1%

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

      1. associate-/l* 70.6%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 70.6%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around 0 65.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 59.9%

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

      2. associate-*r* 59.9%

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

      3. *-commutative 59.9%

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

      4. associate-*r/ 59.9%

         \[\leadsto z \cdot \color{blue}{\frac{-1 \cdot y}{a}} \]

      5. neg-mul-1 59.9%

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

   10. Simplified 59.9%

       \[\leadsto \color{blue}{z \cdot \frac{-y}{a}} \]
   11. Step-by-step derivation

       1. distribute-frac-neg 59.9%

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

       2. distribute-frac-neg2 59.9%

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

       3. associate-*r/ 65.1%

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

   12. Applied egg-rr 65.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-248}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{elif}\;a \leq 0.36:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+79} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+216}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -2e+79) (not (<= t_1 2e+216)))
     (+ x (* y (/ (- t z) a)))
     (- x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -2e+79) || !(t_1 <= 2e+216)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - (t_1 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if ((t_1 <= (-2d+79)) .or. (.not. (t_1 <= 2d+216))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x - (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -2e+79) || !(t_1 <= 2e+216)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -2e+79) or not (t_1 <= 2e+216):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x - (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -2e+79) || !(t_1 <= 2e+216))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x - Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -2e+79) || ~((t_1 <= 2e+216)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x - (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+79], N[Not[LessEqual[t$95$1, 2e+216]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -1.99999999999999993e79 or 2e216 < (*.f64 y (-.f64 z t))

   1. Initial program 87.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   if -1.99999999999999993e79 < (*.f64 y (-.f64 z t)) < 2e216

   1. Initial program 99.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+79} \lor \neg \left(y \cdot \left(z - t\right) \leq 2 \cdot 10^{+216}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-48} \lor \neg \left(a \leq -8.5 \cdot 10^{-73}\right) \land a \leq 0.74:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+26)
   x
   (if (or (<= a -5.4e-48) (and (not (<= a -8.5e-73)) (<= a 0.74)))
     (* t (/ y a))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+26) {
		tmp = x;
	} else if ((a <= -5.4e-48) || (!(a <= -8.5e-73) && (a <= 0.74))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+26)) then
        tmp = x
    else if ((a <= (-5.4d-48)) .or. (.not. (a <= (-8.5d-73))) .and. (a <= 0.74d0)) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+26) {
		tmp = x;
	} else if ((a <= -5.4e-48) || (!(a <= -8.5e-73) && (a <= 0.74))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+26:
		tmp = x
	elif (a <= -5.4e-48) or (not (a <= -8.5e-73) and (a <= 0.74)):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+26)
		tmp = x;
	elseif ((a <= -5.4e-48) || (!(a <= -8.5e-73) && (a <= 0.74)))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+26)
		tmp = x;
	elseif ((a <= -5.4e-48) || (~((a <= -8.5e-73)) && (a <= 0.74)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+26], x, If[Or[LessEqual[a, -5.4e-48], And[N[Not[LessEqual[a, -8.5e-73]], $MachinePrecision], LessEqual[a, 0.74]]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.5e26 or -5.40000000000000023e-48 < a < -8.4999999999999996e-73 or 0.73999999999999999 < a

   1. Initial program 91.2%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 86.4%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 86.4%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around inf 68.1%

      \[\leadsto \color{blue}{x} \]

   if -2.5e26 < a < -5.40000000000000023e-48 or -8.4999999999999996e-73 < a < 0.73999999999999999

   1. Initial program 99.8%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 64.9%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 64.9%

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

      2. mul-1-neg 64.9%

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

      3. distribute-lft-neg-out 64.9%

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

      4. *-commutative 64.9%

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

      5. associate-/l* 58.6%

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

      6. distribute-neg-frac 58.6%

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

      7. distribute-neg-frac2 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in x around 0 51.1%

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

      1. associate-*r/ 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-48} \lor \neg \left(a \leq -8.5 \cdot 10^{-73}\right) \land a \leq 0.74:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.235:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.7e+25)
   x
   (if (<= a -1.7e-47)
     (* t (/ y a))
     (if (<= a -4.4e-73) x (if (<= a 0.235) (/ t (/ a y)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+25) {
		tmp = x;
	} else if (a <= -1.7e-47) {
		tmp = t * (y / a);
	} else if (a <= -4.4e-73) {
		tmp = x;
	} else if (a <= 0.235) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.7d+25)) then
        tmp = x
    else if (a <= (-1.7d-47)) then
        tmp = t * (y / a)
    else if (a <= (-4.4d-73)) then
        tmp = x
    else if (a <= 0.235d0) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.7e+25) {
		tmp = x;
	} else if (a <= -1.7e-47) {
		tmp = t * (y / a);
	} else if (a <= -4.4e-73) {
		tmp = x;
	} else if (a <= 0.235) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.7e+25:
		tmp = x
	elif a <= -1.7e-47:
		tmp = t * (y / a)
	elif a <= -4.4e-73:
		tmp = x
	elif a <= 0.235:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.7e+25)
		tmp = x;
	elseif (a <= -1.7e-47)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= -4.4e-73)
		tmp = x;
	elseif (a <= 0.235)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.7e+25)
		tmp = x;
	elseif (a <= -1.7e-47)
		tmp = t * (y / a);
	elseif (a <= -4.4e-73)
		tmp = x;
	elseif (a <= 0.235)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.7e+25], x, If[LessEqual[a, -1.7e-47], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.4e-73], x, If[LessEqual[a, 0.235], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.6999999999999999e25 or -1.7000000000000001e-47 < a < -4.4e-73 or 0.23499999999999999 < a

   1. Initial program 91.2%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 86.4%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 86.4%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around inf 68.1%

      \[\leadsto \color{blue}{x} \]

   if -3.6999999999999999e25 < a < -1.7000000000000001e-47

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 70.6%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 70.6%

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

      2. mul-1-neg 70.6%

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

      3. distribute-lft-neg-out 70.6%

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

      4. *-commutative 70.6%

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

      5. associate-/l* 70.9%

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

      6. distribute-neg-frac 70.9%

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

      7. distribute-neg-frac2 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in x around 0 51.6%

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

      1. associate-*r/ 51.9%

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

   10. Simplified 51.9%

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

   if -4.4e-73 < a < 0.23499999999999999

   1. Initial program 99.9%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 63.8%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 63.8%

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

      2. mul-1-neg 63.8%

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

      3. distribute-lft-neg-out 63.8%

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

      4. *-commutative 63.8%

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

      5. associate-/l* 56.1%

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

      6. distribute-neg-frac 56.1%

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

      7. distribute-neg-frac2 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in x around 0 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 44.3%

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

   10. Applied egg-rr 44.3%

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

       1. associate-*r/ 50.9%

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

       2. associate-*l/ 52.8%

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

       3. *-commutative 52.8%

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

       4. clear-num 52.8%

          \[\leadsto t \cdot \color{blue}{\frac{1}{\frac{a}{y}}} \]

       5. un-div-inv 52.9%

          \[\leadsto \color{blue}{\frac{t}{\frac{a}{y}}} \]

   12. Applied egg-rr 52.9%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.235:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+139} \lor \neg \left(z \leq 1.65 \cdot 10^{+202}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+139) (not (<= z 1.65e+202)))
   (* z (/ y (- a)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+139) || !(z <= 1.65e+202)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.1d+139)) .or. (.not. (z <= 1.65d+202))) then
        tmp = z * (y / -a)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.1e+139) || !(z <= 1.65e+202)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.1e+139) or not (z <= 1.65e+202):
		tmp = z * (y / -a)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.1e+139) || !(z <= 1.65e+202))
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.1e+139) || ~((z <= 1.65e+202)))
		tmp = z * (y / -a);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.1e+139], N[Not[LessEqual[z, 1.65e+202]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e139 or 1.6499999999999999e202 < z

   1. Initial program 83.3%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 79.8%

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

      1. associate-/l* 84.3%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 84.3%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   8. Taylor expanded in x around 0 60.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. associate-*l/ 70.2%

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

      2. associate-*r* 70.2%

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

      3. *-commutative 70.2%

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

      4. associate-*r/ 70.2%

         \[\leadsto z \cdot \color{blue}{\frac{-1 \cdot y}{a}} \]

      5. neg-mul-1 70.2%

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

   10. Simplified 70.2%

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

   if -2.0999999999999999e139 < z < 1.6499999999999999e202

   1. Initial program 98.4%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 82.0%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 82.0%

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

      2. mul-1-neg 82.0%

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

      3. distribute-lft-neg-out 82.0%

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

      4. *-commutative 82.0%

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

      5. associate-/l* 79.3%

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

      6. distribute-neg-frac 79.3%

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

      7. distribute-neg-frac2 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in y around 0 82.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+139} \lor \neg \left(z \leq 1.65 \cdot 10^{+202}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-70} \lor \neg \left(t \leq 4.4 \cdot 10^{+43}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e-70) (not (<= t 4.4e+43)))
   (+ x (/ (* y t) a))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-70) || !(t <= 4.4e+43)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1d-70)) .or. (.not. (t <= 4.4d+43))) then
        tmp = x + ((y * t) / a)
    else
        tmp = x - (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e-70) || !(t <= 4.4e+43)) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e-70) or not (t <= 4.4e+43):
		tmp = x + ((y * t) / a)
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e-70) || !(t <= 4.4e+43))
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1e-70) || ~((t <= 4.4e+43)))
		tmp = x + ((y * t) / a);
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e-70], N[Not[LessEqual[t, 4.4e+43]], $MachinePrecision]], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999996e-71 or 4.40000000000000001e43 < t

   1. Initial program 93.9%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 83.4%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 83.4%

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

      2. mul-1-neg 83.4%

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

      3. distribute-lft-neg-out 83.4%

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

      4. *-commutative 83.4%

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

      5. associate-/l* 81.3%

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

      6. distribute-neg-frac 81.3%

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

      7. distribute-neg-frac2 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in y around 0 83.4%

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

   if -9.99999999999999996e-71 < t < 4.40000000000000001e43

   1. Initial program 96.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 92.6%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 92.6%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-70} \lor \neg \left(t \leq 4.4 \cdot 10^{+43}\right):\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.4e-70)
   (+ x (* y (/ t a)))
   (if (<= t 3.4e+45) (- x (* y (/ z a))) (+ x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e-70) {
		tmp = x + (y * (t / a));
	} else if (t <= 3.4e+45) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.4d-70)) then
        tmp = x + (y * (t / a))
    else if (t <= 3.4d+45) then
        tmp = x - (y * (z / a))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.4e-70) {
		tmp = x + (y * (t / a));
	} else if (t <= 3.4e+45) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.4e-70:
		tmp = x + (y * (t / a))
	elif t <= 3.4e+45:
		tmp = x - (y * (z / a))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.4e-70)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 3.4e+45)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.4e-70)
		tmp = x + (y * (t / a));
	elseif (t <= 3.4e+45)
		tmp = x - (y * (z / a));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.4e-70], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+45], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999995e-70

   1. Initial program 92.6%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 80.6%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 80.6%

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

      2. mul-1-neg 80.6%

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

      3. distribute-lft-neg-out 80.6%

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

      4. *-commutative 80.6%

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

      5. associate-/l* 81.9%

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

      6. distribute-neg-frac 81.9%

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

      7. distribute-neg-frac2 81.9%

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

   7. Simplified 81.9%

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

   if -3.39999999999999995e-70 < t < 3.4e45

   1. Initial program 96.3%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 90.6%

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

      1. associate-/l* 92.6%

         \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   7. Simplified 92.6%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

   if 3.4e45 < t

   1. Initial program 95.9%

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

      1. associate-/l* 84.4%

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

   3. Simplified 84.4%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 87.9%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 87.9%

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

      2. mul-1-neg 87.9%

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

      3. distribute-lft-neg-out 87.9%

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

      4. *-commutative 87.9%

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

      5. associate-/l* 80.4%

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

      6. distribute-neg-frac 80.4%

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

      7. distribute-neg-frac2 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in y around 0 87.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-70}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+45}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.32 \cdot 10^{+222}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.32e+222) (+ x (* y (/ (- t z) a))) (- x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.32e+222) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 1.32d+222) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x - (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.32e+222) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.32e+222:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x - (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.32e+222)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x - Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.32e+222)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x - (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1.32e+222], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.31999999999999997e222

   1. Initial program 97.0%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   if 1.31999999999999997e222 < z

   1. Initial program 74.6%

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

      1. associate-/l* 77.9%

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

   3. Simplified 77.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.6%

      \[\leadsto x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 74.6%

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

      2. associate-*r/ 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in z around inf 74.6%

      \[\leadsto x - \color{blue}{\frac{y \cdot z}{a}} \]
   9. Step-by-step derivation

      1. *-commutative 74.6%

         \[\leadsto x - \frac{\color{blue}{z \cdot y}}{a} \]

      2. *-lft-identity 74.6%

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

      3. associate-*l/ 74.5%

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

      4. *-commutative 74.5%

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

      5. associate-*r* 98.0%

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

      6. associate-/r/ 98.0%

         \[\leadsto x - \color{blue}{\frac{1}{\frac{a}{y}}} \cdot z \]

      7. associate-*l/ 98.0%

         \[\leadsto x - \color{blue}{\frac{1 \cdot z}{\frac{a}{y}}} \]

      8. *-lft-identity 98.0%

         \[\leadsto x - \frac{\color{blue}{z}}{\frac{a}{y}} \]

   10. Simplified 98.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.32 \cdot 10^{+222}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-188}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e-188) (+ x (* y (/ (- t z) a))) (- x (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e-188) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - ((z - t) * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1d-188)) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x - ((z - t) * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e-188) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x - ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1e-188:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x - ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1e-188)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1e-188)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x - ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1e-188], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999995e-189

   1. Initial program 92.8%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   if -9.9999999999999995e-189 < y

   1. Initial program 96.7%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 96.7%

      \[\leadsto x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 96.7%

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

      2. associate-*r/ 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-188}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 95.1%

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

   1. associate-/l* 94.7%

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

3. Simplified 94.7%

   \[\leadsto \color{blue}{x - y \cdot \frac{z - t}{a}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 70.7%

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

   1. associate-/l* 71.7%

      \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

7. Simplified 71.7%

   \[\leadsto x - \color{blue}{y \cdot \frac{z}{a}} \]

8. Taylor expanded in x around inf 44.1%

   \[\leadsto \color{blue}{x} \]

9. Final simplification 44.1%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))