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

Percentage Accurate: 93.2% → 97.0%

Time: 7.5s

Alternatives: 9

Speedup: 1.0×

• 25.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. *-commutative 93.3%

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

   2. associate-/l* 98.0%

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

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

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

Alternative 2: 48.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+157}:\\ \;\;\;\;\frac{z \cdot y}{-a}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.72 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= y -7.8e+157)
     (/ (* z y) (- a))
     (if (<= y -9.2e+51)
       (* t (/ y a))
       (if (<= y -1.72e-40)
         (* y (/ z (- a)))
         (if (<= y 2.1e-44)
           x
           (if (<= y 6.7e+65)
             t_1
             (if (<= y 1.9e+130)
               (/ y (/ a (- z)))
               (if (<= y 8.5e+273) t_1 (* z (/ y (- a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (y <= -7.8e+157) {
		tmp = (z * y) / -a;
	} else if (y <= -9.2e+51) {
		tmp = t * (y / a);
	} else if (y <= -1.72e-40) {
		tmp = y * (z / -a);
	} else if (y <= 2.1e-44) {
		tmp = x;
	} else if (y <= 6.7e+65) {
		tmp = t_1;
	} else if (y <= 1.9e+130) {
		tmp = y / (a / -z);
	} else if (y <= 8.5e+273) {
		tmp = t_1;
	} else {
		tmp = z * (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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (y <= (-7.8d+157)) then
        tmp = (z * y) / -a
    else if (y <= (-9.2d+51)) then
        tmp = t * (y / a)
    else if (y <= (-1.72d-40)) then
        tmp = y * (z / -a)
    else if (y <= 2.1d-44) then
        tmp = x
    else if (y <= 6.7d+65) then
        tmp = t_1
    else if (y <= 1.9d+130) then
        tmp = y / (a / -z)
    else if (y <= 8.5d+273) then
        tmp = t_1
    else
        tmp = z * (y / -a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (y <= -7.8e+157) {
		tmp = (z * y) / -a;
	} else if (y <= -9.2e+51) {
		tmp = t * (y / a);
	} else if (y <= -1.72e-40) {
		tmp = y * (z / -a);
	} else if (y <= 2.1e-44) {
		tmp = x;
	} else if (y <= 6.7e+65) {
		tmp = t_1;
	} else if (y <= 1.9e+130) {
		tmp = y / (a / -z);
	} else if (y <= 8.5e+273) {
		tmp = t_1;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if y <= -7.8e+157:
		tmp = (z * y) / -a
	elif y <= -9.2e+51:
		tmp = t * (y / a)
	elif y <= -1.72e-40:
		tmp = y * (z / -a)
	elif y <= 2.1e-44:
		tmp = x
	elif y <= 6.7e+65:
		tmp = t_1
	elif y <= 1.9e+130:
		tmp = y / (a / -z)
	elif y <= 8.5e+273:
		tmp = t_1
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (y <= -7.8e+157)
		tmp = Float64(Float64(z * y) / Float64(-a));
	elseif (y <= -9.2e+51)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= -1.72e-40)
		tmp = Float64(y * Float64(z / Float64(-a)));
	elseif (y <= 2.1e-44)
		tmp = x;
	elseif (y <= 6.7e+65)
		tmp = t_1;
	elseif (y <= 1.9e+130)
		tmp = Float64(y / Float64(a / Float64(-z)));
	elseif (y <= 8.5e+273)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (y <= -7.8e+157)
		tmp = (z * y) / -a;
	elseif (y <= -9.2e+51)
		tmp = t * (y / a);
	elseif (y <= -1.72e-40)
		tmp = y * (z / -a);
	elseif (y <= 2.1e-44)
		tmp = x;
	elseif (y <= 6.7e+65)
		tmp = t_1;
	elseif (y <= 1.9e+130)
		tmp = y / (a / -z);
	elseif (y <= 8.5e+273)
		tmp = t_1;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e+157], N[(N[(z * y), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[y, -9.2e+51], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.72e-40], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-44], x, If[LessEqual[y, 6.7e+65], t$95$1, If[LessEqual[y, 1.9e+130], N[(y / N[(a / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+273], t$95$1, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -7.79999999999999941e157

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-/l* 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 72.3%

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

      1. associate-*r/ 72.3%

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

      2. *-commutative 72.3%

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

      3. neg-mul-1 72.3%

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

      4. distribute-lft-neg-in 72.3%

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

      5. *-commutative 72.3%

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

   7. Simplified 72.3%

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

   if -7.79999999999999941e157 < y < -9.2000000000000002e51

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 62.7%

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

      1. associate-*r/ 77.0%

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

   7. Simplified 77.0%

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

   if -9.2000000000000002e51 < y < -1.7199999999999999e-40

   1. Initial program 95.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-/l* 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. distribute-neg-frac2 70.9%

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

   7. Simplified 70.9%

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

   if -1.7199999999999999e-40 < y < 2.10000000000000001e-44

   1. Initial program 99.9%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 67.7%

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

   if 2.10000000000000001e-44 < y < 6.6999999999999997e65 or 1.9000000000000001e130 < y < 8.5000000000000002e273

   1. Initial program 92.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 51.3%

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

      1. *-commutative 51.3%

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

      2. associate-/l* 55.5%

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

   7. Simplified 55.5%

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

   if 6.6999999999999997e65 < y < 1.9000000000000001e130

   1. Initial program 82.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-/l* 65.3%

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

      3. distribute-rgt-neg-in 65.3%

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

      4. distribute-neg-frac2 65.3%

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

   7. Simplified 65.3%

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

      1. associate-*r/ 54.6%

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

      2. add-sqr-sqrt 30.0%

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

      3. sqrt-unprod 30.1%

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

      4. sqr-neg 30.1%

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

      5. sqrt-unprod 0.7%

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

      6. add-sqr-sqrt 1.2%

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

      7. associate-*l/ 6.7%

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

      8. associate-/r/ 1.1%

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

      9. frac-2neg 1.1%

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

      10. distribute-neg-frac2 1.1%

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

      11. add-sqr-sqrt 1.0%

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

      12. sqrt-unprod 36.3%

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

      13. sqr-neg 36.3%

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

      14. sqrt-unprod 35.4%

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

      15. add-sqr-sqrt 65.4%

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

   9. Applied egg-rr 65.4%

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

   if 8.5000000000000002e273 < y

   1. Initial program 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-/l* 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in z around inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. associate-*l/ 77.9%

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

      3. distribute-rgt-neg-in 77.9%

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

   7. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(-z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+157}:\\ \;\;\;\;\frac{z \cdot y}{-a}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.72 \cdot 10^{-40}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+130}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+273}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-z}{a}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+65} \lor \neg \left(y \leq 1.65 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z) a))))
   (if (<= y -2.15e+157)
     t_1
     (if (<= y -4e+52)
       (* t (/ y a))
       (if (<= y -4.5e-41)
         t_1
         (if (<= y 2.2e-44)
           x
           (if (or (<= y 8e+65) (not (<= y 1.65e+130)))
             (* y (/ t a))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (y <= -2.15e+157) {
		tmp = t_1;
	} else if (y <= -4e+52) {
		tmp = t * (y / a);
	} else if (y <= -4.5e-41) {
		tmp = t_1;
	} else if (y <= 2.2e-44) {
		tmp = x;
	} else if ((y <= 8e+65) || !(y <= 1.65e+130)) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-z / a)
    if (y <= (-2.15d+157)) then
        tmp = t_1
    else if (y <= (-4d+52)) then
        tmp = t * (y / a)
    else if (y <= (-4.5d-41)) then
        tmp = t_1
    else if (y <= 2.2d-44) then
        tmp = x
    else if ((y <= 8d+65) .or. (.not. (y <= 1.65d+130))) then
        tmp = y * (t / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (y <= -2.15e+157) {
		tmp = t_1;
	} else if (y <= -4e+52) {
		tmp = t * (y / a);
	} else if (y <= -4.5e-41) {
		tmp = t_1;
	} else if (y <= 2.2e-44) {
		tmp = x;
	} else if ((y <= 8e+65) || !(y <= 1.65e+130)) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-z / a)
	tmp = 0
	if y <= -2.15e+157:
		tmp = t_1
	elif y <= -4e+52:
		tmp = t * (y / a)
	elif y <= -4.5e-41:
		tmp = t_1
	elif y <= 2.2e-44:
		tmp = x
	elif (y <= 8e+65) or not (y <= 1.65e+130):
		tmp = y * (t / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-z) / a))
	tmp = 0.0
	if (y <= -2.15e+157)
		tmp = t_1;
	elseif (y <= -4e+52)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= -4.5e-41)
		tmp = t_1;
	elseif (y <= 2.2e-44)
		tmp = x;
	elseif ((y <= 8e+65) || !(y <= 1.65e+130))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-z / a);
	tmp = 0.0;
	if (y <= -2.15e+157)
		tmp = t_1;
	elseif (y <= -4e+52)
		tmp = t * (y / a);
	elseif (y <= -4.5e-41)
		tmp = t_1;
	elseif (y <= 2.2e-44)
		tmp = x;
	elseif ((y <= 8e+65) || ~((y <= 1.65e+130)))
		tmp = y * (t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.15e+157], t$95$1, If[LessEqual[y, -4e+52], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-41], t$95$1, If[LessEqual[y, 2.2e-44], x, If[Or[LessEqual[y, 8e+65], N[Not[LessEqual[y, 1.65e+130]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.15e157 or -4e52 < y < -4.5e-41 or 7.9999999999999999e65 < y < 1.65e130

   1. Initial program 88.7%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. associate-/l* 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. distribute-neg-frac2 66.2%

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

   7. Simplified 66.2%

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

   if -2.15e157 < y < -4e52

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 62.7%

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

      1. associate-*r/ 77.0%

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

   7. Simplified 77.0%

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

   if -4.5e-41 < y < 2.20000000000000012e-44

   1. Initial program 99.9%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 67.7%

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

   if 2.20000000000000012e-44 < y < 7.9999999999999999e65 or 1.65e130 < y

   1. Initial program 89.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 49.3%

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

      1. *-commutative 49.3%

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

      2. associate-/l* 54.3%

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

   7. Simplified 54.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+65} \lor \neg \left(y \leq 1.65 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= y -7.2e+157)
     t_1
     (if (<= y -5.5e+52)
       (* t (/ y a))
       (if (<= y -1.75e-36)
         (* y (/ z (- a)))
         (if (<= y 3.2e-44) x (if (<= y 5.5e+64) (* y (/ t a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (y <= -7.2e+157) {
		tmp = t_1;
	} else if (y <= -5.5e+52) {
		tmp = t * (y / a);
	} else if (y <= -1.75e-36) {
		tmp = y * (z / -a);
	} else if (y <= 3.2e-44) {
		tmp = x;
	} else if (y <= 5.5e+64) {
		tmp = y * (t / 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 = z * (y / -a)
    if (y <= (-7.2d+157)) then
        tmp = t_1
    else if (y <= (-5.5d+52)) then
        tmp = t * (y / a)
    else if (y <= (-1.75d-36)) then
        tmp = y * (z / -a)
    else if (y <= 3.2d-44) then
        tmp = x
    else if (y <= 5.5d+64) then
        tmp = y * (t / 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 = z * (y / -a);
	double tmp;
	if (y <= -7.2e+157) {
		tmp = t_1;
	} else if (y <= -5.5e+52) {
		tmp = t * (y / a);
	} else if (y <= -1.75e-36) {
		tmp = y * (z / -a);
	} else if (y <= 3.2e-44) {
		tmp = x;
	} else if (y <= 5.5e+64) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if y <= -7.2e+157:
		tmp = t_1
	elif y <= -5.5e+52:
		tmp = t * (y / a)
	elif y <= -1.75e-36:
		tmp = y * (z / -a)
	elif y <= 3.2e-44:
		tmp = x
	elif y <= 5.5e+64:
		tmp = y * (t / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (y <= -7.2e+157)
		tmp = t_1;
	elseif (y <= -5.5e+52)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= -1.75e-36)
		tmp = Float64(y * Float64(z / Float64(-a)));
	elseif (y <= 3.2e-44)
		tmp = x;
	elseif (y <= 5.5e+64)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (y <= -7.2e+157)
		tmp = t_1;
	elseif (y <= -5.5e+52)
		tmp = t * (y / a);
	elseif (y <= -1.75e-36)
		tmp = y * (z / -a);
	elseif (y <= 3.2e-44)
		tmp = x;
	elseif (y <= 5.5e+64)
		tmp = y * (t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+157], t$95$1, If[LessEqual[y, -5.5e+52], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-36], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-44], x, If[LessEqual[y, 5.5e+64], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.20000000000000049e157 or 5.4999999999999996e64 < y

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-/l* 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in z around inf 51.5%

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

      1. mul-1-neg 51.5%

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

      2. associate-*l/ 57.3%

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

      3. distribute-rgt-neg-in 57.3%

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

   7. Simplified 57.3%

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

   if -7.20000000000000049e157 < y < -5.49999999999999996e52

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 62.7%

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

      1. associate-*r/ 77.0%

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

   7. Simplified 77.0%

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

   if -5.49999999999999996e52 < y < -1.75e-36

   1. Initial program 95.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. associate-/l* 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. distribute-neg-frac2 70.9%

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

   7. Simplified 70.9%

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

   if -1.75e-36 < y < 3.19999999999999995e-44

   1. Initial program 99.9%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 67.7%

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

   if 3.19999999999999995e-44 < y < 5.4999999999999996e64

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-/l* 52.1%

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

   7. Simplified 52.1%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-36} \lor \neg \left(y \leq 1.35 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.8e-36) (not (<= y 1.35e+29)))
   (* y (/ (- t z) a))
   (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e-36) || !(y <= 1.35e+29)) {
		tmp = y * ((t - 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 ((y <= (-2.8d-36)) .or. (.not. (y <= 1.35d+29))) then
        tmp = y * ((t - 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 ((y <= -2.8e-36) || !(y <= 1.35e+29)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.8e-36) or not (y <= 1.35e+29):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.8e-36) || !(y <= 1.35e+29))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.8e-36) || ~((y <= 1.35e+29)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.8e-36], N[Not[LessEqual[y, 1.35e+29]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8000000000000001e-36 or 1.35e29 < y

   1. Initial program 87.4%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. distribute-frac-neg2 76.4%

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

      3. sub-neg 76.4%

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

      4. +-commutative 76.4%

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

      5. neg-sub0 76.4%

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

      6. associate--r- 76.4%

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

      7. neg-sub0 76.4%

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

      8. associate-*r/ 85.8%

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

      9. distribute-neg-frac 85.8%

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

      10. distribute-neg-frac2 85.8%

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

      11. remove-double-neg 85.8%

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

   7. Simplified 85.8%

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

   if -2.8000000000000001e-36 < y < 1.35e29

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg2 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-/l* 88.9%

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

      5. fma-define 88.9%

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

      6. distribute-frac-neg2 88.9%

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

      7. distribute-neg-frac 88.9%

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

      8. sub-neg 88.9%

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

      9. distribute-neg-in 88.9%

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

      10. remove-double-neg 88.9%

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

      11. +-commutative 88.9%

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

      12. sub-neg 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in z around 0 82.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-36} \lor \neg \left(y \leq 1.35 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-45} \lor \neg \left(y \leq 1.35 \cdot 10^{-139}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-45) (not (<= y 1.35e-139))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-45) || !(y <= 1.35e-139)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.9d-45)) .or. (.not. (y <= 1.35d-139))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-45) || !(y <= 1.35e-139)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-45) or not (y <= 1.35e-139):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-45) || !(y <= 1.35e-139))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e-45) || ~((y <= 1.35e-139)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-45], N[Not[LessEqual[y, 1.35e-139]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e-45 or 1.3499999999999999e-139 < y

   1. Initial program 90.0%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. distribute-frac-neg2 73.6%

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

      3. sub-neg 73.6%

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

      4. +-commutative 73.6%

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

      5. neg-sub0 73.6%

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

      6. associate--r- 73.6%

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

      7. neg-sub0 73.6%

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

      8. associate-*r/ 80.7%

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

      9. distribute-neg-frac 80.7%

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

      10. distribute-neg-frac2 80.7%

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

      11. remove-double-neg 80.7%

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

   7. Simplified 80.7%

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

   if -2.9e-45 < y < 1.3499999999999999e-139

   1. Initial program 99.9%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around inf 74.2%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-45} \lor \neg \left(y \leq 1.35 \cdot 10^{-139}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-36} \lor \neg \left(y \leq 4.8 \cdot 10^{-45}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.05e-36) (not (<= y 4.8e-45))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.05e-36) || !(y <= 4.8e-45)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.05d-36)) .or. (.not. (y <= 4.8d-45))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.05e-36) || !(y <= 4.8e-45)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.05e-36) or not (y <= 4.8e-45):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.05e-36) || !(y <= 4.8e-45))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.05e-36) || ~((y <= 4.8e-45)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.05e-36], N[Not[LessEqual[y, 4.8e-45]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.05000000000000006e-36 or 4.7999999999999998e-45 < y

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-/l* 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in t around inf 38.8%

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

      1. associate-*r/ 45.4%

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

   7. Simplified 45.4%

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

   if -2.05000000000000006e-36 < y < 4.7999999999999998e-45

   1. Initial program 99.9%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 67.7%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-36} \lor \neg \left(y \leq 4.8 \cdot 10^{-45}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. associate-/l* 94.3%

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

3. Simplified 94.3%

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

5. Final simplification 94.3%

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

Alternative 9: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. associate-/l* 94.3%

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

3. Simplified 94.3%

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

5. Taylor expanded in x around inf 36.5%

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

Developer target: 98.9% 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 2024096 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))