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

Percentage Accurate: 93.2% → 99.4%

Time: 9.6s

Alternatives: 12

Speedup: 0.5×

• 25.0% 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: 93.2% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* y (/ (- z t) a)))
     (if (<= t_1 2e+146) (+ x (/ t_1 a)) (+ x (* (- z t) (/ y 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 <= -((double) INFINITY)) {
		tmp = x + (y * ((z - t) / a));
	} else if (t_1 <= 2e+146) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y * ((z - t) / a));
	} else if (t_1 <= 2e+146) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + (y * ((z - t) / a))
	elif t_1 <= 2e+146:
		tmp = x + (t_1 / a)
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t_1 <= 2e+146)
		tmp = Float64(x + Float64(t_1 / 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)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + (y * ((z - t) / a));
	elseif (t_1 <= 2e+146)
		tmp = x + (t_1 / a);
	else
		tmp = x + ((z - t) * (y / 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, (-Infinity)], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+146], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0

   1. Initial program 73.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 73.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 73.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{t - z}{a}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{t - z}{a} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{t - z}{a}\right), \color{blue}{y}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(t - z\right), a\right), y\right)\right) \]

      5. --lowering--.f64 100.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), a\right), y\right)\right) \]

   6. Applied egg-rr 100.0%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 1.99999999999999987e146

   1. Initial program 99.8%

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

   if 1.99999999999999987e146 < (*.f64 y (-.f64 z t))

   1. Initial program 90.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 90.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 90.0%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\left(t - z\right) \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t - z\right) \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(t - z\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(t - z\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\color{blue}{t} - z\right)\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{z - t}{\frac{a}{y}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (/ (- z t) (/ a y))))
   (if (<= t_1 -1e+162) t_2 (if (<= t_1 4e+152) (+ x (/ (* y z) a)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double t_2 = (z - t) / (a / y);
	double tmp;
	if (t_1 <= -1e+162) {
		tmp = t_2;
	} else if (t_1 <= 4e+152) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	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 = (y * (z - t)) / a
    t_2 = (z - t) / (a / y)
    if (t_1 <= (-1d+162)) then
        tmp = t_2
    else if (t_1 <= 4d+152) then
        tmp = x + ((y * z) / a)
    else
        tmp = t_2
    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)) / a;
	double t_2 = (z - t) / (a / y);
	double tmp;
	if (t_1 <= -1e+162) {
		tmp = t_2;
	} else if (t_1 <= 4e+152) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = (z - t) / (a / y)
	tmp = 0
	if t_1 <= -1e+162:
		tmp = t_2
	elif t_1 <= 4e+152:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	t_2 = Float64(Float64(z - t) / Float64(a / y))
	tmp = 0.0
	if (t_1 <= -1e+162)
		tmp = t_2;
	elseif (t_1 <= 4e+152)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	t_2 = (z - t) / (a / y);
	tmp = 0.0;
	if (t_1 <= -1e+162)
		tmp = t_2;
	elseif (t_1 <= 4e+152)
		tmp = x + ((y * z) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+162], t$95$2, If[LessEqual[t$95$1, 4e+152], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -9.9999999999999994e161 or 4.0000000000000002e152 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 88.4%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - z\right)}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(t - z\right)}{a}\right) \]

      2. distribute-neg-frac N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(t - z\right)\right)\right), \color{blue}{a}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), a\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + -1 \cdot z\right)\right)\right), a\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z + t\right)\right)\right), a\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z\right) + -1 \cdot t\right)\right), a\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot z + -1 \cdot t\right)\right), a\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(1 \cdot z + -1 \cdot t\right)\right), a\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + -1 \cdot t\right)\right), a\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right), a\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), a\right) \]

      16. --lowering--.f64 85.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), a\right) \]

   7. Simplified 85.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

         \[\leadsto \left(z + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + z\right) \cdot \frac{\color{blue}{y}}{a} \]

      5. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{y}{a} \]

      6. distribute-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - z\right)\right)\right) \cdot \frac{y}{a} \]

      8. clear-num N/A

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

      9. un-div-inv N/A

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

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(t - z\right)\right)\right), \color{blue}{\left(\frac{a}{y}\right)}\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), \left(\frac{a}{y}\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), \left(\frac{\color{blue}{a}}{y}\right)\right) \]

      13. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(t\right)\right) + z\right), \left(\frac{a}{y}\right)\right) \]

      14. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(z + \left(\mathsf{neg}\left(t\right)\right)\right), \left(\frac{\color{blue}{a}}{y}\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\left(z - t\right), \left(\frac{\color{blue}{a}}{y}\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{\color{blue}{a}}{y}\right)\right) \]

      17. /-lowering-/.f64 90.3%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 90.3%

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

   if -9.9999999999999994e161 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.0000000000000002e152

   1. Initial program 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 99.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{a}\right)\right)\right)\right) \]

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right)\right) \]

      6. *-lowering-*.f64 84.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   7. Simplified 84.7%

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

Alternative 3: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+152}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (- z t) (/ y a))))
   (if (<= t_1 -1e+162) t_2 (if (<= t_1 4e+152) (+ x (/ (* y z) a)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double t_2 = (z - t) * (y / a);
	double tmp;
	if (t_1 <= -1e+162) {
		tmp = t_2;
	} else if (t_1 <= 4e+152) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	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 = (y * (z - t)) / a
    t_2 = (z - t) * (y / a)
    if (t_1 <= (-1d+162)) then
        tmp = t_2
    else if (t_1 <= 4d+152) then
        tmp = x + ((y * z) / a)
    else
        tmp = t_2
    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)) / a;
	double t_2 = (z - t) * (y / a);
	double tmp;
	if (t_1 <= -1e+162) {
		tmp = t_2;
	} else if (t_1 <= 4e+152) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = (z - t) * (y / a)
	tmp = 0
	if t_1 <= -1e+162:
		tmp = t_2
	elif t_1 <= 4e+152:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	t_2 = Float64(Float64(z - t) * Float64(y / a))
	tmp = 0.0
	if (t_1 <= -1e+162)
		tmp = t_2;
	elseif (t_1 <= 4e+152)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	t_2 = (z - t) * (y / a);
	tmp = 0.0;
	if (t_1 <= -1e+162)
		tmp = t_2;
	elseif (t_1 <= 4e+152)
		tmp = x + ((y * z) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+162], t$95$2, If[LessEqual[t$95$1, 4e+152], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -9.9999999999999994e161 or 4.0000000000000002e152 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.4%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 88.4%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - z\right)}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(t - z\right)}{a}\right) \]

      2. distribute-neg-frac N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(t - z\right)\right)\right), \color{blue}{a}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), a\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + -1 \cdot z\right)\right)\right), a\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z + t\right)\right)\right), a\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z\right) + -1 \cdot t\right)\right), a\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot z + -1 \cdot t\right)\right), a\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(1 \cdot z + -1 \cdot t\right)\right), a\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + -1 \cdot t\right)\right), a\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right), a\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), a\right) \]

      16. --lowering--.f64 85.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), a\right) \]

   7. Simplified 85.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

         \[\leadsto \left(z + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + z\right) \cdot \frac{\color{blue}{y}}{a} \]

      5. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{y}{a} \]

      6. distribute-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - z\right)\right)\right) \cdot \frac{y}{a} \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\left(t - z\right) \cdot \frac{y}{a}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{a} \cdot \left(t - z\right)\right) \]

      10. distribute-rgt-neg-in N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(z + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(z - \color{blue}{t}\right)\right) \]

      18. --lowering--.f64 90.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 90.3%

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

   if -9.9999999999999994e161 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.0000000000000002e152

   1. Initial program 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 99.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{a}\right)\right)\right)\right) \]

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right)\right) \]

      6. *-lowering-*.f64 84.7%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   7. Simplified 84.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+162}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+152}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+235}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (+ x (* (- z t) (/ y a)))))
   (if (<= t_1 -1e+235) t_2 (if (<= t_1 2e+146) (+ x (/ t_1 a)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (t_1 <= -1e+235) {
		tmp = t_2;
	} else if (t_1 <= 2e+146) {
		tmp = x + (t_1 / a);
	} else {
		tmp = t_2;
	}
	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 = y * (z - t)
    t_2 = x + ((z - t) * (y / a))
    if (t_1 <= (-1d+235)) then
        tmp = t_2
    else if (t_1 <= 2d+146) then
        tmp = x + (t_1 / a)
    else
        tmp = t_2
    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 t_2 = x + ((z - t) * (y / a));
	double tmp;
	if (t_1 <= -1e+235) {
		tmp = t_2;
	} else if (t_1 <= 2e+146) {
		tmp = x + (t_1 / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	t_2 = x + ((z - t) * (y / a))
	tmp = 0
	if t_1 <= -1e+235:
		tmp = t_2
	elif t_1 <= 2e+146:
		tmp = x + (t_1 / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(x + Float64(Float64(z - t) * Float64(y / a)))
	tmp = 0.0
	if (t_1 <= -1e+235)
		tmp = t_2;
	elseif (t_1 <= 2e+146)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = x + ((z - t) * (y / a));
	tmp = 0.0;
	if (t_1 <= -1e+235)
		tmp = t_2;
	elseif (t_1 <= 2e+146)
		tmp = x + (t_1 / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+235], t$95$2, If[LessEqual[t$95$1, 2e+146], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -1.0000000000000001e235 or 1.99999999999999987e146 < (*.f64 y (-.f64 z t))

   1. Initial program 85.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 85.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 85.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{\left(t - z\right) \cdot y}{a}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\left(t - z\right) \cdot \color{blue}{\frac{y}{a}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{a} \cdot \color{blue}{\left(t - z\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(t - z\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\color{blue}{t} - z\right)\right)\right) \]

      6. --lowering--.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 99.9%

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

   if -1.0000000000000001e235 < (*.f64 y (-.f64 z t)) < 1.99999999999999987e146

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -1 \cdot 10^{+235}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY)) (* y (/ (- z t) 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 <= -((double) INFINITY)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = y * ((z - t) / 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 <= -math.inf:
		tmp = y * ((z - t) / 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 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(z - t) / 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 <= -Inf)
		tmp = y * ((z - t) / 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[LessEqual[t$95$1, (-Infinity)], N[(y * N[(N[(z - t), $MachinePrecision] / a), $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)) < -inf.0

   1. Initial program 73.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 73.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 73.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - z\right)}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(t - z\right)}{a}\right) \]

      2. distribute-neg-frac N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(t - z\right)\right)\right), \color{blue}{a}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), a\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + -1 \cdot z\right)\right)\right), a\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z + t\right)\right)\right), a\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z\right) + -1 \cdot t\right)\right), a\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot z + -1 \cdot t\right)\right), a\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(1 \cdot z + -1 \cdot t\right)\right), a\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + -1 \cdot t\right)\right), a\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right), a\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), a\right) \]

      16. --lowering--.f64 73.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), a\right) \]

   7. Simplified 73.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

         \[\leadsto \frac{1}{\frac{\mathsf{neg}\left(a\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} \cdot y \]

      5. frac-2neg N/A

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

      6. sub-neg N/A

         \[\leadsto \frac{1}{\frac{a}{z + \left(\mathsf{neg}\left(t\right)\right)}} \cdot y \]

      7. +-commutative N/A

         \[\leadsto \frac{1}{\frac{a}{\left(\mathsf{neg}\left(t\right)\right) + z}} \cdot y \]

      8. remove-double-neg N/A

         \[\leadsto \frac{1}{\frac{a}{\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}} \cdot y \]

      9. distribute-neg-in N/A

         \[\leadsto \frac{1}{\frac{a}{\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)}} \cdot y \]

      10. sub-neg N/A

          \[\leadsto \frac{1}{\frac{a}{\mathsf{neg}\left(\left(t - z\right)\right)}} \cdot y \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{a}{t - z}\right)} \cdot y \]

      12. clear-num N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{1}{\frac{t - z}{a}}\right)} \cdot y \]

      13. distribute-neg-frac2 N/A

          \[\leadsto \frac{1}{\frac{1}{\mathsf{neg}\left(\frac{t - z}{a}\right)}} \cdot y \]

      14. remove-double-div N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{t - z}{a}\right)\right) \cdot y \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{t - z}{a}\right)\right), \color{blue}{y}\right) \]

   9. Applied egg-rr 89.3%

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

   if -inf.0 < (*.f64 y (-.f64 z t))

   1. Initial program 97.7%

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

4. Final simplification 96.8%

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

Alternative 6: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+111)
   (* y (/ (- z t) a))
   (if (<= t 2.6e+146) (+ x (/ y (/ a z))) (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+111) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.6e+146) {
		tmp = x + (y / (a / z));
	} else {
		tmp = (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 (t <= (-4d+111)) then
        tmp = y * ((z - t) / a)
    else if (t <= 2.6d+146) then
        tmp = x + (y / (a / z))
    else
        tmp = (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 (t <= -4e+111) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.6e+146) {
		tmp = x + (y / (a / z));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4e+111:
		tmp = y * ((z - t) / a)
	elif t <= 2.6e+146:
		tmp = x + (y / (a / z))
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+111)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 2.6e+146)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	else
		tmp = 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 (t <= -4e+111)
		tmp = y * ((z - t) / a);
	elseif (t <= 2.6e+146)
		tmp = x + (y / (a / z));
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+111], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+146], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999983e111

   1. Initial program 97.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 97.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 97.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - z\right)}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(t - z\right)}{a}\right) \]

      2. distribute-neg-frac N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(t - z\right)\right)\right), \color{blue}{a}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), a\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + -1 \cdot z\right)\right)\right), a\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z + t\right)\right)\right), a\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z\right) + -1 \cdot t\right)\right), a\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot z + -1 \cdot t\right)\right), a\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(1 \cdot z + -1 \cdot t\right)\right), a\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + -1 \cdot t\right)\right), a\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right), a\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), a\right) \]

      16. --lowering--.f64 74.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), a\right) \]

   7. Simplified 74.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

         \[\leadsto \frac{1}{\frac{\mathsf{neg}\left(a\right)}{\mathsf{neg}\left(\left(z - t\right)\right)}} \cdot y \]

      5. frac-2neg N/A

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

      6. sub-neg N/A

         \[\leadsto \frac{1}{\frac{a}{z + \left(\mathsf{neg}\left(t\right)\right)}} \cdot y \]

      7. +-commutative N/A

         \[\leadsto \frac{1}{\frac{a}{\left(\mathsf{neg}\left(t\right)\right) + z}} \cdot y \]

      8. remove-double-neg N/A

         \[\leadsto \frac{1}{\frac{a}{\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}} \cdot y \]

      9. distribute-neg-in N/A

         \[\leadsto \frac{1}{\frac{a}{\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)}} \cdot y \]

      10. sub-neg N/A

          \[\leadsto \frac{1}{\frac{a}{\mathsf{neg}\left(\left(t - z\right)\right)}} \cdot y \]

      11. distribute-neg-frac2 N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{a}{t - z}\right)} \cdot y \]

      12. clear-num N/A

          \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{1}{\frac{t - z}{a}}\right)} \cdot y \]

      13. distribute-neg-frac2 N/A

          \[\leadsto \frac{1}{\frac{1}{\mathsf{neg}\left(\frac{t - z}{a}\right)}} \cdot y \]

      14. remove-double-div N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{t - z}{a}\right)\right) \cdot y \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\mathsf{neg}\left(\frac{t - z}{a}\right)\right), \color{blue}{y}\right) \]

   9. Applied egg-rr 72.0%

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

   if -3.99999999999999983e111 < t < 2.60000000000000014e146

   1. Initial program 95.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 95.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{a}\right)\right)\right)\right) \]

      3. remove-double-neg N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot z}{a}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right)\right) \]

      6. *-lowering-*.f64 86.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right)\right) \]

   7. Simplified 86.0%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{z}{a}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{a}{z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 84.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 84.9%

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

   if 2.60000000000000014e146 < t

   1. Initial program 89.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 89.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 89.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - z\right)}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(t - z\right)}{a}\right) \]

      2. distribute-neg-frac N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(t - z\right)\right)\right), \color{blue}{a}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), a\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + -1 \cdot z\right)\right)\right), a\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z + t\right)\right)\right), a\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z\right) + -1 \cdot t\right)\right), a\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot z + -1 \cdot t\right)\right), a\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(1 \cdot z + -1 \cdot t\right)\right), a\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + -1 \cdot t\right)\right), a\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right), a\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), a\right) \]

      16. --lowering--.f64 68.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), a\right) \]

   7. Simplified 68.9%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

         \[\leadsto \left(z + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + z\right) \cdot \frac{\color{blue}{y}}{a} \]

      5. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{y}{a} \]

      6. distribute-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - z\right)\right)\right) \cdot \frac{y}{a} \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\left(t - z\right) \cdot \frac{y}{a}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{a} \cdot \left(t - z\right)\right) \]

      10. distribute-rgt-neg-in N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(z + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(z - \color{blue}{t}\right)\right) \]

      18. --lowering--.f64 76.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 76.4%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 50000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.2e+23) x (if (<= a 50000.0) (* (- z t) (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+23) {
		tmp = x;
	} else if (a <= 50000.0) {
		tmp = (z - 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 <= (-2.2d+23)) then
        tmp = x
    else if (a <= 50000.0d0) then
        tmp = (z - 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 <= -2.2e+23) {
		tmp = x;
	} else if (a <= 50000.0) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.2e+23:
		tmp = x
	elif a <= 50000.0:
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.2e+23)
		tmp = x;
	elseif (a <= 50000.0)
		tmp = Float64(Float64(z - 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 <= -2.2e+23)
		tmp = x;
	elseif (a <= 50000.0)
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.2e+23], x, If[LessEqual[a, 50000.0], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.20000000000000008e23 or 5e4 < a

   1. Initial program 89.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 89.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 89.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 64.5%

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

   if -2.20000000000000008e23 < a < 5e4

   1. Initial program 99.8%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 99.8%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(t - z\right)}{a}} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(\frac{y \cdot \left(t - z\right)}{a}\right) \]

      2. distribute-neg-frac N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(y \cdot \left(t - z\right)\right)\right), \color{blue}{a}\right) \]

      4. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), a\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t - z\right)\right)\right), a\right) \]

      7. sub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right), a\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(t + -1 \cdot z\right)\right)\right), a\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z + t\right)\right)\right), a\right) \]

      10. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(-1 \cdot \left(-1 \cdot z\right) + -1 \cdot t\right)\right), a\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\left(-1 \cdot -1\right) \cdot z + -1 \cdot t\right)\right), a\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(1 \cdot z + -1 \cdot t\right)\right), a\right) \]

      13. *-lft-identity N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + -1 \cdot t\right)\right), a\right) \]

      14. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z + \left(\mathsf{neg}\left(t\right)\right)\right)\right), a\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(z - t\right)\right), a\right) \]

      16. --lowering--.f64 80.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(z, t\right)\right), a\right) \]

   7. Simplified 80.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

         \[\leadsto \left(z + \left(\mathsf{neg}\left(t\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + z\right) \cdot \frac{\color{blue}{y}}{a} \]

      5. remove-double-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(t\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{y}{a} \]

      6. distribute-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right) \cdot \frac{\color{blue}{y}}{a} \]

      7. sub-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(\left(t - z\right)\right)\right) \cdot \frac{y}{a} \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{neg}\left(\left(t - z\right) \cdot \frac{y}{a}\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{a} \cdot \left(t - z\right)\right) \]

      10. distribute-rgt-neg-in N/A

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

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{\left(\mathsf{neg}\left(\left(t - z\right)\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\color{blue}{\left(t - z\right)}\right)\right)\right) \]

      13. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right) \]

      14. distribute-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(t\right)\right) + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right)}\right)\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(\left(\mathsf{neg}\left(t\right)\right) + z\right)\right) \]

      16. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(z + \color{blue}{\left(\mathsf{neg}\left(t\right)\right)}\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \left(z - \color{blue}{t}\right)\right) \]

      18. --lowering--.f64 76.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 76.8%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 50000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)))
   (if (<= z -5.5e+115) t_1 (if (<= z 4.3e+28) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (z <= -5.5e+115) {
		tmp = t_1;
	} else if (z <= 4.3e+28) {
		tmp = x;
	} else {
		tmp = 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 = (y * z) / a
    if (z <= (-5.5d+115)) then
        tmp = t_1
    else if (z <= 4.3d+28) then
        tmp = x
    else
        tmp = 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 = (y * z) / a;
	double tmp;
	if (z <= -5.5e+115) {
		tmp = t_1;
	} else if (z <= 4.3e+28) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	tmp = 0
	if z <= -5.5e+115:
		tmp = t_1
	elif z <= 4.3e+28:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (z <= -5.5e+115)
		tmp = t_1;
	elseif (z <= 4.3e+28)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	tmp = 0.0;
	if (z <= -5.5e+115)
		tmp = t_1;
	elseif (z <= 4.3e+28)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -5.5e+115], t$95$1, If[LessEqual[z, 4.3e+28], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e115 or 4.29999999999999975e28 < z

   1. Initial program 94.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 94.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 64.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   7. Simplified 64.8%

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

   if -5.5e115 < z < 4.29999999999999975e28

   1. Initial program 95.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 95.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 53.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.44 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+115) (/ y (/ a z)) (if (<= z 1.44e+26) x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+115) {
		tmp = y / (a / z);
	} else if (z <= 1.44e+26) {
		tmp = x;
	} else {
		tmp = 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 <= (-5.5d+115)) then
        tmp = y / (a / z)
    else if (z <= 1.44d+26) then
        tmp = x
    else
        tmp = 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 <= -5.5e+115) {
		tmp = y / (a / z);
	} else if (z <= 1.44e+26) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+115:
		tmp = y / (a / z)
	elif z <= 1.44e+26:
		tmp = x
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+115)
		tmp = Float64(y / Float64(a / z));
	elseif (z <= 1.44e+26)
		tmp = x;
	else
		tmp = Float64(z / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+115)
		tmp = y / (a / z);
	elseif (z <= 1.44e+26)
		tmp = x;
	else
		tmp = z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+115], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.44e+26], x, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5e115

   1. Initial program 91.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 91.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   7. Simplified 65.1%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{z}\right)}\right) \]

      4. /-lowering-/.f64 64.8%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 64.8%

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

   if -5.5e115 < z < 1.44000000000000006e26

   1. Initial program 95.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 95.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 53.0%

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

   if 1.44000000000000006e26 < z

   1. Initial program 96.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 96.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 96.2%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 64.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   7. Simplified 64.5%

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

      1. associate-*l/ N/A

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

      2. clear-num N/A

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

      3. associate-*l/ N/A

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

      4. *-lft-identity N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{a}{y}\right)}\right) \]

      6. /-lowering-/.f64 63.0%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(a, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 63.0%

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

Alternative 10: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e+115) (/ y (/ a z)) (if (<= z 5.3e+26) x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e+115) {
		tmp = y / (a / z);
	} else if (z <= 5.3e+26) {
		tmp = x;
	} else {
		tmp = z * (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 (z <= (-6d+115)) then
        tmp = y / (a / z)
    else if (z <= 5.3d+26) then
        tmp = x
    else
        tmp = z * (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 (z <= -6e+115) {
		tmp = y / (a / z);
	} else if (z <= 5.3e+26) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e+115:
		tmp = y / (a / z)
	elif z <= 5.3e+26:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e+115)
		tmp = Float64(y / Float64(a / z));
	elseif (z <= 5.3e+26)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e+115)
		tmp = y / (a / z);
	elseif (z <= 5.3e+26)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e+115], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e+26], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000001e115

   1. Initial program 91.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 91.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 91.2%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   7. Simplified 65.1%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{a}{z}\right)}\right) \]

      4. /-lowering-/.f64 64.8%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 64.8%

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

   if -6.0000000000000001e115 < z < 5.29999999999999969e26

   1. Initial program 95.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 95.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 53.0%

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

   if 5.29999999999999969e26 < z

   1. Initial program 96.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 96.2%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 96.2%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 64.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   7. Simplified 64.5%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 63.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), z\right) \]

   9. Applied egg-rr 63.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))))
   (if (<= z -5.8e+115) t_1 (if (<= z 4.4e+26) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (z <= -5.8e+115) {
		tmp = t_1;
	} else if (z <= 4.4e+26) {
		tmp = x;
	} else {
		tmp = 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 = z * (y / a)
    if (z <= (-5.8d+115)) then
        tmp = t_1
    else if (z <= 4.4d+26) then
        tmp = x
    else
        tmp = 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 = z * (y / a);
	double tmp;
	if (z <= -5.8e+115) {
		tmp = t_1;
	} else if (z <= 4.4e+26) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	tmp = 0
	if z <= -5.8e+115:
		tmp = t_1
	elif z <= 4.4e+26:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (z <= -5.8e+115)
		tmp = t_1;
	elseif (z <= 4.4e+26)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / a);
	tmp = 0.0;
	if (z <= -5.8e+115)
		tmp = t_1;
	elseif (z <= 4.4e+26)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+115], t$95$1, If[LessEqual[z, 4.4e+26], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000009e115 or 4.40000000000000014e26 < z

   1. Initial program 94.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 94.0%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot z\right), \color{blue}{a}\right) \]

      2. *-lowering-*.f64 64.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), a\right) \]

   7. Simplified 64.8%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{a}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 63.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, a\right), z\right) \]

   9. Applied egg-rr 63.7%

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

   if -5.80000000000000009e115 < z < 4.40000000000000014e26

   1. Initial program 95.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

      11. associate-*l/ N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

      13. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

      14. --lowering--.f64 95.7%

          \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 53.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 39.3% 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 95.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. cancel-sign-sub N/A

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

   4. sub0-neg N/A

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

   5. associate-+l- N/A

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

   6. neg-sub0 N/A

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

   7. +-commutative N/A

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

   8. sub-neg N/A

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

   9. *-commutative N/A

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

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{a} \cdot \left(t - z\right)\right)}\right) \]

   11. associate-*l/ N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot \left(t - z\right)}{\color{blue}{a}}\right)\right) \]

   12. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(t - z\right)\right), \color{blue}{a}\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(t - z\right)\right), a\right)\right) \]

   14. --lowering--.f64 95.0%

       \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(t, z\right)\right), a\right)\right) \]

3. Simplified 95.0%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 41.7%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 99.2% 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 2024152 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

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