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

Percentage Accurate: 93.6% → 97.5%

Time: 8.6s

Alternatives: 9

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% 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 92.9%

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

   1. associate-*l/ 97.5%

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

3. Simplified 97.5%

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

4. Final simplification 97.5%

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

Alternative 2: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+194} \lor \neg \left(z \leq 2.2 \cdot 10^{+101} \lor \neg \left(z \leq 4.5 \cdot 10^{+138}\right) \land z \leq 1.6 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.05e+194)
         (not
          (or (<= z 2.2e+101) (and (not (<= z 4.5e+138)) (<= z 1.6e+203)))))
   (* (/ y a) (- z))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+194) || !((z <= 2.2e+101) || (!(z <= 4.5e+138) && (z <= 1.6e+203)))) {
		tmp = (y / a) * -z;
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.05d+194)) .or. (.not. (z <= 2.2d+101) .or. (.not. (z <= 4.5d+138)) .and. (z <= 1.6d+203))) then
        tmp = (y / a) * -z
    else
        tmp = x + ((y / a) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.05e+194) || !((z <= 2.2e+101) || (!(z <= 4.5e+138) && (z <= 1.6e+203)))) {
		tmp = (y / a) * -z;
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.05e+194) or not ((z <= 2.2e+101) or (not (z <= 4.5e+138) and (z <= 1.6e+203))):
		tmp = (y / a) * -z
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.05e+194) || !((z <= 2.2e+101) || (!(z <= 4.5e+138) && (z <= 1.6e+203))))
		tmp = Float64(Float64(y / a) * Float64(-z));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.05e+194) || ~(((z <= 2.2e+101) || (~((z <= 4.5e+138)) && (z <= 1.6e+203)))))
		tmp = (y / a) * -z;
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.05e+194], N[Not[Or[LessEqual[z, 2.2e+101], And[N[Not[LessEqual[z, 4.5e+138]], $MachinePrecision], LessEqual[z, 1.6e+203]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05e194 or 2.2000000000000001e101 < z < 4.49999999999999982e138 or 1.5999999999999998e203 < z

   1. Initial program 90.0%

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

      1. associate-*r/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*l/ 85.8%

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

      3. *-commutative 85.8%

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

      4. distribute-rgt-neg-in 85.8%

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

      5. distribute-frac-neg 85.8%

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

   6. Simplified 85.8%

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

   if -2.05e194 < z < 2.2000000000000001e101 or 4.49999999999999982e138 < z < 1.5999999999999998e203

   1. Initial program 93.5%

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

      1. associate-*r/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 80.0%

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

      1. sub-neg 80.0%

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

      2. mul-1-neg 80.0%

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

      3. remove-double-neg 80.0%

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

      4. +-commutative 80.0%

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

      5. associate-*l/ 83.8%

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

      6. *-commutative 83.8%

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

   6. Simplified 83.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+194} \lor \neg \left(z \leq 2.2 \cdot 10^{+101} \lor \neg \left(z \leq 4.5 \cdot 10^{+138}\right) \land z \leq 1.6 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 3: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{a} \cdot t\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y a) t))))
   (if (<= t -5.5e+77)
     t_1
     (if (<= t -2.2e+17)
       (* (/ y a) (- t z))
       (if (<= t -7.2e-19)
         (+ x (/ y (/ a t)))
         (if (<= t 3.6e-18) (- x (* y (/ z a))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * t);
	double tmp;
	if (t <= -5.5e+77) {
		tmp = t_1;
	} else if (t <= -2.2e+17) {
		tmp = (y / a) * (t - z);
	} else if (t <= -7.2e-19) {
		tmp = x + (y / (a / t));
	} else if (t <= 3.6e-18) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / a) * t)
    if (t <= (-5.5d+77)) then
        tmp = t_1
    else if (t <= (-2.2d+17)) then
        tmp = (y / a) * (t - z)
    else if (t <= (-7.2d-19)) then
        tmp = x + (y / (a / t))
    else if (t <= 3.6d-18) then
        tmp = x - (y * (z / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y / a) * t);
	double tmp;
	if (t <= -5.5e+77) {
		tmp = t_1;
	} else if (t <= -2.2e+17) {
		tmp = (y / a) * (t - z);
	} else if (t <= -7.2e-19) {
		tmp = x + (y / (a / t));
	} else if (t <= 3.6e-18) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y / a) * t)
	tmp = 0
	if t <= -5.5e+77:
		tmp = t_1
	elif t <= -2.2e+17:
		tmp = (y / a) * (t - z)
	elif t <= -7.2e-19:
		tmp = x + (y / (a / t))
	elif t <= 3.6e-18:
		tmp = x - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y / a) * t))
	tmp = 0.0
	if (t <= -5.5e+77)
		tmp = t_1;
	elseif (t <= -2.2e+17)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (t <= -7.2e-19)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (t <= 3.6e-18)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y / a) * t);
	tmp = 0.0;
	if (t <= -5.5e+77)
		tmp = t_1;
	elseif (t <= -2.2e+17)
		tmp = (y / a) * (t - z);
	elseif (t <= -7.2e-19)
		tmp = x + (y / (a / t));
	elseif (t <= 3.6e-18)
		tmp = x - (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+77], t$95$1, If[LessEqual[t, -2.2e+17], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-19], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-18], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.50000000000000036e77 or 3.6000000000000001e-18 < t

   1. Initial program 90.5%

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

      1. associate-*r/ 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around 0 80.3%

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

      1. sub-neg 80.3%

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

      2. mul-1-neg 80.3%

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

      3. remove-double-neg 80.3%

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

      4. +-commutative 80.3%

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

      5. associate-*l/ 88.6%

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

      6. *-commutative 88.6%

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

   6. Simplified 88.6%

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

   if -5.50000000000000036e77 < t < -2.2e17

   1. Initial program 91.8%

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

      1. associate-*r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 91.8%

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

      1. associate-*l/ 99.9%

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

      2. associate-*r* 99.9%

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

      3. neg-mul-1 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   if -2.2e17 < t < -7.2000000000000002e-19

   1. Initial program 99.7%

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

      1. associate-*r/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 95.8%

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

      1. sub-neg 95.8%

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

      2. mul-1-neg 95.8%

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

      3. remove-double-neg 95.8%

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

      4. +-commutative 95.8%

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

      5. associate-*l/ 95.8%

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

      6. *-commutative 95.8%

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

   6. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-/r/ 96.1%

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

   8. Applied egg-rr 96.1%

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

   if -7.2000000000000002e-19 < t < 3.6000000000000001e-18

   1. Initial program 95.0%

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

      1. associate-*r/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 88.3%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+77}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-18}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 4: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-299}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+18)
   (* (/ y a) t)
   (if (<= t -3.3e-235)
     x
     (if (<= t -2.6e-299)
       (* (/ y a) (- z))
       (if (<= t 1.5e+118) x (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+18) {
		tmp = (y / a) * t;
	} else if (t <= -3.3e-235) {
		tmp = x;
	} else if (t <= -2.6e-299) {
		tmp = (y / a) * -z;
	} else if (t <= 1.5e+118) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d+18)) then
        tmp = (y / a) * t
    else if (t <= (-3.3d-235)) then
        tmp = x
    else if (t <= (-2.6d-299)) then
        tmp = (y / a) * -z
    else if (t <= 1.5d+118) then
        tmp = x
    else
        tmp = t / (a / y)
    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 <= -2.1e+18) {
		tmp = (y / a) * t;
	} else if (t <= -3.3e-235) {
		tmp = x;
	} else if (t <= -2.6e-299) {
		tmp = (y / a) * -z;
	} else if (t <= 1.5e+118) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+18:
		tmp = (y / a) * t
	elif t <= -3.3e-235:
		tmp = x
	elif t <= -2.6e-299:
		tmp = (y / a) * -z
	elif t <= 1.5e+118:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+18)
		tmp = Float64(Float64(y / a) * t);
	elseif (t <= -3.3e-235)
		tmp = x;
	elseif (t <= -2.6e-299)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (t <= 1.5e+118)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+18)
		tmp = (y / a) * t;
	elseif (t <= -3.3e-235)
		tmp = x;
	elseif (t <= -2.6e-299)
		tmp = (y / a) * -z;
	elseif (t <= 1.5e+118)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+18], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, -3.3e-235], x, If[LessEqual[t, -2.6e-299], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[t, 1.5e+118], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1e18

   1. Initial program 89.5%

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

      1. associate-*r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 56.3%

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

      1. associate-*l/ 65.0%

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

      2. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if -2.1e18 < t < -3.30000000000000028e-235 or -2.5999999999999999e-299 < t < 1.5e118

   1. Initial program 96.4%

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

      1. associate-*r/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 49.9%

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

   if -3.30000000000000028e-235 < t < -2.5999999999999999e-299

   1. Initial program 86.1%

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

      1. associate-*r/ 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 68.7%

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

      1. mul-1-neg 68.7%

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

      2. associate-*l/ 82.4%

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

      3. *-commutative 82.4%

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

      4. distribute-rgt-neg-in 82.4%

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

      5. distribute-frac-neg 82.4%

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

   6. Simplified 82.4%

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

   if 1.5e118 < t

   1. Initial program 87.8%

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

      1. associate-*r/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in t around inf 59.1%

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

      1. associate-*l/ 68.4%

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

      2. *-commutative 68.4%

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

   6. Simplified 68.4%

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

      1. clear-num 68.4%

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

      2. un-div-inv 68.4%

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

   8. Applied egg-rr 68.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-299}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-22} \lor \neg \left(t \leq 2.2 \cdot 10^{-20}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.5e-22) (not (<= t 2.2e-20)))
   (+ x (* (/ y a) t))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e-22) || !(t <= 2.2e-20)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y * (z / 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 <= (-5.5d-22)) .or. (.not. (t <= 2.2d-20))) then
        tmp = x + ((y / a) * t)
    else
        tmp = x - (y * (z / 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 <= -5.5e-22) || !(t <= 2.2e-20)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.5e-22) or not (t <= 2.2e-20):
		tmp = x + ((y / a) * t)
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.5e-22) || !(t <= 2.2e-20))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.5e-22) || ~((t <= 2.2e-20)))
		tmp = x + ((y / a) * t);
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.5e-22], N[Not[LessEqual[t, 2.2e-20]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.5000000000000001e-22 or 2.19999999999999991e-20 < t

   1. Initial program 90.9%

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

      1. associate-*r/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 79.2%

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

      1. sub-neg 79.2%

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

      2. mul-1-neg 79.2%

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

      3. remove-double-neg 79.2%

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

      4. +-commutative 79.2%

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

      5. associate-*l/ 86.5%

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

      6. *-commutative 86.5%

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

   6. Simplified 86.5%

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

   if -5.5000000000000001e-22 < t < 2.19999999999999991e-20

   1. Initial program 95.0%

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

      1. associate-*r/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 88.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-22} \lor \neg \left(t \leq 2.2 \cdot 10^{-20}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]

Alternative 6: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+18} \lor \neg \left(t \leq 3 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+18) (not (<= t 3e+119))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+18) || !(t <= 3e+119)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.4d+18)) .or. (.not. (t <= 3d+119))) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+18) || !(t <= 3e+119)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+18) or not (t <= 3e+119):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+18) || !(t <= 3e+119))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+18) || ~((t <= 3e+119)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+18], N[Not[LessEqual[t, 3e+119]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.4e18 or 3.00000000000000001e119 < t

   1. Initial program 88.9%

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

      1. associate-*r/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around inf 57.3%

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

      1. associate-*l/ 66.2%

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

      2. *-commutative 66.2%

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

   6. Simplified 66.2%

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

   if -1.4e18 < t < 3.00000000000000001e119

   1. Initial program 95.9%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around inf 48.5%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+18} \lor \neg \left(t \leq 3 \cdot 10^{+119}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.5e+18) (* (/ y a) t) (if (<= t 1.4e+118) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.5e+18) {
		tmp = (y / a) * t;
	} else if (t <= 1.4e+118) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.5d+18)) then
        tmp = (y / a) * t
    else if (t <= 1.4d+118) then
        tmp = x
    else
        tmp = t / (a / y)
    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 <= -2.5e+18) {
		tmp = (y / a) * t;
	} else if (t <= 1.4e+118) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.5e+18:
		tmp = (y / a) * t
	elif t <= 1.4e+118:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.5e+18)
		tmp = Float64(Float64(y / a) * t);
	elseif (t <= 1.4e+118)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.5e+18)
		tmp = (y / a) * t;
	elseif (t <= 1.4e+118)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.5e+18], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t, 1.4e+118], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e18

   1. Initial program 89.5%

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

      1. associate-*r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in t around inf 56.3%

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

      1. associate-*l/ 65.0%

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

      2. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if -2.5e18 < t < 1.39999999999999993e118

   1. Initial program 95.9%

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

      1. associate-*r/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around inf 48.5%

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

   if 1.39999999999999993e118 < t

   1. Initial program 87.8%

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

      1. associate-*r/ 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in t around inf 59.1%

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

      1. associate-*l/ 68.4%

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

      2. *-commutative 68.4%

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

   6. Simplified 68.4%

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

      1. clear-num 68.4%

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

      2. un-div-inv 68.4%

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

   8. Applied egg-rr 68.4%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

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 92.9%

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

   1. associate-*r/ 95.0%

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

3. Simplified 95.0%

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

4. Final simplification 95.0%

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

Alternative 9: 39.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*r/ 95.0%

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

3. Simplified 95.0%

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

4. Taylor expanded in x around inf 36.9%

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

5. Final simplification 36.9%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× 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 2023192 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (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)))