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

Percentage Accurate: 92.9% → 97.0%

Time: 9.5s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% 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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / a) * (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 92.9%

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

3. Simplified 92.9%

   \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
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 97.2%

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

6. Applied egg-rr 97.2%

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

7. Final simplification 97.2%

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

Alternative 2: 87.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+103}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 (- INFINITY))
     (/ y (/ a (- z t)))
     (if (<= t_1 -5e+161)
       t_1
       (if (<= t_1 1e-188)
         (+ x (/ (* y z) a))
         (if (<= t_1 1e+103)
           (- x (* y (/ t a)))
           (if (<= t_1 1e+301) t_1 (* y (/ (- z t) a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y / (a / (z - t));
	} else if (t_1 <= -5e+161) {
		tmp = t_1;
	} else if (t_1 <= 1e-188) {
		tmp = x + ((y * z) / a);
	} else if (t_1 <= 1e+103) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (a / (z - t));
	} else if (t_1 <= -5e+161) {
		tmp = t_1;
	} else if (t_1 <= 1e-188) {
		tmp = x + ((y * z) / a);
	} else if (t_1 <= 1e+103) {
		tmp = x - (y * (t / a));
	} else if (t_1 <= 1e+301) {
		tmp = t_1;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y / (a / (z - t))
	elif t_1 <= -5e+161:
		tmp = t_1
	elif t_1 <= 1e-188:
		tmp = x + ((y * z) / a)
	elif t_1 <= 1e+103:
		tmp = x - (y * (t / a))
	elif t_1 <= 1e+301:
		tmp = t_1
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y / Float64(a / Float64(z - t)));
	elseif (t_1 <= -5e+161)
		tmp = t_1;
	elseif (t_1 <= 1e-188)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t_1 <= 1e+103)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y / (a / (z - t));
	elseif (t_1 <= -5e+161)
		tmp = t_1;
	elseif (t_1 <= 1e-188)
		tmp = x + ((y * z) / a);
	elseif (t_1 <= 1e+103)
		tmp = x - (y * (t / a));
	elseif (t_1 <= 1e+301)
		tmp = t_1;
	else
		tmp = y * ((z - t) / a);
	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]}, If[LessEqual[t$95$1, (-Infinity)], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+161], t$95$1, If[LessEqual[t$95$1, 1e-188], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+103], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+301], t$95$1, N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 82.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 82.4%

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

   3. Simplified 82.4%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 82.4%

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

   7. Simplified 82.4%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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. associate-/r/ N/A

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

      11. distribute-neg-frac2 N/A

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

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

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

      13. distribute-neg-frac2 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. sub-neg N/A

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

      16. distribute-neg-in N/A

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

      17. remove-double-neg N/A

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

      18. +-commutative N/A

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

      19. sub-neg N/A

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

      20. --lowering--.f64 92.7%

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

   9. Applied egg-rr 92.7%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < -4.9999999999999997e161 or 1e103 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.00000000000000005e301

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 99.6%

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

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 92.8%

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

   7. Simplified 92.8%

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

   if -4.9999999999999997e161 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.9999999999999995e-189

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 90.6%

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

   7. Simplified 90.6%

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

   if 9.9999999999999995e-189 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1e103

   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. 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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf

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

   9. Simplified 88.4%

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

       1. *-commutative N/A

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

       2. frac-2neg N/A

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

       3. frac-2neg N/A

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

       4. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \frac{1 \cdot y}{a}\right)\right) \]

       5. associate-*l/ N/A

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

       6. associate-*r* N/A

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

       7. div-inv N/A

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

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

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

       9. /-lowering-/.f64 88.4%

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

   11. Applied egg-rr 88.4%

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

   if 1.00000000000000005e301 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 77.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 77.1%

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

   3. Simplified 77.1%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 77.1%

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

   7. Simplified 77.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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. sub-neg N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. sub-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. clear-num N/A

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

      11. distribute-neg-frac2 N/A

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

      12. remove-double-div N/A

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

      13. *-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 97.5%

      \[\leadsto \color{blue}{\frac{z - t}{a} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+161}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+103}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+301}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{z - t}{\frac{a}{y}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+161}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+103}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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+161)
     t_2
     (if (<= t_1 1e-188)
       (+ x (/ (* y z) a))
       (if (<= t_1 1e+103) (- x (* y (/ t 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+161) {
		tmp = t_2;
	} else if (t_1 <= 1e-188) {
		tmp = x + ((y * z) / a);
	} else if (t_1 <= 1e+103) {
		tmp = x - (y * (t / 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+161)) then
        tmp = t_2
    else if (t_1 <= 1d-188) then
        tmp = x + ((y * z) / a)
    else if (t_1 <= 1d+103) then
        tmp = x - (y * (t / 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+161) {
		tmp = t_2;
	} else if (t_1 <= 1e-188) {
		tmp = x + ((y * z) / a);
	} else if (t_1 <= 1e+103) {
		tmp = x - (y * (t / 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+161:
		tmp = t_2
	elif t_1 <= 1e-188:
		tmp = x + ((y * z) / a)
	elif t_1 <= 1e+103:
		tmp = x - (y * (t / 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+161)
		tmp = t_2;
	elseif (t_1 <= 1e-188)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t_1 <= 1e+103)
		tmp = Float64(x - Float64(y * Float64(t / 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+161)
		tmp = t_2;
	elseif (t_1 <= 1e-188)
		tmp = x + ((y * z) / a);
	elseif (t_1 <= 1e+103)
		tmp = x - (y * (t / 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+161], t$95$2, If[LessEqual[t$95$1, 1e-188], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+103], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1e161 or 1e103 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 86.0%

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

   3. Simplified 86.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 84.0%

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

   7. Simplified 84.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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. clear-num N/A

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

      4. un-div-inv N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. remove-double-neg N/A

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

      8. distribute-neg-in N/A

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

      9. sub-neg N/A

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

      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 92.1%

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

   9. Applied egg-rr 92.1%

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

   if -1e161 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.9999999999999995e-189

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 90.5%

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

   7. Simplified 90.5%

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

   if 9.9999999999999995e-189 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1e103

   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. 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 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf

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

   9. Simplified 88.4%

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

       1. *-commutative N/A

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

       2. frac-2neg N/A

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

       3. frac-2neg N/A

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

       4. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \frac{1 \cdot y}{a}\right)\right) \]

       5. associate-*l/ N/A

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

       6. associate-*r* N/A

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

       7. div-inv N/A

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

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

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

       9. /-lowering-/.f64 88.4%

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

   11. Applied egg-rr 88.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+161}:\\ \;\;\;\;\frac{z - t}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{-188}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+103}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+304}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -5e+304) (/ y (/ a (- z t))) (+ 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 <= -5e+304) {
		tmp = y / (a / (z - t));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if (t_1 <= (-5d+304)) then
        tmp = y / (a / (z - t))
    else
        tmp = x + (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+304) {
		tmp = y / (a / (z - t));
	} 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 <= -5e+304:
		tmp = y / (a / (z - t))
	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 <= -5e+304)
		tmp = Float64(y / Float64(a / Float64(z - t)));
	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 <= -5e+304)
		tmp = y / (a / (z - t));
	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, -5e+304], N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -4.9999999999999997e304

   1. Initial program 64.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 64.0%

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

   3. Simplified 64.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 64.0%

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

   7. Simplified 64.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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. associate-/r/ N/A

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

      11. distribute-neg-frac2 N/A

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

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

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

      13. distribute-neg-frac2 N/A

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

      14. /-lowering-/.f64 N/A

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

      15. sub-neg N/A

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

      16. distribute-neg-in N/A

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

      17. remove-double-neg N/A

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

      18. +-commutative N/A

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

      19. sub-neg N/A

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

      20. --lowering--.f64 87.8%

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

   9. Applied egg-rr 87.8%

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

   if -4.9999999999999997e304 < (*.f64 y (-.f64 z t))

   1. Initial program 98.1%

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

Alternative 5: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 16600000000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.6e+34)
   (- x (/ y (/ a t)))
   (if (<= t 16600000000.0) (+ x (/ (* y z) a)) (- x (* (/ y a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.6e+34) {
		tmp = x - (y / (a / t));
	} else if (t <= 16600000000.0) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x - ((y / a) * t);
	}
	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 <= (-1.6d+34)) then
        tmp = x - (y / (a / t))
    else if (t <= 16600000000.0d0) then
        tmp = x + ((y * z) / a)
    else
        tmp = x - ((y / a) * t)
    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 <= -1.6e+34) {
		tmp = x - (y / (a / t));
	} else if (t <= 16600000000.0) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x - ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.6e+34:
		tmp = x - (y / (a / t))
	elif t <= 16600000000.0:
		tmp = x + ((y * z) / a)
	else:
		tmp = x - ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.6e+34)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	elseif (t <= 16600000000.0)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x - Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.6e+34)
		tmp = x - (y / (a / t));
	elseif (t <= 16600000000.0)
		tmp = x + ((y * z) / a);
	else
		tmp = x - ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.6e+34], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 16600000000.0], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5999999999999999e34

   1. Initial program 90.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 90.3%

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

   3. Simplified 90.3%

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

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

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. --lowering--.f64 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{t}\right)\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 85.6%

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

   if -1.5999999999999999e34 < t < 1.66e10

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 86.9%

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

   7. Simplified 86.9%

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

   if 1.66e10 < t

   1. Initial program 92.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 92.0%

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

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in t around inf

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

   9. Simplified 84.4%

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

Alternative 6: 83.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 102000000000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+33)
   (- x (* y (/ t a)))
   (if (<= t 102000000000.0) (+ x (/ (* y z) a)) (- x (* (/ y a) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+33) {
		tmp = x - (y * (t / a));
	} else if (t <= 102000000000.0) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x - ((y / a) * t);
	}
	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 <= (-1.3d+33)) then
        tmp = x - (y * (t / a))
    else if (t <= 102000000000.0d0) then
        tmp = x + ((y * z) / a)
    else
        tmp = x - ((y / a) * t)
    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 <= -1.3e+33) {
		tmp = x - (y * (t / a));
	} else if (t <= 102000000000.0) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x - ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e+33:
		tmp = x - (y * (t / a))
	elif t <= 102000000000.0:
		tmp = x + ((y * z) / a)
	else:
		tmp = x - ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+33)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (t <= 102000000000.0)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x - Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e+33)
		tmp = x - (y * (t / a));
	elseif (t <= 102000000000.0)
		tmp = x + ((y * z) / a);
	else
		tmp = x - ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+33], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 102000000000.0], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2999999999999999e33

   1. Initial program 90.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 90.3%

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

   3. Simplified 90.3%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in t around inf

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

   9. Simplified 84.8%

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

       1. *-commutative N/A

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

       2. frac-2neg N/A

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

       3. frac-2neg N/A

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

       4. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \frac{1 \cdot y}{a}\right)\right) \]

       5. associate-*l/ N/A

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

       6. associate-*r* N/A

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

       7. div-inv N/A

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

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

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

       9. /-lowering-/.f64 85.6%

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

   11. Applied egg-rr 85.6%

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

   if -1.2999999999999999e33 < t < 1.02e11

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 86.9%

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

   7. Simplified 86.9%

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

   if 1.02e11 < t

   1. Initial program 92.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 92.0%

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

   3. Simplified 92.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in t around inf

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

   9. Simplified 84.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 102000000000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \frac{t}{a}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 210000000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y (/ t a)))))
   (if (<= t -7.5e+34) t_1 (if (<= t 210000000.0) (+ x (/ (* y z) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * (t / a));
	double tmp;
	if (t <= -7.5e+34) {
		tmp = t_1;
	} else if (t <= 210000000.0) {
		tmp = x + ((y * z) / a);
	} 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 = x - (y * (t / a))
    if (t <= (-7.5d+34)) then
        tmp = t_1
    else if (t <= 210000000.0d0) then
        tmp = x + ((y * z) / a)
    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 = x - (y * (t / a));
	double tmp;
	if (t <= -7.5e+34) {
		tmp = t_1;
	} else if (t <= 210000000.0) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y * (t / a))
	tmp = 0
	if t <= -7.5e+34:
		tmp = t_1
	elif t <= 210000000.0:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * Float64(t / a)))
	tmp = 0.0
	if (t <= -7.5e+34)
		tmp = t_1;
	elseif (t <= 210000000.0)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y * (t / a));
	tmp = 0.0;
	if (t <= -7.5e+34)
		tmp = t_1;
	elseif (t <= 210000000.0)
		tmp = x + ((y * z) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.5e+34], t$95$1, If[LessEqual[t, 210000000.0], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.49999999999999976e34 or 2.1e8 < t

   1. Initial program 91.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 91.3%

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

   3. Simplified 91.3%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in t around inf

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

   9. Simplified 84.5%

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

       1. *-commutative N/A

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

       2. frac-2neg N/A

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

       3. frac-2neg N/A

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

       4. *-lft-identity N/A

          \[\leadsto \mathsf{\_.f64}\left(x, \left(t \cdot \frac{1 \cdot y}{a}\right)\right) \]

       5. associate-*l/ N/A

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

       6. associate-*r* N/A

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

       7. div-inv N/A

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

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

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

       9. /-lowering-/.f64 84.6%

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

   11. Applied egg-rr 84.6%

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

   if -7.49999999999999976e34 < t < 2.1e8

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 86.9%

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

   7. Simplified 86.9%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+34}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 210000000:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))))
   (if (<= y -5.6e+20) t_1 (if (<= y 9e-14) (+ x (/ (* y z) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -5.6e+20) {
		tmp = t_1;
	} else if (y <= 9e-14) {
		tmp = x + ((y * z) / a);
	} 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 - t) / a)
    if (y <= (-5.6d+20)) then
        tmp = t_1
    else if (y <= 9d-14) then
        tmp = x + ((y * z) / a)
    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 - t) / a);
	double tmp;
	if (y <= -5.6e+20) {
		tmp = t_1;
	} else if (y <= 9e-14) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	tmp = 0
	if y <= -5.6e+20:
		tmp = t_1
	elif y <= 9e-14:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	tmp = 0.0
	if (y <= -5.6e+20)
		tmp = t_1;
	elseif (y <= 9e-14)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	tmp = 0.0;
	if (y <= -5.6e+20)
		tmp = t_1;
	elseif (y <= 9e-14)
		tmp = x + ((y * z) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+20], t$95$1, If[LessEqual[y, 9e-14], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6e20 or 8.9999999999999995e-14 < y

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 86.9%

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

   3. Simplified 86.9%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 70.1%

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

   7. Simplified 70.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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. sub-neg N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. sub-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. clear-num N/A

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

      11. distribute-neg-frac2 N/A

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

      12. remove-double-div N/A

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

      13. *-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 79.4%

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

   if -5.6e20 < y < 8.9999999999999995e-14

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+20}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.4e+58) x (if (<= x 3.6e+93) (* y (/ (- z t) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.4e+58) {
		tmp = x;
	} else if (x <= 3.6e+93) {
		tmp = y * ((z - t) / 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 (x <= (-7.4d+58)) then
        tmp = x
    else if (x <= 3.6d+93) then
        tmp = y * ((z - t) / 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 (x <= -7.4e+58) {
		tmp = x;
	} else if (x <= 3.6e+93) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.4e+58:
		tmp = x
	elif x <= 3.6e+93:
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.4e+58)
		tmp = x;
	elseif (x <= 3.6e+93)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.4e+58)
		tmp = x;
	elseif (x <= 3.6e+93)
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.4e+58], x, If[LessEqual[x, 3.6e+93], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -7.4000000000000004e58 or 3.5999999999999999e93 < x

   1. Initial program 93.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 63.8%

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

   if -7.4000000000000004e58 < x < 3.5999999999999999e93

   1. Initial program 92.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 92.8%

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

   3. Simplified 92.8%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 73.1%

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

   7. Simplified 73.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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. sub-neg N/A

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

      5. +-commutative N/A

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

      6. remove-double-neg N/A

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

      7. distribute-neg-in N/A

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

      8. sub-neg N/A

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

      9. distribute-neg-frac2 N/A

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

      10. clear-num N/A

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

      11. distribute-neg-frac2 N/A

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

      12. remove-double-div N/A

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

      13. *-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 74.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ a y))))
   (if (<= z -2.3e+30) t_1 (if (<= z 5.9e+63) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a / y);
	double tmp;
	if (z <= -2.3e+30) {
		tmp = t_1;
	} else if (z <= 5.9e+63) {
		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 / (a / y)
    if (z <= (-2.3d+30)) then
        tmp = t_1
    else if (z <= 5.9d+63) 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 / (a / y);
	double tmp;
	if (z <= -2.3e+30) {
		tmp = t_1;
	} else if (z <= 5.9e+63) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a / y)
	tmp = 0
	if z <= -2.3e+30:
		tmp = t_1
	elif z <= 5.9e+63:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a / y))
	tmp = 0.0
	if (z <= -2.3e+30)
		tmp = t_1;
	elseif (z <= 5.9e+63)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a / y);
	tmp = 0.0;
	if (z <= -2.3e+30)
		tmp = t_1;
	elseif (z <= 5.9e+63)
		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[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+30], t$95$1, If[LessEqual[z, 5.9e+63], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e30 or 5.90000000000000029e63 < z

   1. Initial program 89.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.0%

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

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 58.7%

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

   7. Simplified 58.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

      6. /-lowering-/.f64 63.3%

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

   9. Applied egg-rr 63.3%

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

   if -2.3e30 < z < 5.90000000000000029e63

   1. Initial program 96.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 49.3%

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

Alternative 11: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot z\\ \mathbf{if}\;z \leq -9 \cdot 10^{+36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) z)))
   (if (<= z -9e+36) t_1 (if (<= z 1.72e+62) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (z <= -9e+36) {
		tmp = t_1;
	} else if (z <= 1.72e+62) {
		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 / a) * z
    if (z <= (-9d+36)) then
        tmp = t_1
    else if (z <= 1.72d+62) 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 / a) * z;
	double tmp;
	if (z <= -9e+36) {
		tmp = t_1;
	} else if (z <= 1.72e+62) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * z
	tmp = 0
	if z <= -9e+36:
		tmp = t_1
	elif z <= 1.72e+62:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (z <= -9e+36)
		tmp = t_1;
	elseif (z <= 1.72e+62)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * z;
	tmp = 0.0;
	if (z <= -9e+36)
		tmp = t_1;
	elseif (z <= 1.72e+62)
		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 / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -9e+36], t$95$1, If[LessEqual[z, 1.72e+62], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999994e36 or 1.7200000000000001e62 < z

   1. Initial program 89.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.0%

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

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 58.7%

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

   7. Simplified 58.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

      5. /-lowering-/.f64 63.3%

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

   9. Applied egg-rr 63.3%

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

   if -8.99999999999999994e36 < z < 1.7200000000000001e62

   1. Initial program 96.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 49.3%

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

Alternative 12: 39.5% 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 92.9%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 92.9%

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

3. Simplified 92.9%

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

5. Taylor expanded in x around inf

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

7. Simplified 36.9%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 99.0% 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 2024138 
(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)))