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

Percentage Accurate: 93.1% → 97.6%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+257}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+274}:\\ \;\;\;\;x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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+257) t_2 (if (<= t_1 4e+274) (+ x t_1) 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+257) {
		tmp = t_2;
	} else if (t_1 <= 4e+274) {
		tmp = x + t_1;
	} 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+257)) then
        tmp = t_2
    else if (t_1 <= 4d+274) then
        tmp = x + t_1
    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+257) {
		tmp = t_2;
	} else if (t_1 <= 4e+274) {
		tmp = x + t_1;
	} 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+257:
		tmp = t_2
	elif t_1 <= 4e+274:
		tmp = x + t_1
	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+257)
		tmp = t_2;
	elseif (t_1 <= 4e+274)
		tmp = Float64(x + t_1);
	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+257)
		tmp = t_2;
	elseif (t_1 <= 4e+274)
		tmp = x + t_1;
	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+257], t$95$2, If[LessEqual[t$95$1, 4e+274], N[(x + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.00000000000000006e257 or 3.99999999999999969e274 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 74.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. cancel-sign-sub N/A

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

      4. sub0-neg N/A

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

      5. associate-+l- N/A

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

      6. neg-sub0 N/A

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

      7. +-commutative N/A

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

      8. sub-neg N/A

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

      9. *-commutative N/A

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

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

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

      11. associate-*l/ N/A

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

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

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

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

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

      14. --lowering--.f64 74.2%

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

   3. Simplified 74.2%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. --lowering--.f64 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. associate-/r/ N/A

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

      2. --lowering--.f64 N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. /-lowering-/.f64 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. neg-mul-1 N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. distribute-rgt-in N/A

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. distribute-neg-in N/A

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

       9. sub-neg N/A

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

       10. div-sub N/A

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

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

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

       12. neg-mul-1 N/A

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

       13. associate-*r/ N/A

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

       14. *-commutative N/A

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

       15. associate-*r* N/A

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

       16. associate-*r/ N/A

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

       17. distribute-rgt-out-- N/A

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

       18. sub-neg N/A

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

       19. mul-1-neg N/A

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

       20. distribute-lft-in N/A

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

       21. mul-1-neg N/A

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

   11. Simplified 93.4%

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

   if -2.00000000000000006e257 < (/.f64 (*.f64 y (-.f64 z t)) a) < 3.99999999999999969e274

   1. Initial program 99.2%

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

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+32}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+58}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1e+32) t_2 (if (<= t_1 1e+58) (+ x (/ (* z y) 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 <= -1e+32) {
		tmp = t_2;
	} else if (t_1 <= 1e+58) {
		tmp = x + ((z * y) / 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 <= (-1d+32)) then
        tmp = t_2
    else if (t_1 <= 1d+58) then
        tmp = x + ((z * y) / 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 <= -1e+32) {
		tmp = t_2;
	} else if (t_1 <= 1e+58) {
		tmp = x + ((z * y) / 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 <= -1e+32:
		tmp = t_2
	elif t_1 <= 1e+58:
		tmp = x + ((z * y) / 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 <= -1e+32)
		tmp = t_2;
	elseif (t_1 <= 1e+58)
		tmp = Float64(x + Float64(Float64(z * y) / 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 <= -1e+32)
		tmp = t_2;
	elseif (t_1 <= 1e+58)
		tmp = x + ((z * y) / 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, -1e+32], t$95$2, If[LessEqual[t$95$1, 1e+58], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1.00000000000000005e32 or 9.99999999999999944e57 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 84.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 84.9%

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

   3. Simplified 84.9%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 97.3%

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

   6. Applied egg-rr 97.3%

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

      1. associate-/r/ N/A

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

      2. --lowering--.f64 N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. /-lowering-/.f64 97.5%

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

   8. Applied egg-rr 97.5%

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

   9. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. neg-mul-1 N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. distribute-rgt-in N/A

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. distribute-neg-in N/A

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

       9. sub-neg N/A

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

       10. div-sub N/A

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

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

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

       12. neg-mul-1 N/A

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

       13. associate-*r/ N/A

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

       14. *-commutative N/A

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

       15. associate-*r* N/A

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

       16. associate-*r/ N/A

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

       17. distribute-rgt-out-- N/A

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

       18. sub-neg N/A

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

       19. mul-1-neg N/A

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

       20. distribute-lft-in N/A

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

       21. mul-1-neg N/A

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

   11. Simplified 86.5%

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

   if -1.00000000000000005e32 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.99999999999999944e57

   1. Initial program 99.0%

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

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

   3. Simplified 99.0%

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

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+32}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+58}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+60}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z t))))
   (if (<= t -7.2e+225) t_1 (if (<= t 4.4e+60) (+ x (* z (/ y a))) 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 (t <= -7.2e+225) {
		tmp = t_1;
	} else if (t <= 4.4e+60) {
		tmp = x + (z * (y / 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 / a) * (z - t)
    if (t <= (-7.2d+225)) then
        tmp = t_1
    else if (t <= 4.4d+60) then
        tmp = x + (z * (y / 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 / a) * (z - t);
	double tmp;
	if (t <= -7.2e+225) {
		tmp = t_1;
	} else if (t <= 4.4e+60) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (z - t)
	tmp = 0
	if t <= -7.2e+225:
		tmp = t_1
	elif t <= 4.4e+60:
		tmp = x + (z * (y / a))
	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 (t <= -7.2e+225)
		tmp = t_1;
	elseif (t <= 4.4e+60)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	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 (t <= -7.2e+225)
		tmp = t_1;
	elseif (t <= 4.4e+60)
		tmp = x + (z * (y / a));
	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[t, -7.2e+225], t$95$1, If[LessEqual[t, 4.4e+60], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999996e225 or 4.39999999999999992e60 < t

   1. Initial program 85.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 85.9%

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

   3. Simplified 85.9%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 97.9%

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

   6. Applied egg-rr 97.9%

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

      1. associate-/r/ N/A

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

      2. --lowering--.f64 N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. /-lowering-/.f64 97.7%

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

   8. Applied egg-rr 97.7%

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

   9. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. neg-mul-1 N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. distribute-rgt-in N/A

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. distribute-neg-in N/A

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

       9. sub-neg N/A

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

       10. div-sub N/A

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

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

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

       12. neg-mul-1 N/A

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

       13. associate-*r/ N/A

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

       14. *-commutative N/A

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

       15. associate-*r* N/A

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

       16. associate-*r/ N/A

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

       17. distribute-rgt-out-- N/A

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

       18. sub-neg N/A

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

       19. mul-1-neg N/A

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

       20. distribute-lft-in N/A

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

       21. mul-1-neg N/A

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

   11. Simplified 82.3%

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

   if -7.1999999999999996e225 < t < 4.39999999999999992e60

   1. Initial program 92.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 92.4%

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

   3. Simplified 92.4%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 96.7%

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

   6. Applied egg-rr 96.7%

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

      1. associate-/r/ N/A

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

      2. --lowering--.f64 N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. /-lowering-/.f64 97.0%

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

   8. Applied egg-rr 97.0%

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

   9. Taylor expanded in t around 0

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

       1. cancel-sign-sub-inv N/A

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

       2. metadata-eval N/A

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

       3. *-lft-identity 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. *-commutative N/A

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

       6. associate-*r/ N/A

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

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

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

       8. /-lowering-/.f64 82.8%

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

   11. Simplified 82.8%

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

Alternative 4: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.36e+90) x (if (<= a 1.65e+107) (* (/ y a) (- z t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.36e+90) {
		tmp = x;
	} else if (a <= 1.65e+107) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.36d+90)) then
        tmp = x
    else if (a <= 1.65d+107) then
        tmp = (y / a) * (z - t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.36e+90) {
		tmp = x;
	} else if (a <= 1.65e+107) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.36e+90:
		tmp = x
	elif a <= 1.65e+107:
		tmp = (y / a) * (z - t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.36e+90)
		tmp = x;
	elseif (a <= 1.65e+107)
		tmp = Float64(Float64(y / a) * Float64(z - t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.36e+90)
		tmp = x;
	elseif (a <= 1.65e+107)
		tmp = (y / a) * (z - t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.36e+90], x, If[LessEqual[a, 1.65e+107], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3600000000000001e90 or 1.65000000000000016e107 < a

   1. Initial program 77.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 68.2%

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

   if -1.3600000000000001e90 < a < 1.65000000000000016e107

   1. Initial program 97.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 97.5%

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

   6. Applied egg-rr 97.5%

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

      1. associate-/r/ N/A

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

      2. --lowering--.f64 N/A

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

      3. associate-/r/ N/A

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

      4. *-commutative N/A

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

      5. clear-num N/A

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

      6. un-div-inv N/A

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

      7. /-lowering-/.f64 N/A

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

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

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

      9. /-lowering-/.f64 97.8%

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

   8. Applied egg-rr 97.8%

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

   9. Taylor expanded in x around 0

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

       1. associate-*r/ N/A

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

       2. neg-mul-1 N/A

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

       3. sub-neg N/A

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

       4. mul-1-neg N/A

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

       5. distribute-rgt-in N/A

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

       6. associate-*r* N/A

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

       7. *-commutative N/A

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

       8. distribute-neg-in N/A

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

       9. sub-neg N/A

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

       10. div-sub N/A

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

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

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

       12. neg-mul-1 N/A

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

       13. associate-*r/ N/A

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

       14. *-commutative N/A

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

       15. associate-*r* N/A

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

       16. associate-*r/ N/A

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

       17. distribute-rgt-out-- N/A

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

       18. sub-neg N/A

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

       19. mul-1-neg N/A

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

       20. distribute-lft-in N/A

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

       21. mul-1-neg N/A

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

   11. Simplified 75.5%

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

Alternative 5: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.3e+35) x (if (<= a 4.4e-62) (/ (* z y) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+35) {
		tmp = x;
	} else if (a <= 4.4e-62) {
		tmp = (z * y) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.3d+35)) then
        tmp = x
    else if (a <= 4.4d-62) then
        tmp = (z * y) / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.3e+35) {
		tmp = x;
	} else if (a <= 4.4e-62) {
		tmp = (z * y) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.3e+35:
		tmp = x
	elif a <= 4.4e-62:
		tmp = (z * y) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.3e+35)
		tmp = x;
	elseif (a <= 4.4e-62)
		tmp = Float64(Float64(z * y) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.3e+35)
		tmp = x;
	elseif (a <= 4.4e-62)
		tmp = (z * y) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.3e+35], x, If[LessEqual[a, 4.4e-62], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2999999999999998e35 or 4.40000000000000035e-62 < a

   1. Initial program 83.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 56.0%

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

   if -2.2999999999999998e35 < a < 4.40000000000000035e-62

   1. Initial program 99.0%

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

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 54.1%

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

   7. Simplified 54.1%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-62}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+32) x (if (<= a 5.5e-62) (/ z (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+32) {
		tmp = x;
	} else if (a <= 5.5e-62) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.2d+32)) then
        tmp = x
    else if (a <= 5.5d-62) then
        tmp = z / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+32) {
		tmp = x;
	} else if (a <= 5.5e-62) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+32:
		tmp = x
	elif a <= 5.5e-62:
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.2e+32)
		tmp = x;
	elseif (a <= 5.5e-62)
		tmp = Float64(z / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.2e+32)
		tmp = x;
	elseif (a <= 5.5e-62)
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+32], x, If[LessEqual[a, 5.5e-62], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.19999999999999996e32 or 5.50000000000000022e-62 < a

   1. Initial program 83.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 56.0%

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

   if -1.19999999999999996e32 < a < 5.50000000000000022e-62

   1. Initial program 99.0%

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

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 54.1%

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

   7. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   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 53.1%

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

   9. Applied egg-rr 53.1%

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

Alternative 7: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e+32) x (if (<= a 1.05e-61) (* z (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+32) {
		tmp = x;
	} else if (a <= 1.05e-61) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.5d+32)) then
        tmp = x
    else if (a <= 1.05d-61) then
        tmp = z * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e+32) {
		tmp = x;
	} else if (a <= 1.05e-61) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e+32:
		tmp = x
	elif a <= 1.05e-61:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e+32)
		tmp = x;
	elseif (a <= 1.05e-61)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.5e+32)
		tmp = x;
	elseif (a <= 1.05e-61)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e+32], x, If[LessEqual[a, 1.05e-61], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4999999999999999e32 or 1.05e-61 < a

   1. Initial program 83.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 56.0%

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

   if -2.4999999999999999e32 < a < 1.05e-61

   1. Initial program 99.0%

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

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

   3. Simplified 99.0%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
   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 54.1%

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

   7. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a}} \]
   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. *-lowering-*.f64 N/A

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

      4. /-lowering-/.f64 52.8%

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

   9. Applied egg-rr 52.8%

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

Alternative 8: 97.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{z - t}{\frac{a}{y}} \end{array} \]

FPCore

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

C

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

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 + ((z - t) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.7%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 90.7%

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

3. Simplified 90.7%

   \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
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 97.0%

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

6. Applied egg-rr 97.0%

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

   1. associate-/r/ N/A

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

   2. --lowering--.f64 N/A

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

   3. associate-/r/ N/A

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

   4. *-commutative N/A

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

   5. clear-num N/A

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

   6. un-div-inv N/A

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

   7. /-lowering-/.f64 N/A

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

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

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

   9. /-lowering-/.f64 97.1%

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

8. Applied egg-rr 97.1%

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

9. Final simplification 97.1%

   \[\leadsto x + \frac{z - t}{\frac{a}{y}} \]
10. Add Preprocessing

Alternative 9: 97.3% 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 90.7%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 90.7%

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

3. Simplified 90.7%

   \[\leadsto \color{blue}{x - \frac{y \cdot \left(t - z\right)}{a}} \]
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 97.0%

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

6. Applied egg-rr 97.0%

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

7. Final simplification 97.0%

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

Alternative 10: 39.7% 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 90.7%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 90.7%

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

3. Simplified 90.7%

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

5. Taylor expanded in x around inf

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

7. Simplified 38.7%

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

Developer Target 1: 99.3% 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 2024149 
(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)))