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

Percentage Accurate: 93.5% → 96.9%

Time: 9.4s

Alternatives: 8

Speedup: 1.0×

• 24.1% 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: 93.5% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

   1. *-commutative 96.5%

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

   2. clear-num 96.5%

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

   3. un-div-inv 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -1.2e+133)
     (/ (- y) (/ a t))
     (if (<= t 4.5e+108)
       t_1
       (if (<= t 4.1e+139)
         (* y (/ (- t) a))
         (if (<= t 7.8e+242) t_1 (/ (* t (- y)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.2e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = t_1;
	} else if (t <= 4.1e+139) {
		tmp = y * (-t / a);
	} else if (t <= 7.8e+242) {
		tmp = t_1;
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-1.2d+133)) then
        tmp = -y / (a / t)
    else if (t <= 4.5d+108) then
        tmp = t_1
    else if (t <= 4.1d+139) then
        tmp = y * (-t / a)
    else if (t <= 7.8d+242) then
        tmp = t_1
    else
        tmp = (t * -y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.2e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = t_1;
	} else if (t <= 4.1e+139) {
		tmp = y * (-t / a);
	} else if (t <= 7.8e+242) {
		tmp = t_1;
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -1.2e+133:
		tmp = -y / (a / t)
	elif t <= 4.5e+108:
		tmp = t_1
	elif t <= 4.1e+139:
		tmp = y * (-t / a)
	elif t <= 7.8e+242:
		tmp = t_1
	else:
		tmp = (t * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.2e+133)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 4.5e+108)
		tmp = t_1;
	elseif (t <= 4.1e+139)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (t <= 7.8e+242)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -1.2e+133)
		tmp = -y / (a / t);
	elseif (t <= 4.5e+108)
		tmp = t_1;
	elseif (t <= 4.1e+139)
		tmp = y * (-t / a);
	elseif (t <= 7.8e+242)
		tmp = t_1;
	else
		tmp = (t * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+133], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+108], t$95$1, If[LessEqual[t, 4.1e+139], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e+242], t$95$1, N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1999999999999999e133

   1. Initial program 84.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-/l* 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in x around 0 66.9%

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

      1. associate-/l* 74.4%

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

      2. associate-*r/ 74.4%

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

      3. neg-mul-1 74.4%

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

      4. associate-/r/ 74.5%

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

      5. *-commutative 74.5%

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

      6. distribute-frac-neg 74.5%

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

   9. Simplified 74.5%

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

       1. distribute-rgt-neg-out 74.5%

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

       2. clear-num 74.4%

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

       3. div-inv 74.5%

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

       4. distribute-neg-frac 74.5%

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

   11. Applied egg-rr 74.5%

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

   if -1.1999999999999999e133 < t < 4.5e108 or 4.1000000000000002e139 < t < 7.8000000000000003e242

   1. Initial program 95.0%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in z around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*r/ 80.6%

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

   6. Simplified 80.6%

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

   if 4.5e108 < t < 4.1000000000000002e139

   1. Initial program 82.7%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 65.0%

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

      1. associate-/l* 82.0%

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

      2. associate-*r/ 82.0%

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

      3. neg-mul-1 82.0%

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

      4. associate-/r/ 82.3%

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

      5. *-commutative 82.3%

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

      6. distribute-frac-neg 82.3%

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

   9. Simplified 82.3%

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

   if 7.8000000000000003e242 < t

   1. Initial program 93.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 93.1%

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

      1. mul-1-neg 93.1%

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

      2. unsub-neg 93.1%

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

      3. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in x around 0 86.0%

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

      1. associate-/l* 85.8%

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

      2. associate-*r/ 85.8%

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

      3. neg-mul-1 85.8%

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

      4. associate-/r/ 79.6%

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

      5. *-commutative 79.6%

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

      6. distribute-frac-neg 79.6%

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

   9. Simplified 79.6%

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

       1. distribute-neg-frac 79.6%

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

       2. associate-*r/ 86.0%

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

   11. Applied egg-rr 86.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+242}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+244}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+133)
   (/ (- y) (/ a t))
   (if (<= t 4.5e+108)
     (+ x (/ z (/ a y)))
     (if (<= t 2.8e+140)
       (* y (/ (- t) a))
       (if (<= t 4.1e+244) (+ x (* z (/ y a))) (/ (* t (- y)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = x + (z / (a / y));
	} else if (t <= 2.8e+140) {
		tmp = y * (-t / a);
	} else if (t <= 4.1e+244) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.5d+133)) then
        tmp = -y / (a / t)
    else if (t <= 4.5d+108) then
        tmp = x + (z / (a / y))
    else if (t <= 2.8d+140) then
        tmp = y * (-t / a)
    else if (t <= 4.1d+244) then
        tmp = x + (z * (y / a))
    else
        tmp = (t * -y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = x + (z / (a / y));
	} else if (t <= 2.8e+140) {
		tmp = y * (-t / a);
	} else if (t <= 4.1e+244) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+133:
		tmp = -y / (a / t)
	elif t <= 4.5e+108:
		tmp = x + (z / (a / y))
	elif t <= 2.8e+140:
		tmp = y * (-t / a)
	elif t <= 4.1e+244:
		tmp = x + (z * (y / a))
	else:
		tmp = (t * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+133)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 4.5e+108)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 2.8e+140)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (t <= 4.1e+244)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(Float64(t * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+133)
		tmp = -y / (a / t);
	elseif (t <= 4.5e+108)
		tmp = x + (z / (a / y));
	elseif (t <= 2.8e+140)
		tmp = y * (-t / a);
	elseif (t <= 4.1e+244)
		tmp = x + (z * (y / a));
	else
		tmp = (t * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+133], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+108], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+140], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+244], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.50000000000000003e133

   1. Initial program 84.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-/l* 94.9%

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

   6. Simplified 94.9%

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

   7. Taylor expanded in x around 0 66.9%

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

      1. associate-/l* 74.4%

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

      2. associate-*r/ 74.4%

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

      3. neg-mul-1 74.4%

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

      4. associate-/r/ 74.5%

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

      5. *-commutative 74.5%

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

      6. distribute-frac-neg 74.5%

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

   9. Simplified 74.5%

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

       1. distribute-rgt-neg-out 74.5%

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

       2. clear-num 74.4%

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

       3. div-inv 74.5%

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

       4. distribute-neg-frac 74.5%

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

   11. Applied egg-rr 74.5%

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

   if -1.50000000000000003e133 < t < 4.5e108

   1. Initial program 95.1%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. associate-*r/ 82.4%

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

   6. Simplified 82.4%

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

      1. clear-num 82.4%

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

      2. div-inv 82.9%

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

   8. Applied egg-rr 82.9%

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

   if 4.5e108 < t < 2.79999999999999983e140

   1. Initial program 82.7%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

      3. associate-/l* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 65.0%

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

      1. associate-/l* 82.0%

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

      2. associate-*r/ 82.0%

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

      3. neg-mul-1 82.0%

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

      4. associate-/r/ 82.3%

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

      5. *-commutative 82.3%

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

      6. distribute-frac-neg 82.3%

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

   9. Simplified 82.3%

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

   if 2.79999999999999983e140 < t < 4.09999999999999993e244

   1. Initial program 94.4%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-*r/ 63.0%

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

   6. Simplified 63.0%

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

   if 4.09999999999999993e244 < t

   1. Initial program 93.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 93.1%

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

      1. mul-1-neg 93.1%

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

      2. unsub-neg 93.1%

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

      3. associate-/l* 92.9%

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

   6. Simplified 92.9%

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

   7. Taylor expanded in x around 0 86.0%

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

      1. associate-/l* 85.8%

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

      2. associate-*r/ 85.8%

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

      3. neg-mul-1 85.8%

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

      4. associate-/r/ 79.6%

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

      5. *-commutative 79.6%

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

      6. distribute-frac-neg 79.6%

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

   9. Simplified 79.6%

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

       1. distribute-neg-frac 79.6%

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

       2. associate-*r/ 86.0%

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

   11. Applied egg-rr 86.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+244}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]

Alternative 4: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -880000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -880000000000.0)
   (+ x (/ z (/ a y)))
   (if (<= z 6.2e-29) (- x (/ t (/ a y))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -880000000000.0) {
		tmp = x + (z / (a / y));
	} else if (z <= 6.2e-29) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (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) :: tmp
    if (z <= (-880000000000.0d0)) then
        tmp = x + (z / (a / y))
    else if (z <= 6.2d-29) then
        tmp = x - (t / (a / y))
    else
        tmp = x + (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 tmp;
	if (z <= -880000000000.0) {
		tmp = x + (z / (a / y));
	} else if (z <= 6.2e-29) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -880000000000.0:
		tmp = x + (z / (a / y))
	elif z <= 6.2e-29:
		tmp = x - (t / (a / y))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -880000000000.0)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 6.2e-29)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -880000000000.0)
		tmp = x + (z / (a / y));
	elseif (z <= 6.2e-29)
		tmp = x - (t / (a / y));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -880000000000.0], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-29], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.8e11

   1. Initial program 94.3%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in z around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*r/ 84.3%

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

   6. Simplified 84.3%

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

      1. clear-num 84.3%

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

      2. div-inv 84.4%

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

   8. Applied egg-rr 84.4%

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

   if -8.8e11 < z < 6.20000000000000052e-29

   1. Initial program 95.5%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

      3. associate-/l* 91.7%

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

   6. Simplified 91.7%

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

   if 6.20000000000000052e-29 < z

   1. Initial program 88.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 77.6%

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

      1. *-commutative 77.6%

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

      2. associate-*r/ 84.3%

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

   6. Simplified 84.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -880000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 49.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+114} \lor \neg \left(y \leq 5.4\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.5e+114) (not (<= y 5.4))) (* y (/ (- t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e+114) || !(y <= 5.4)) {
		tmp = y * (-t / 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 <= (-1.5d+114)) .or. (.not. (y <= 5.4d0))) then
        tmp = y * (-t / 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 <= -1.5e+114) || !(y <= 5.4)) {
		tmp = y * (-t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.5e+114) or not (y <= 5.4):
		tmp = y * (-t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.5e+114) || !(y <= 5.4))
		tmp = Float64(y * Float64(Float64(-t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.5e+114) || ~((y <= 5.4)))
		tmp = y * (-t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.5e+114], N[Not[LessEqual[y, 5.4]], $MachinePrecision]], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e114 or 5.4000000000000004 < y

   1. Initial program 87.5%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. unsub-neg 63.3%

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

      3. associate-/l* 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in x around 0 49.9%

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

      1. associate-/l* 54.0%

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

      2. associate-*r/ 54.0%

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

      3. neg-mul-1 54.0%

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

      4. associate-/r/ 54.1%

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

      5. *-commutative 54.1%

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

      6. distribute-frac-neg 54.1%

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

   9. Simplified 54.1%

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

   if -1.5e114 < y < 5.4000000000000004

   1. Initial program 97.3%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around inf 52.7%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+114} \lor \neg \left(y \leq 5.4\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq 600:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.5e+51) (* t (/ y (- a))) (if (<= y 600.0) x (* y (/ (- t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.5e+51) {
		tmp = t * (y / -a);
	} else if (y <= 600.0) {
		tmp = x;
	} else {
		tmp = y * (-t / 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 <= (-1.5d+51)) then
        tmp = t * (y / -a)
    else if (y <= 600.0d0) then
        tmp = x
    else
        tmp = y * (-t / 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 <= -1.5e+51) {
		tmp = t * (y / -a);
	} else if (y <= 600.0) {
		tmp = x;
	} else {
		tmp = y * (-t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.5e+51:
		tmp = t * (y / -a)
	elif y <= 600.0:
		tmp = x
	else:
		tmp = y * (-t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.5e+51)
		tmp = Float64(t * Float64(y / Float64(-a)));
	elseif (y <= 600.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.5e+51)
		tmp = t * (y / -a);
	elseif (y <= 600.0)
		tmp = x;
	else
		tmp = y * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.5e+51], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 600.0], x, N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e51

   1. Initial program 91.4%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. unsub-neg 61.1%

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

      3. associate-/l* 63.3%

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

   6. Simplified 63.3%

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

   7. Taylor expanded in x around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. associate-*r/ 48.2%

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

      3. distribute-rgt-neg-out 48.2%

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

      4. distribute-neg-frac 48.2%

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

      5. associate-*r/ 45.9%

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

      6. associate-/l* 46.2%

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

   9. Simplified 46.2%

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

       1. associate-/l* 45.9%

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

       2. associate-*r/ 48.2%

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

       3. *-commutative 48.2%

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

       4. frac-2neg 48.2%

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

       5. remove-double-neg 48.2%

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

   11. Applied egg-rr 48.2%

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

   if -1.5e51 < y < 600

   1. Initial program 98.5%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 54.3%

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

   if 600 < y

   1. Initial program 84.4%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. unsub-neg 62.1%

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

      3. associate-/l* 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in x around 0 48.8%

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

      1. associate-/l* 54.7%

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

      2. associate-*r/ 54.7%

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

      3. neg-mul-1 54.7%

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

      4. associate-/r/ 55.0%

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

      5. *-commutative 55.0%

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

      6. distribute-frac-neg 55.0%

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

   9. Simplified 55.0%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq 600:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 7: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / 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-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 8: 39.8% 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-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Taylor expanded in x around inf 36.4%

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

5. Final simplification 36.4%

   \[\leadsto x \]

Developer target: 99.2% 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 2023297 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))