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

Percentage Accurate: 93.6% → 99.0%

Time: 8.9s

Alternatives: 9

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: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+258}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -5e+258)
     (+ x (* (/ y a) (- t z)))
     (if (<= t_1 5e+37) (- x (/ t_1 a)) (+ x (/ (- t z) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+258) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 5e+37) {
		tmp = x - (t_1 / a);
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if (t_1 <= (-5d+258)) then
        tmp = x + ((y / a) * (t - z))
    else if (t_1 <= 5d+37) then
        tmp = x - (t_1 / a)
    else
        tmp = x + ((t - z) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+258) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 5e+37) {
		tmp = x - (t_1 / a);
	} else {
		tmp = x + ((t - z) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -5e+258:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 5e+37:
		tmp = x - (t_1 / a)
	else:
		tmp = x + ((t - z) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+258)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 5e+37)
		tmp = Float64(x - Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+258)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 5e+37)
		tmp = x - (t_1 / a);
	else
		tmp = x + ((t - z) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+258], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+37], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -5e258

   1. Initial program 62.0%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 99.9%

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

   3. Simplified 99.9%

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

   if -5e258 < (*.f64 y (-.f64 z t)) < 4.99999999999999989e37

   1. Initial program 99.9%

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

   if 4.99999999999999989e37 < (*.f64 y (-.f64 z t))

   1. Initial program 86.0%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. /-lowering-/.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -5 \cdot 10^{+258}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (+ x (* (/ y a) (- t z)))))
   (if (<= t_1 -5e+258) t_2 (if (<= t_1 5e+37) (- x (/ t_1 a)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = x + ((y / a) * (t - z));
	double tmp;
	if (t_1 <= -5e+258) {
		tmp = t_2;
	} else if (t_1 <= 5e+37) {
		tmp = x - (t_1 / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z - t)
    t_2 = x + ((y / a) * (t - z))
    if (t_1 <= (-5d+258)) then
        tmp = t_2
    else if (t_1 <= 5d+37) then
        tmp = x - (t_1 / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = x + ((y / a) * (t - z));
	double tmp;
	if (t_1 <= -5e+258) {
		tmp = t_2;
	} else if (t_1 <= 5e+37) {
		tmp = x - (t_1 / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	t_2 = x + ((y / a) * (t - z))
	tmp = 0
	if t_1 <= -5e+258:
		tmp = t_2
	elif t_1 <= 5e+37:
		tmp = x - (t_1 / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(x + Float64(Float64(y / a) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -5e+258)
		tmp = t_2;
	elseif (t_1 <= 5e+37)
		tmp = Float64(x - Float64(t_1 / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = x + ((y / a) * (t - z));
	tmp = 0.0;
	if (t_1 <= -5e+258)
		tmp = t_2;
	elseif (t_1 <= 5e+37)
		tmp = x - (t_1 / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+258], t$95$2, If[LessEqual[t$95$1, 5e+37], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -5e258 or 4.99999999999999989e37 < (*.f64 y (-.f64 z t))

   1. Initial program 76.6%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 99.8%

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

   3. Simplified 99.8%

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

   if -5e258 < (*.f64 y (-.f64 z t)) < 4.99999999999999989e37

   1. Initial program 99.9%

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

Alternative 3: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.94:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -3.2e-25) t_1 (if (<= t 0.94) (- x (* y (/ z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -3.2e-25) {
		tmp = t_1;
	} else if (t <= 0.94) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (t * (y / a))
    if (t <= (-3.2d-25)) then
        tmp = t_1
    else if (t <= 0.94d0) then
        tmp = x - (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -3.2e-25) {
		tmp = t_1;
	} else if (t <= 0.94) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -3.2e-25:
		tmp = t_1
	elif t <= 0.94:
		tmp = x - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -3.2e-25)
		tmp = t_1;
	elseif (t <= 0.94)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -3.2e-25)
		tmp = t_1;
	elseif (t <= 0.94)
		tmp = x - (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e-25], t$95$1, If[LessEqual[t, 0.94], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000001e-25 or 0.93999999999999995 < t

   1. Initial program 87.8%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 89.9%

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

   if -3.2000000000000001e-25 < t < 0.93999999999999995

   1. Initial program 95.6%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 95.0%

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

   3. Simplified 95.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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. mul-1-neg N/A

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

      2. sub-neg N/A

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

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

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

      4. associate-/l* N/A

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

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

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

      6. /-lowering-/.f64 87.6%

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

   7. Simplified 87.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-25}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 0.94:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.01:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= y -3.8e-8) t_1 (if (<= y 0.01) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -3.8e-8) {
		tmp = t_1;
	} else if (y <= 0.01) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * (t - z)
    if (y <= (-3.8d-8)) then
        tmp = t_1
    else if (y <= 0.01d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -3.8e-8) {
		tmp = t_1;
	} else if (y <= 0.01) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if y <= -3.8e-8:
		tmp = t_1
	elif y <= 0.01:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (y <= -3.8e-8)
		tmp = t_1;
	elseif (y <= 0.01)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (y <= -3.8e-8)
		tmp = t_1;
	elseif (y <= 0.01)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-8], t$95$1, If[LessEqual[y, 0.01], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000028e-8 or 0.0100000000000000002 < y

   1. Initial program 82.6%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 76.2%

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

   7. Simplified 76.2%

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

   if -3.80000000000000028e-8 < y < 0.0100000000000000002

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 63.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 0.01:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.1e+105) (/ t (/ a y)) (if (<= t 1.5e+140) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+105) {
		tmp = t / (a / y);
	} else if (t <= 1.5e+140) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.1d+105)) then
        tmp = t / (a / y)
    else if (t <= 1.5d+140) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.1e+105) {
		tmp = t / (a / y);
	} else if (t <= 1.5e+140) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.1e+105:
		tmp = t / (a / y)
	elif t <= 1.5e+140:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.1e+105)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= 1.5e+140)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.1e+105)
		tmp = t / (a / y);
	elseif (t <= 1.5e+140)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.1e+105], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+140], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.10000000000000003e105

   1. Initial program 78.5%

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. clear-num N/A

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

      4. un-div-inv N/A

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

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

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

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

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

      7. /-lowering-/.f64 94.9%

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

   4. Applied egg-rr 94.9%

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

   5. Taylor expanded in t around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 58.2%

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

   7. Simplified 58.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/r/ N/A

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

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

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

      5. /-lowering-/.f64 71.6%

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

   9. Applied egg-rr 71.6%

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

   if -1.10000000000000003e105 < t < 1.49999999999999998e140

   1. Initial program 95.1%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 54.2%

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

   if 1.49999999999999998e140 < t

   1. Initial program 89.5%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 76.2%

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

Alternative 6: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+140}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -3.8e+100) t_1 (if (<= t 2.7e+140) x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -3.8e+100) {
		tmp = t_1;
	} else if (t <= 2.7e+140) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-3.8d+100)) then
        tmp = t_1
    else if (t <= 2.7d+140) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -3.8e+100) {
		tmp = t_1;
	} else if (t <= 2.7e+140) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -3.8e+100:
		tmp = t_1
	elif t <= 2.7e+140:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -3.8e+100)
		tmp = t_1;
	elseif (t <= 2.7e+140)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -3.8e+100)
		tmp = t_1;
	elseif (t <= 2.7e+140)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.8e+100], t$95$1, If[LessEqual[t, 2.7e+140], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.79999999999999963e100 or 2.70000000000000018e140 < t

   1. Initial program 83.0%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 79.8%

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

   7. Simplified 79.8%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 73.2%

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

   if -3.79999999999999963e100 < t < 2.70000000000000018e140

   1. Initial program 95.6%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 54.2%

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

Alternative 7: 75.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z 8.8e+43) (+ x (* t (/ y a))) (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 8.8e+43) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 8.8d+43) then
        tmp = x + (t * (y / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 8.8e+43) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 8.8e+43:
		tmp = x + (t * (y / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 8.8e+43)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 8.8e+43)
		tmp = x + (t * (y / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 8.8e+43], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.80000000000000002e43

   1. Initial program 92.9%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf

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

   7. Simplified 84.3%

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

   if 8.80000000000000002e43 < z

   1. Initial program 87.7%

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

      1. sub-neg N/A

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

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

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

      3. distribute-neg-frac N/A

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

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

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

      5. associate-*l/ N/A

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

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

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

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

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. --lowering--.f64 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

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

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

      5. /-lowering-/.f64 74.4%

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

   7. Simplified 74.4%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{+43}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. sub-neg N/A

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

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

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

   3. distribute-neg-frac N/A

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

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

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

   5. associate-*l/ N/A

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

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

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

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

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

   8. sub-neg N/A

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

   9. +-commutative N/A

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

   10. distribute-neg-in N/A

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

   11. unsub-neg N/A

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

   12. remove-double-neg N/A

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

   13. --lowering--.f64 96.2%

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

3. Simplified 96.2%

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

Alternative 9: 39.0% 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 91.8%

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

   1. sub-neg N/A

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

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

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

   3. distribute-neg-frac N/A

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

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

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

   5. associate-*l/ N/A

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

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

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

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

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

   8. sub-neg N/A

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

   9. +-commutative N/A

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

   10. distribute-neg-in N/A

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

   11. unsub-neg N/A

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

   12. remove-double-neg N/A

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

   13. --lowering--.f64 96.2%

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

3. Simplified 96.2%

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

5. Taylor expanded in x around inf

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

7. Simplified 43.4%

   \[\leadsto \color{blue}{x} \]
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 2024161 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))