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

Percentage Accurate: 93.3% → 99.1%

Time: 10.1s

Alternatives: 13

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: 93.3% 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: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+277}:\\ \;\;\;\;x + \frac{\frac{y}{\frac{-1}{z - t}}}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -5e+267)
     (+ x (/ (- t z) (/ a y)))
     (if (<= t_1 4e+277)
       (+ x (/ (/ y (/ -1.0 (- z t))) a))
       (+ x (* (/ y a) (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 4e+277) {
		tmp = x + ((y / (-1.0 / (z - t))) / a);
	} else {
		tmp = x + ((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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= (-5d+267)) then
        tmp = x + ((t - z) / (a / y))
    else if (t_1 <= 4d+277) then
        tmp = x + ((y / ((-1.0d0) / (z - t))) / a)
    else
        tmp = x + ((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 t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 4e+277) {
		tmp = x + ((y / (-1.0 / (z - t))) / a);
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -5e+267:
		tmp = x + ((t - z) / (a / y))
	elif t_1 <= 4e+277:
		tmp = x + ((y / (-1.0 / (z - t))) / a)
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -5e+267)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	elseif (t_1 <= 4e+277)
		tmp = Float64(x + Float64(Float64(y / Float64(-1.0 / Float64(z - t))) / a));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -5e+267)
		tmp = x + ((t - z) / (a / y));
	elseif (t_1 <= 4e+277)
		tmp = x + ((y / (-1.0 / (z - t))) / a);
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+267], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+277], N[(x + N[(N[(y / N[(-1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -4.9999999999999999e267

   1. Initial program 81.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 100.0%

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

   4. Applied egg-rr 100.0%

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

   if -4.9999999999999999e267 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.00000000000000001e277

   1. Initial program 99.8%

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

      1. flip-- N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. +-commutative N/A

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

      6. clear-num N/A

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

      7. +-commutative N/A

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

      8. flip-- N/A

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

      9. /-lowering-/.f64 N/A

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

      10. --lowering--.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

   if 4.00000000000000001e277 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+267}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+277}:\\ \;\;\;\;x + \frac{\frac{y}{\frac{-1}{z - t}}}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+267}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+277}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -5e+267)
     (+ x (/ (- t z) (/ a y)))
     (if (<= t_1 4e+277)
       (+ x (/ (* y (- t z)) a))
       (+ x (* (/ y a) (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 4e+277) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + ((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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= (-5d+267)) then
        tmp = x + ((t - z) / (a / y))
    else if (t_1 <= 4d+277) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = x + ((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 t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -5e+267) {
		tmp = x + ((t - z) / (a / y));
	} else if (t_1 <= 4e+277) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -5e+267:
		tmp = x + ((t - z) / (a / y))
	elif t_1 <= 4e+277:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -5e+267)
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	elseif (t_1 <= 4e+277)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -5e+267)
		tmp = x + ((t - z) / (a / y));
	elseif (t_1 <= 4e+277)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+267], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+277], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -4.9999999999999999e267

   1. Initial program 81.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 100.0%

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

   4. Applied egg-rr 100.0%

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

   if -4.9999999999999999e267 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.00000000000000001e277

   1. Initial program 99.8%

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

   if 4.00000000000000001e277 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+267}:\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+277}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.4% accurate, 0.3× speedup

Math

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

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z - t)
    t_2 = x + ((y / a) * (t - z))
    if (t_1 <= (-1d+235)) then
        tmp = t_2
    else if (t_1 <= 2d+146) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = x + ((y / a) * (t - z));
	double tmp;
	if (t_1 <= -1e+235) {
		tmp = t_2;
	} else if (t_1 <= 2e+146) {
		tmp = x + ((y * (t - z)) / 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 <= -1e+235:
		tmp = t_2
	elif t_1 <= 2e+146:
		tmp = x + ((y * (t - z)) / 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 <= -1e+235)
		tmp = t_2;
	elseif (t_1 <= 2e+146)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	t_2 = x + ((y / a) * (t - z));
	tmp = 0.0;
	if (t_1 <= -1e+235)
		tmp = t_2;
	elseif (t_1 <= 2e+146)
		tmp = x + ((y * (t - z)) / 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, -1e+235], t$95$2, If[LessEqual[t$95$1, 2e+146], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 85.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 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 -1.0000000000000001e235 < (*.f64 y (-.f64 z t)) < 1.99999999999999987e146

   1. Initial program 99.8%

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

4. Final simplification 99.9%

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

Alternative 4: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+148}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.2e+129)
   (+ x (/ (* y t) a))
   (if (<= t 1.9e+148) (- x (/ z (/ a y))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.2e+129) {
		tmp = x + ((y * t) / a);
	} else if (t <= 1.9e+148) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (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 <= (-1.2d+129)) then
        tmp = x + ((y * t) / a)
    else if (t <= 1.9d+148) then
        tmp = x - (z / (a / y))
    else
        tmp = x + (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 <= -1.2e+129) {
		tmp = x + ((y * t) / a);
	} else if (t <= 1.9e+148) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.2e+129:
		tmp = x + ((y * t) / a)
	elif t <= 1.9e+148:
		tmp = x - (z / (a / y))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.2e+129)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (t <= 1.9e+148)
		tmp = Float64(x - Float64(z / Float64(a / y)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.2e+129)
		tmp = x + ((y * t) / a);
	elseif (t <= 1.9e+148)
		tmp = x - (z / (a / y));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.2e+129], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e+148], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1999999999999999e129

   1. Initial program 97.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.3%

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

   4. Applied egg-rr 94.3%

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

   5. Taylor expanded in z around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 97.0%

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

   7. Simplified 97.0%

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

   if -1.1999999999999999e129 < t < 1.8999999999999999e148

   1. Initial program 95.8%

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

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

   3. Simplified 96.4%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 84.6%

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

   7. Simplified 84.6%

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

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

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

      2. *-commutative N/A

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

      3. associate-/r/ N/A

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

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

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

      5. /-lowering-/.f64 87.2%

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

   9. Applied egg-rr 87.2%

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

   if 1.8999999999999999e148 < 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 97.2%

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

   3. Simplified 97.2%

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

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+129}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+148}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+148}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.95e+111)
   (+ x (/ (* y t) a))
   (if (<= t 1.1e+148) (- x (* y (/ z a))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.95e+111) {
		tmp = x + ((y * t) / a);
	} else if (t <= 1.1e+148) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (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 <= (-1.95d+111)) then
        tmp = x + ((y * t) / a)
    else if (t <= 1.1d+148) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (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 <= -1.95e+111) {
		tmp = x + ((y * t) / a);
	} else if (t <= 1.1e+148) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.95e+111:
		tmp = x + ((y * t) / a)
	elif t <= 1.1e+148:
		tmp = x - (y * (z / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.95e+111)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (t <= 1.1e+148)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.95e+111)
		tmp = x + ((y * t) / a);
	elseif (t <= 1.1e+148)
		tmp = x - (y * (z / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.95e+111], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+148], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9499999999999999e111

   1. Initial program 97.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.6%

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

   4. Applied egg-rr 94.6%

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

   5. Taylor expanded in z around 0

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

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 94.6%

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

   7. Simplified 94.6%

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

   if -1.9499999999999999e111 < t < 1.0999999999999999e148

   1. Initial program 95.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in 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 85.0%

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

   7. Simplified 85.0%

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

   if 1.0999999999999999e148 < 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 97.2%

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

   3. Simplified 97.2%

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

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+111}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+148}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;z \leq -3.25 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= z -3.25e+118) t_1 (if (<= z 3.1e+62) (+ x (* t (/ y a))) 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 (z <= -3.25e+118) {
		tmp = t_1;
	} else if (z <= 3.1e+62) {
		tmp = x + (t * (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) * (t - z)
    if (z <= (-3.25d+118)) then
        tmp = t_1
    else if (z <= 3.1d+62) then
        tmp = x + (t * (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) * (t - z);
	double tmp;
	if (z <= -3.25e+118) {
		tmp = t_1;
	} else if (z <= 3.1e+62) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if z <= -3.25e+118:
		tmp = t_1
	elif z <= 3.1e+62:
		tmp = x + (t * (y / a))
	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 (z <= -3.25e+118)
		tmp = t_1;
	elseif (z <= 3.1e+62)
		tmp = Float64(x + Float64(t * 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) * (t - z);
	tmp = 0.0;
	if (z <= -3.25e+118)
		tmp = t_1;
	elseif (z <= 3.1e+62)
		tmp = x + (t * (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[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.25e+118], t$95$1, If[LessEqual[z, 3.1e+62], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.25e118 or 3.10000000000000014e62 < z

   1. Initial program 93.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.8%

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

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 76.9%

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

   7. Simplified 76.9%

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

   if -3.25e118 < z < 3.10000000000000014e62

   1. Initial program 95.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 95.9%

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

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 85.7%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+62}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 48000:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.6e-7) x (if (<= a 48000.0) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.6e-7) {
		tmp = x;
	} else if (a <= 48000.0) {
		tmp = (y / a) * (t - z);
	} 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 <= (-4.6d-7)) then
        tmp = x
    else if (a <= 48000.0d0) then
        tmp = (y / a) * (t - z)
    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 <= -4.6e-7) {
		tmp = x;
	} else if (a <= 48000.0) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.6e-7:
		tmp = x
	elif a <= 48000.0:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.6e-7)
		tmp = x;
	elseif (a <= 48000.0)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.6e-7)
		tmp = x;
	elseif (a <= 48000.0)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.6e-7], x, If[LessEqual[a, 48000.0], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.5999999999999999e-7 or 48000 < a

   1. Initial program 90.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 64.1%

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

   if -4.5999999999999999e-7 < a < 48000

   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 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 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 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 48000:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+111}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7e+111) (/ (* y t) a) (if (<= t 3.2e+146) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7e+111) {
		tmp = (y * t) / a;
	} else if (t <= 3.2e+146) {
		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 <= (-7d+111)) then
        tmp = (y * t) / a
    else if (t <= 3.2d+146) 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 <= -7e+111) {
		tmp = (y * t) / a;
	} else if (t <= 3.2e+146) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7e+111:
		tmp = (y * t) / a
	elif t <= 3.2e+146:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7e+111)
		tmp = Float64(Float64(y * t) / a);
	elseif (t <= 3.2e+146)
		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 <= -7e+111)
		tmp = (y * t) / a;
	elseif (t <= 3.2e+146)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7e+111], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 3.2e+146], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.0000000000000004e111

   1. Initial program 97.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.6%

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

   4. Applied egg-rr 94.6%

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

   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 72.6%

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

   7. Simplified 72.6%

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

   if -7.0000000000000004e111 < t < 3.2e146

   1. Initial program 95.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.3%

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

   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 48.2%

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

   if 3.2e146 < t

   1. Initial program 89.7%

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

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 76.6%

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

   7. Simplified 76.6%

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

   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 66.1%

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

Alternative 9: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.65 \cdot 10^{+111}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+146}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.65e+111) (/ y (/ a t)) (if (<= t 3.3e+146) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.65e+111) {
		tmp = y / (a / t);
	} else if (t <= 3.3e+146) {
		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 <= (-4.65d+111)) then
        tmp = y / (a / t)
    else if (t <= 3.3d+146) 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 <= -4.65e+111) {
		tmp = y / (a / t);
	} else if (t <= 3.3e+146) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.65e+111:
		tmp = y / (a / t)
	elif t <= 3.3e+146:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.65e+111)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 3.3e+146)
		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 <= -4.65e+111)
		tmp = y / (a / t);
	elseif (t <= 3.3e+146)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.65e+111], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+146], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.65000000000000006e111

   1. Initial program 97.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.6%

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

   3. Simplified 94.6%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 69.7%

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

   7. Simplified 69.7%

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

   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 67.1%

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

       1. associate-*r/ N/A

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

       2. *-commutative N/A

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

       3. associate-/l* N/A

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

       4. clear-num N/A

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

       5. un-div-inv N/A

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

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

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

       7. /-lowering-/.f64 70.0%

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

   12. Applied egg-rr 70.0%

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

   if -4.65000000000000006e111 < t < 3.30000000000000016e146

   1. Initial program 95.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.3%

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

   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 48.2%

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

   if 3.30000000000000016e146 < t

   1. Initial program 89.7%

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

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 76.6%

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

   7. Simplified 76.6%

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

   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 66.1%

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

Alternative 10: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+111}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+111) (* y (/ t a)) (if (<= t 6.2e+145) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+111) {
		tmp = y * (t / a);
	} else if (t <= 6.2e+145) {
		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 <= (-6.2d+111)) then
        tmp = y * (t / a)
    else if (t <= 6.2d+145) 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 <= -6.2e+111) {
		tmp = y * (t / a);
	} else if (t <= 6.2e+145) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+111:
		tmp = y * (t / a)
	elif t <= 6.2e+145:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+111)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 6.2e+145)
		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 <= -6.2e+111)
		tmp = y * (t / a);
	elseif (t <= 6.2e+145)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+111], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+145], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.2000000000000001e111

   1. Initial program 97.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

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

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

      4. /-lowering-/.f64 69.9%

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

   7. Simplified 69.9%

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

   if -6.2000000000000001e111 < t < 6.19999999999999977e145

   1. Initial program 95.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.3%

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

   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 48.2%

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

   if 6.19999999999999977e145 < t

   1. Initial program 89.7%

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

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 76.6%

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

   7. Simplified 76.6%

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

   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 66.1%

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

Alternative 11: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -5.9e+111) t_1 (if (<= t 6.2e+145) 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 <= -5.9e+111) {
		tmp = t_1;
	} else if (t <= 6.2e+145) {
		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 <= (-5.9d+111)) then
        tmp = t_1
    else if (t <= 6.2d+145) 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 <= -5.9e+111) {
		tmp = t_1;
	} else if (t <= 6.2e+145) {
		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 <= -5.9e+111:
		tmp = t_1
	elif t <= 6.2e+145:
		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 <= -5.9e+111)
		tmp = t_1;
	elseif (t <= 6.2e+145)
		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 <= -5.9e+111)
		tmp = t_1;
	elseif (t <= 6.2e+145)
		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, -5.9e+111], t$95$1, If[LessEqual[t, 6.2e+145], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9e111 or 6.19999999999999977e145 < t

   1. Initial program 93.4%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.0%

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

   3. Simplified 96.0%

      \[\leadsto \color{blue}{x + \frac{y}{a} \cdot \left(t - z\right)} \]
   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 73.2%

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

   7. Simplified 73.2%

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

   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 66.6%

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

   if -5.9e111 < t < 6.19999999999999977e145

   1. Initial program 95.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 96.3%

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

   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 48.2%

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

Alternative 12: 97.3% 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 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 96.2%

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

3. Simplified 96.2%

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

Alternative 13: 39.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 96.2%

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

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 41.9%

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

Developer Target 1: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, 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)))