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

Percentage Accurate: 93.2% → 98.8%

Time: 10.5s

Alternatives: 11

Speedup: 0.8×

• 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: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+301}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (<= t_1 -2e+301)
     (+ x (* y (/ (- t z) a)))
     (if (<= t_1 1e+304) (+ x (/ (* y (- t z)) a)) (* (/ y a) (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if (t_1 <= -2e+301) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 1e+304) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * y
    if (t_1 <= (-2d+301)) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 1d+304) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if (t_1 <= -2e+301) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 1e+304) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if t_1 <= -2e+301:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 1e+304:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if (t_1 <= -2e+301)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 1e+304)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if (t_1 <= -2e+301)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 1e+304)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+301], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -2.00000000000000011e301

   1. Initial program 71.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -2.00000000000000011e301 < (*.f64 y (-.f64 z t)) < 9.9999999999999994e303

   1. Initial program 99.4%

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

   if 9.9999999999999994e303 < (*.f64 y (-.f64 z t))

   1. Initial program 77.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around 0 77.3%

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

      1. associate-*r/ 77.3%

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

      2. neg-mul-1 77.3%

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

      3. *-commutative 77.3%

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

      4. distribute-lft-neg-in 77.3%

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

      5. associate-*r/ 99.9%

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

      6. *-commutative 99.9%

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

      7. neg-sub0 99.9%

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

      8. sub-neg 99.9%

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

      9. +-commutative 99.9%

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

      10. associate--r+ 99.9%

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

      11. neg-sub0 99.9%

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

      12. remove-double-neg 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -2 \cdot 10^{+301}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \leq 10^{+304}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -3.3e+56)
     t_1
     (if (<= t -6.2e-10) (* z (/ y (- a))) (if (<= t 2.05e+123) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -3.3e+56) {
		tmp = t_1;
	} else if (t <= -6.2e-10) {
		tmp = z * (y / -a);
	} else if (t <= 2.05e+123) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-3.3d+56)) then
        tmp = t_1
    else if (t <= (-6.2d-10)) then
        tmp = z * (y / -a)
    else if (t <= 2.05d+123) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -3.3e+56) {
		tmp = t_1;
	} else if (t <= -6.2e-10) {
		tmp = z * (y / -a);
	} else if (t <= 2.05e+123) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -3.3e+56:
		tmp = t_1
	elif t <= -6.2e-10:
		tmp = z * (y / -a)
	elif t <= 2.05e+123:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -3.3e+56)
		tmp = t_1;
	elseif (t <= -6.2e-10)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (t <= 2.05e+123)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -3.3e+56)
		tmp = t_1;
	elseif (t <= -6.2e-10)
		tmp = z * (y / -a);
	elseif (t <= 2.05e+123)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+56], t$95$1, If[LessEqual[t, -6.2e-10], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+123], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.30000000000000002e56 or 2.04999999999999995e123 < t

   1. Initial program 92.6%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. div-inv 87.7%

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

      4. associate-*l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 66.4%

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

      1. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

   if -3.30000000000000002e56 < t < -6.2000000000000003e-10

   1. Initial program 81.0%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. associate-/l* 55.4%

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

      3. distribute-rgt-neg-in 55.4%

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

      4. distribute-frac-neg2 55.4%

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

   7. Simplified 55.4%

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

   8. Taylor expanded in y around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. associate-*l/ 68.3%

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

      3. distribute-rgt-neg-in 68.3%

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

   10. Simplified 68.3%

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

   if -6.2000000000000003e-10 < t < 2.04999999999999995e123

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 52.7%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+56} \lor \neg \left(t \leq 2.9 \cdot 10^{+121}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+56) (not (<= t 2.9e+121)))
   (+ x (* t (/ y a)))
   (- x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+56) || !(t <= 2.9e+121)) {
		tmp = x + (t * (y / a));
	} 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 ((t <= (-2.4d+56)) .or. (.not. (t <= 2.9d+121))) then
        tmp = x + (t * (y / a))
    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 ((t <= -2.4e+56) || !(t <= 2.9e+121)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+56) or not (t <= 2.9e+121):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+56) || !(t <= 2.9e+121))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 ((t <= -2.4e+56) || ~((t <= 2.9e+121)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+56], N[Not[LessEqual[t, 2.9e+121]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.40000000000000013e56 or 2.8999999999999999e121 < t

   1. Initial program 92.6%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. div-inv 87.7%

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

      4. associate-*l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. distribute-neg-frac2 87.4%

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

      3. associate-*r/ 94.1%

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

   7. Simplified 94.1%

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

      1. sub-neg 94.1%

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

      2. distribute-rgt-neg-in 94.1%

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

      3. distribute-frac-neg 94.1%

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

      4. frac-2neg 94.1%

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

   9. Applied egg-rr 94.1%

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

   if -2.40000000000000013e56 < t < 2.8999999999999999e121

   1. Initial program 94.1%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 84.9%

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

      1. *-commutative 84.9%

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

      2. associate-/l* 87.1%

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

   7. Applied egg-rr 87.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+56} \lor \neg \left(t \leq 2.9 \cdot 10^{+121}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+56} \lor \neg \left(t \leq 2.9 \cdot 10^{+121}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.7e+56) (not (<= t 2.9e+121)))
   (+ x (* t (/ y a)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.7e+56) || !(t <= 2.9e+121)) {
		tmp = x + (t * (y / a));
	} 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 <= (-2.7d+56)) .or. (.not. (t <= 2.9d+121))) then
        tmp = x + (t * (y / a))
    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 <= -2.7e+56) || !(t <= 2.9e+121)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.7e+56) or not (t <= 2.9e+121):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.7e+56) || !(t <= 2.9e+121))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 <= -2.7e+56) || ~((t <= 2.9e+121)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.7e+56], N[Not[LessEqual[t, 2.9e+121]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.7000000000000001e56 or 2.8999999999999999e121 < t

   1. Initial program 92.6%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. div-inv 87.7%

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

      4. associate-*l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 87.4%

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

      1. mul-1-neg 87.4%

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

      2. distribute-neg-frac2 87.4%

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

      3. associate-*r/ 94.1%

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

   7. Simplified 94.1%

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

      1. sub-neg 94.1%

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

      2. distribute-rgt-neg-in 94.1%

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

      3. distribute-frac-neg 94.1%

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

      4. frac-2neg 94.1%

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

   9. Applied egg-rr 94.1%

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

   if -2.7000000000000001e56 < t < 2.8999999999999999e121

   1. Initial program 94.1%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 84.9%

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

      1. associate-/l* 85.6%

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

   7. Simplified 85.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+56} \lor \neg \left(t \leq 2.9 \cdot 10^{+121}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+91} \lor \neg \left(z \leq 8.5 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.8e+91) (not (<= z 8.5e+95)))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.8e+91) || !(z <= 8.5e+95)) {
		tmp = (y / a) * (t - z);
	} 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 ((z <= (-5.8d+91)) .or. (.not. (z <= 8.5d+95))) then
        tmp = (y / a) * (t - z)
    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 ((z <= -5.8e+91) || !(z <= 8.5e+95)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.8e+91) or not (z <= 8.5e+95):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.8e+91) || !(z <= 8.5e+95))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.8e+91) || ~((z <= 8.5e+95)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.8e+91], N[Not[LessEqual[z, 8.5e+95]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000028e91 or 8.5000000000000002e95 < z

   1. Initial program 87.6%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

      3. *-commutative 71.4%

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

      4. distribute-lft-neg-in 71.4%

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

      5. associate-*r/ 81.0%

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

      6. *-commutative 81.0%

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

      7. neg-sub0 81.0%

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

      8. sub-neg 81.0%

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

      9. +-commutative 81.0%

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

      10. associate--r+ 81.0%

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

      11. neg-sub0 81.0%

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

      12. remove-double-neg 81.0%

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

   7. Simplified 81.0%

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

   if -5.80000000000000028e91 < z < 8.5000000000000002e95

   1. Initial program 96.2%

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

      1. associate-*r/ 96.2%

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

      2. *-commutative 96.2%

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

      3. div-inv 96.2%

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

      4. associate-*l* 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-neg-frac2 83.4%

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

      3. associate-*r/ 88.2%

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

   7. Simplified 88.2%

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

      1. sub-neg 88.2%

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

      2. distribute-rgt-neg-in 88.2%

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

      3. distribute-frac-neg 88.2%

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

      4. frac-2neg 88.2%

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

   9. Applied egg-rr 88.2%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+91} \lor \neg \left(z \leq 8.5 \cdot 10^{+95}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.05 \cdot 10^{+113}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.05e+113) x (if (<= a 9.8e+152) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.05e+113) {
		tmp = x;
	} else if (a <= 9.8e+152) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.05d+113)) then
        tmp = x
    else if (a <= 9.8d+152) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.05e+113) {
		tmp = x;
	} else if (a <= 9.8e+152) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.05e+113:
		tmp = x
	elif a <= 9.8e+152:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.05e+113)
		tmp = x;
	elseif (a <= 9.8e+152)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.05e+113)
		tmp = x;
	elseif (a <= 9.8e+152)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.05e+113], x, If[LessEqual[a, 9.8e+152], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.04999999999999998e113 or 9.8000000000000008e152 < a

   1. Initial program 83.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 80.1%

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

   if -3.04999999999999998e113 < a < 9.8000000000000008e152

   1. Initial program 97.0%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around 0 71.2%

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

      1. associate-*r/ 71.2%

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

      2. neg-mul-1 71.2%

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

      3. *-commutative 71.2%

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

      4. distribute-lft-neg-in 71.2%

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

      5. associate-*r/ 71.2%

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

      6. *-commutative 71.2%

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

      7. neg-sub0 71.2%

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

      8. sub-neg 71.2%

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

      9. +-commutative 71.2%

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

      10. associate--r+ 71.2%

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

      11. neg-sub0 71.2%

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

      12. remove-double-neg 71.2%

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

   7. Simplified 71.2%

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

Alternative 7: 52.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+47} \lor \neg \left(t \leq 2.9 \cdot 10^{+121}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+47) (not (<= t 2.9e+121))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+47) || !(t <= 2.9e+121)) {
		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 ((t <= (-1.4d+47)) .or. (.not. (t <= 2.9d+121))) 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 ((t <= -1.4e+47) || !(t <= 2.9e+121)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+47) or not (t <= 2.9e+121):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+47) || !(t <= 2.9e+121))
		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 ((t <= -1.4e+47) || ~((t <= 2.9e+121)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+47], N[Not[LessEqual[t, 2.9e+121]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.39999999999999994e47 or 2.8999999999999999e121 < t

   1. Initial program 93.0%

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

      1. associate-*r/ 88.3%

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

      2. *-commutative 88.3%

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

      3. div-inv 88.3%

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

      4. associate-*l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 65.4%

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

      1. associate-/l* 70.2%

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

   7. Simplified 70.2%

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

   if -1.39999999999999994e47 < t < 2.8999999999999999e121

   1. Initial program 94.0%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 51.4%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+47} \lor \neg \left(t \leq 2.9 \cdot 10^{+121}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{+124}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 8.2e+124) (+ x (* y (/ (- t z) a))) (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 8.2e+124) {
		tmp = x + (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 (t <= 8.2d+124) then
        tmp = x + (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 (t <= 8.2e+124) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 8.2e+124:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 8.2e+124)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 8.2e+124)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 8.2e+124], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 8.20000000000000002e124

   1. Initial program 93.5%

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

      1. associate-/l* 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. Add Preprocessing

   if 8.20000000000000002e124 < t

   1. Initial program 94.3%

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

      1. associate-*r/ 75.1%

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

      2. *-commutative 75.1%

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

      3. div-inv 75.2%

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

      4. associate-*l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 94.3%

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

      1. mul-1-neg 94.3%

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

      2. distribute-neg-frac2 94.3%

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

      3. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. frac-2neg 100.0%

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

   9. Applied egg-rr 100.0%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 8.2 \cdot 10^{+124}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{a}\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- z t) (* y (/ -1.0 a)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((z - t) * (y * (-1.0 / 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 * ((-1.0d0) / a)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((z - t) * (y * (-1.0 / a)));
}

Python

def code(x, y, z, t, a):
	return x + ((z - t) * (y * (-1.0 / a)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(z - t) * Float64(y * Float64(-1.0 / a))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((z - t) * (y * (-1.0 / a)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(z - t), $MachinePrecision] * N[(y * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.6%

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

   1. associate-*r/ 92.9%

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

   2. *-commutative 92.9%

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

   3. div-inv 92.9%

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

   4. associate-*l* 97.5%

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

4. Applied egg-rr 97.5%

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

5. Final simplification 97.5%

   \[\leadsto x + \left(z - t\right) \cdot \left(y \cdot \frac{-1}{a}\right) \]
6. Add Preprocessing

Alternative 10: 39.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 1.75e-68) x (* a (/ x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.75e-68) {
		tmp = x;
	} else {
		tmp = a * (x / 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 <= 1.75d-68) then
        tmp = x
    else
        tmp = a * (x / 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 <= 1.75e-68) {
		tmp = x;
	} else {
		tmp = a * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.75e-68:
		tmp = x
	else:
		tmp = a * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.75e-68)
		tmp = x;
	else
		tmp = Float64(a * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.75e-68)
		tmp = x;
	else
		tmp = a * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.75e-68], x, N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.75000000000000006e-68

   1. Initial program 95.6%

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

      1. associate-/l* 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. Add Preprocessing

   5. Taylor expanded in x around inf 45.5%

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

   if 1.75000000000000006e-68 < y

   1. Initial program 89.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 a around 0 78.1%

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

   6. Taylor expanded in a around inf 16.0%

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

      1. associate-/l* 35.0%

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

   8. Applied egg-rr 35.0%

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

Alternative 11: 39.6% 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 93.6%

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

   1. associate-/l* 92.9%

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

3. Simplified 92.9%

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

5. Taylor expanded in x around inf 40.6%

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

Developer Target 1: 99.1% 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 2024137 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t)))))))

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