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

Percentage Accurate: 93.2% → 97.6%

Time: 8.9s

Alternatives: 8

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 10^{+227}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \end{array} \]

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 1e+227) (+ x t_1) (* (/ y a) (- z t))))))

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 <= 1e+227) {
		tmp = x + t_1;
	} else {
		tmp = (y / a) * (z - t);
	}
	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 <= 1e+227) {
		tmp = x + t_1;
	} else {
		tmp = (y / a) * (z - t);
	}
	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 <= 1e+227:
		tmp = x + t_1
	else:
		tmp = (y / a) * (z - t)
	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 <= 1e+227)
		tmp = Float64(x + t_1);
	else
		tmp = Float64(Float64(y / a) * Float64(z - t));
	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 <= 1e+227)
		tmp = x + t_1;
	else
		tmp = (y / a) * (z - t);
	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, 1e+227], N[(x + t$95$1), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 81.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 81.1%

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

   3. Simplified 81.1%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 81.1%

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

   7. Simplified 81.1%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

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

      7. sub-neg N/A

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

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

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

      9. *-commutative N/A

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

      10. 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 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.0000000000000001e227

   1. Initial program 98.9%

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

   if 1.0000000000000001e227 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 82.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. associate-*l/ N/A

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

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

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

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

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

      14. --lowering--.f64 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 82.7%

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

   7. Simplified 82.7%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. sub-neg N/A

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

      4. +-commutative N/A

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

      5. remove-double-neg N/A

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

      6. distribute-neg-in N/A

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

      7. sub-neg N/A

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

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

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

      9. *-commutative N/A

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

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

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

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

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

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

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

      13. sub-neg N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. +-commutative N/A

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

      17. sub-neg N/A

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

      18. --lowering--.f64 95.9%

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

   9. Applied egg-rr 95.9%

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

Alternative 2: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+53}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (/ y a) (- z t))))
   (if (<= t_1 -2e+30) t_2 (if (<= t_1 5e+53) (+ x (/ (* y z) a)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double t_2 = (y / a) * (z - t);
	double tmp;
	if (t_1 <= -2e+30) {
		tmp = t_2;
	} else if (t_1 <= 5e+53) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    t_2 = (y / a) * (z - t)
    if (t_1 <= (-2d+30)) then
        tmp = t_2
    else if (t_1 <= 5d+53) then
        tmp = x + ((y * z) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double t_2 = (y / a) * (z - t);
	double tmp;
	if (t_1 <= -2e+30) {
		tmp = t_2;
	} else if (t_1 <= 5e+53) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = (y / a) * (z - t)
	tmp = 0
	if t_1 <= -2e+30:
		tmp = t_2
	elif t_1 <= 5e+53:
		tmp = x + ((y * z) / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	t_2 = Float64(Float64(y / a) * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+30)
		tmp = t_2;
	elseif (t_1 <= 5e+53)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	t_2 = (y / a) * (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+30)
		tmp = t_2;
	elseif (t_1 <= 5e+53)
		tmp = x + ((y * z) / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+30], t$95$2, If[LessEqual[t$95$1, 5e+53], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2e30 or 5.0000000000000004e53 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 89.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.3%

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

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 81.4%

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

   7. Simplified 81.4%

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

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

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

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

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

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

      13. sub-neg N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. +-commutative N/A

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

      17. sub-neg N/A

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

      18. --lowering--.f64 90.1%

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

   9. Applied egg-rr 90.1%

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

   if -2e30 < (/.f64 (*.f64 y (-.f64 z t)) a) < 5.0000000000000004e53

   1. Initial program 98.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 88.3%

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

   7. Simplified 88.3%

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

Alternative 3: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z t))))
   (if (<= y -2.7e-75) t_1 (if (<= y 3.9e-43) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (z - t);
	double tmp;
	if (y <= -2.7e-75) {
		tmp = t_1;
	} else if (y <= 3.9e-43) {
		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 - t)
    if (y <= (-2.7d-75)) then
        tmp = t_1
    else if (y <= 3.9d-43) 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 - t);
	double tmp;
	if (y <= -2.7e-75) {
		tmp = t_1;
	} else if (y <= 3.9e-43) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (z - t)
	tmp = 0
	if y <= -2.7e-75:
		tmp = t_1
	elif y <= 3.9e-43:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(z - t))
	tmp = 0.0
	if (y <= -2.7e-75)
		tmp = t_1;
	elseif (y <= 3.9e-43)
		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 - t);
	tmp = 0.0;
	if (y <= -2.7e-75)
		tmp = t_1;
	elseif (y <= 3.9e-43)
		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] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-75], t$95$1, If[LessEqual[y, 3.9e-43], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999998e-75 or 3.9e-43 < y

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac N/A

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

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

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

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

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

      5. mul-1-neg N/A

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

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

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

      7. sub-neg N/A

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

      8. mul-1-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-lft-in N/A

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

      11. associate-*r* N/A

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

      12. metadata-eval N/A

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

      13. *-lft-identity N/A

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

      14. mul-1-neg N/A

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

      15. sub-neg N/A

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

      16. --lowering--.f64 74.4%

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

   7. Simplified 74.4%

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

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

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

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

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

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

      13. sub-neg N/A

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

      14. distribute-neg-in N/A

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

      15. remove-double-neg N/A

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

      16. +-commutative N/A

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

      17. sub-neg N/A

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

      18. --lowering--.f64 82.7%

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

   9. Applied egg-rr 82.7%

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

   if -2.6999999999999998e-75 < y < 3.9e-43

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 64.9%

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

Alternative 4: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ a y))))
   (if (<= y -2.3e-75) t_1 (if (<= y 1.06e-42) 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 (y <= -2.3e-75) {
		tmp = t_1;
	} else if (y <= 1.06e-42) {
		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 (y <= (-2.3d-75)) then
        tmp = t_1
    else if (y <= 1.06d-42) 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 (y <= -2.3e-75) {
		tmp = t_1;
	} else if (y <= 1.06e-42) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a / y)
	tmp = 0
	if y <= -2.3e-75:
		tmp = t_1
	elif y <= 1.06e-42:
		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 (y <= -2.3e-75)
		tmp = t_1;
	elseif (y <= 1.06e-42)
		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 (y <= -2.3e-75)
		tmp = t_1;
	elseif (y <= 1.06e-42)
		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[y, -2.3e-75], t$95$1, If[LessEqual[y, 1.06e-42], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e-75 or 1.0600000000000001e-42 < y

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.5%

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

   3. Simplified 89.5%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 46.2%

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

   7. Simplified 46.2%

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

      1. clear-num N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

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

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

      5. /-lowering-/.f64 54.2%

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

   9. Applied egg-rr 54.2%

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

   if -2.3e-75 < y < 1.0600000000000001e-42

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 64.9%

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

Alternative 5: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a z))))
   (if (<= y -3.8e-75) t_1 (if (<= y 5.2e-43) 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 (y <= -3.8e-75) {
		tmp = t_1;
	} else if (y <= 5.2e-43) {
		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 (y <= (-3.8d-75)) then
        tmp = t_1
    else if (y <= 5.2d-43) 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 (y <= -3.8e-75) {
		tmp = t_1;
	} else if (y <= 5.2e-43) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / z)
	tmp = 0
	if y <= -3.8e-75:
		tmp = t_1
	elif y <= 5.2e-43:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / z))
	tmp = 0.0
	if (y <= -3.8e-75)
		tmp = t_1;
	elseif (y <= 5.2e-43)
		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 (y <= -3.8e-75)
		tmp = t_1;
	elseif (y <= 5.2e-43)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-75], t$95$1, If[LessEqual[y, 5.2e-43], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999994e-75 or 5.2e-43 < y

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.5%

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

   3. Simplified 89.5%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 46.2%

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

   7. Simplified 46.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 51.9%

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

   9. Applied egg-rr 51.9%

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

   if -3.79999999999999994e-75 < y < 5.2e-43

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 64.9%

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

Alternative 6: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= y -3.5e-75) t_1 (if (<= y 9.8e-43) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (y <= -3.5e-75) {
		tmp = t_1;
	} else if (y <= 9.8e-43) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (y <= (-3.5d-75)) then
        tmp = t_1
    else if (y <= 9.8d-43) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (y <= -3.5e-75) {
		tmp = t_1;
	} else if (y <= 9.8e-43) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if y <= -3.5e-75:
		tmp = t_1
	elif y <= 9.8e-43:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (y <= -3.5e-75)
		tmp = t_1;
	elseif (y <= 9.8e-43)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (y <= -3.5e-75)
		tmp = t_1;
	elseif (y <= 9.8e-43)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e-75], t$95$1, If[LessEqual[y, 9.8e-43], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.49999999999999985e-75 or 9.79999999999999976e-43 < y

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 89.5%

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

   3. Simplified 89.5%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 46.2%

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

   7. Simplified 46.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 51.8%

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

   9. Applied egg-rr 51.8%

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

   if -3.49999999999999985e-75 < y < 9.79999999999999976e-43

   1. Initial program 98.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 64.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 8: 39.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 36.4%

   \[\leadsto \color{blue}{x} \]
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 2024158 
(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)))