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

Percentage Accurate: 93.1% → 98.8%

Time: 12.9s

Alternatives: 16

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.004:\\ \;\;\;\;x + y \cdot \left(\frac{1}{a} \cdot \left(t - z\right)\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -0.004)
   (+ x (* y (* (/ 1.0 a) (- t z))))
   (if (<= a 1.08e-68) (+ x (/ (* y (- t z)) a)) (+ x (* y (/ (- t z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -0.004) {
		tmp = x + (y * ((1.0 / a) * (t - z)));
	} else if (a <= 1.08e-68) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + (y * ((t - 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 (a <= (-0.004d0)) then
        tmp = x + (y * ((1.0d0 / a) * (t - z)))
    else if (a <= 1.08d-68) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = x + (y * ((t - 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 (a <= -0.004) {
		tmp = x + (y * ((1.0 / a) * (t - z)));
	} else if (a <= 1.08e-68) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -0.004:
		tmp = x + (y * ((1.0 / a) * (t - z)))
	elif a <= 1.08e-68:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -0.004)
		tmp = Float64(x + Float64(y * Float64(Float64(1.0 / a) * Float64(t - z))));
	elseif (a <= 1.08e-68)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -0.004)
		tmp = x + (y * ((1.0 / a) * (t - z)));
	elseif (a <= 1.08e-68)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -0.004], N[(x + N[(y * N[(N[(1.0 / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.08e-68], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.0040000000000000001

   1. Initial program 84.4%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -0.0040000000000000001 < a < 1.0799999999999999e-68

   1. Initial program 99.1%

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

   if 1.0799999999999999e-68 < a

   1. Initial program 85.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.004:\\ \;\;\;\;x + y \cdot \left(\frac{1}{a} \cdot \left(t - z\right)\right)\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 47.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{z}{-a}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))) (t_2 (* y (/ z (- a)))))
   (if (<= z -4e+106)
     t_2
     (if (<= z -1.05e+74)
       x
       (if (<= z -3e+50)
         t_2
         (if (<= z -6e-153)
           t_1
           (if (<= z -1.1e-243)
             x
             (if (<= z 1.8e-265)
               (/ y (/ a t))
               (if (<= z 1.42e-179) x (if (<= z 1.1e+46) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double t_2 = y * (z / -a);
	double tmp;
	if (z <= -4e+106) {
		tmp = t_2;
	} else if (z <= -1.05e+74) {
		tmp = x;
	} else if (z <= -3e+50) {
		tmp = t_2;
	} else if (z <= -6e-153) {
		tmp = t_1;
	} else if (z <= -1.1e-243) {
		tmp = x;
	} else if (z <= 1.8e-265) {
		tmp = y / (a / t);
	} else if (z <= 1.42e-179) {
		tmp = x;
	} else if (z <= 1.1e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / a)
    t_2 = y * (z / -a)
    if (z <= (-4d+106)) then
        tmp = t_2
    else if (z <= (-1.05d+74)) then
        tmp = x
    else if (z <= (-3d+50)) then
        tmp = t_2
    else if (z <= (-6d-153)) then
        tmp = t_1
    else if (z <= (-1.1d-243)) then
        tmp = x
    else if (z <= 1.8d-265) then
        tmp = y / (a / t)
    else if (z <= 1.42d-179) then
        tmp = x
    else if (z <= 1.1d+46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double t_2 = y * (z / -a);
	double tmp;
	if (z <= -4e+106) {
		tmp = t_2;
	} else if (z <= -1.05e+74) {
		tmp = x;
	} else if (z <= -3e+50) {
		tmp = t_2;
	} else if (z <= -6e-153) {
		tmp = t_1;
	} else if (z <= -1.1e-243) {
		tmp = x;
	} else if (z <= 1.8e-265) {
		tmp = y / (a / t);
	} else if (z <= 1.42e-179) {
		tmp = x;
	} else if (z <= 1.1e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	t_2 = y * (z / -a)
	tmp = 0
	if z <= -4e+106:
		tmp = t_2
	elif z <= -1.05e+74:
		tmp = x
	elif z <= -3e+50:
		tmp = t_2
	elif z <= -6e-153:
		tmp = t_1
	elif z <= -1.1e-243:
		tmp = x
	elif z <= 1.8e-265:
		tmp = y / (a / t)
	elif z <= 1.42e-179:
		tmp = x
	elif z <= 1.1e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	t_2 = Float64(y * Float64(z / Float64(-a)))
	tmp = 0.0
	if (z <= -4e+106)
		tmp = t_2;
	elseif (z <= -1.05e+74)
		tmp = x;
	elseif (z <= -3e+50)
		tmp = t_2;
	elseif (z <= -6e-153)
		tmp = t_1;
	elseif (z <= -1.1e-243)
		tmp = x;
	elseif (z <= 1.8e-265)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 1.42e-179)
		tmp = x;
	elseif (z <= 1.1e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	t_2 = y * (z / -a);
	tmp = 0.0;
	if (z <= -4e+106)
		tmp = t_2;
	elseif (z <= -1.05e+74)
		tmp = x;
	elseif (z <= -3e+50)
		tmp = t_2;
	elseif (z <= -6e-153)
		tmp = t_1;
	elseif (z <= -1.1e-243)
		tmp = x;
	elseif (z <= 1.8e-265)
		tmp = y / (a / t);
	elseif (z <= 1.42e-179)
		tmp = x;
	elseif (z <= 1.1e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4e+106], t$95$2, If[LessEqual[z, -1.05e+74], x, If[LessEqual[z, -3e+50], t$95$2, If[LessEqual[z, -6e-153], t$95$1, If[LessEqual[z, -1.1e-243], x, If[LessEqual[z, 1.8e-265], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.42e-179], x, If[LessEqual[z, 1.1e+46], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.00000000000000036e106 or -1.0499999999999999e74 < z < -2.9999999999999998e50 or 1.1e46 < z

   1. Initial program 84.1%

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

      1. associate-/l* 86.2%

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

   3. Simplified 86.2%

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

   5. Taylor expanded in z around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-/l* 61.9%

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

      3. distribute-lft-neg-in 61.9%

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

   7. Simplified 61.9%

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

   if -4.00000000000000036e106 < z < -1.0499999999999999e74 or -6e-153 < z < -1.1e-243 or 1.8000000000000001e-265 < z < 1.42e-179

   1. Initial program 93.4%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 70.3%

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

   if -2.9999999999999998e50 < z < -6e-153 or 1.42e-179 < z < 1.1e46

   1. Initial program 96.9%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in t around inf 55.6%

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

      1. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

   if -1.1e-243 < z < 1.8000000000000001e-265

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-/l* 78.2%

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

   7. Simplified 78.2%

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

      1. clear-num 78.3%

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

      2. un-div-inv 78.3%

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

   9. Applied egg-rr 78.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-243}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+56} \lor \neg \left(a \leq 2 \cdot 10^{-71}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.4e+56) (not (<= a 2e-71)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ (* y (- t z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.4e+56) || !(a <= 2e-71)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - 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 ((a <= (-7.4d+56)) .or. (.not. (a <= 2d-71))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y * (t - 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 ((a <= -7.4e+56) || !(a <= 2e-71)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.4e+56) or not (a <= 2e-71):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.4e+56) || !(a <= 2e-71))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.4e+56) || ~((a <= 2e-71)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.4e+56], N[Not[LessEqual[a, 2e-71]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.39999999999999994e56 or 1.9999999999999998e-71 < a

   1. Initial program 83.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -7.39999999999999994e56 < a < 1.9999999999999998e-71

   1. Initial program 99.1%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+56} \lor \neg \left(a \leq 2 \cdot 10^{-71}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-71} \lor \neg \left(y \leq 3.2 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.5e-71) (not (<= y 3.2e-70))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.5e-71) || !(y <= 3.2e-70)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.5d-71)) .or. (.not. (y <= 3.2d-70))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.5e-71) || !(y <= 3.2e-70)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.5e-71) or not (y <= 3.2e-70):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.5e-71) || !(y <= 3.2e-70))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.5e-71) || ~((y <= 3.2e-70)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.5e-71], N[Not[LessEqual[y, 3.2e-70]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999999e-71 or 3.1999999999999997e-70 < y

   1. Initial program 88.4%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around 0 71.9%

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

       1. mul-1-neg 71.9%

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

       2. associate-*l/ 78.4%

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

       3. distribute-rgt-neg-in 78.4%

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

       4. sub-neg 78.4%

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

       5. distribute-neg-in 78.4%

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

       6. remove-double-neg 78.4%

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

       7. +-commutative 78.4%

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

       8. sub-neg 78.4%

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

       9. associate-*l/ 71.9%

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

       10. associate-/l* 80.5%

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

   11. Simplified 80.5%

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

   if -2.49999999999999999e-71 < y < 3.1999999999999997e-70

   1. Initial program 97.7%

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

      1. associate-/l* 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in x around inf 61.0%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-71} \lor \neg \left(y \leq 3.2 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00026 \lor \neg \left(x \leq 1.12 \cdot 10^{+82}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -0.00026) (not (<= x 1.12e+82)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -0.00026) || !(x <= 1.12e+82)) {
		tmp = x + (y * (t / 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) :: tmp
    if ((x <= (-0.00026d0)) .or. (.not. (x <= 1.12d+82))) then
        tmp = x + (y * (t / 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 tmp;
	if ((x <= -0.00026) || !(x <= 1.12e+82)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -0.00026) or not (x <= 1.12e+82):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -0.00026) || !(x <= 1.12e+82))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -0.00026) || ~((x <= 1.12e+82)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -0.00026], N[Not[LessEqual[x, 1.12e+82]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.59999999999999977e-4 or 1.11999999999999998e82 < x

   1. Initial program 92.1%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

      1. clear-num 90.5%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. clear-num 90.5%

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

      2. associate-/r/ 91.4%

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

   8. Applied egg-rr 91.4%

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

   9. Taylor expanded in z around 0 80.9%

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

       1. sub-neg 80.9%

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

       2. mul-1-neg 80.9%

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

       3. associate-*l/ 80.2%

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

       4. distribute-rgt-neg-in 80.2%

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

       5. distribute-rgt-neg-out 80.2%

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

       6. remove-double-neg 80.2%

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

       7. associate-/r/ 84.4%

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

   11. Simplified 84.4%

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

       1. associate-/r/ 80.2%

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

   13. Applied egg-rr 80.2%

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

   if -2.59999999999999977e-4 < x < 1.11999999999999998e82

   1. Initial program 91.3%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in x around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-*r/ 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. neg-sub0 78.6%

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

      5. div-sub 76.6%

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

      6. associate--r- 76.6%

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

      7. neg-sub0 76.6%

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

      8. +-commutative 76.6%

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

      9. sub-neg 76.6%

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

      10. distribute-lft-out-- 75.9%

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

      11. associate-/l* 75.8%

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

      12. *-commutative 75.8%

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

      13. associate-/l* 74.6%

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

      14. *-commutative 74.6%

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

      15. associate-*l/ 70.9%

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

      16. associate-*r/ 76.4%

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

      17. distribute-rgt-out-- 81.3%

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

   9. Simplified 81.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00026 \lor \neg \left(x \leq 1.12 \cdot 10^{+82}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00026 \lor \neg \left(x \leq 3.25 \cdot 10^{+91}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -0.00026) (not (<= x 3.25e+91)))
   (+ x (/ t (/ a y)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -0.00026) || !(x <= 3.25e+91)) {
		tmp = x + (t / (a / y));
	} 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) :: tmp
    if ((x <= (-0.00026d0)) .or. (.not. (x <= 3.25d+91))) then
        tmp = x + (t / (a / y))
    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 tmp;
	if ((x <= -0.00026) || !(x <= 3.25e+91)) {
		tmp = x + (t / (a / y));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -0.00026) or not (x <= 3.25e+91):
		tmp = x + (t / (a / y))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -0.00026) || !(x <= 3.25e+91))
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -0.00026) || ~((x <= 3.25e+91)))
		tmp = x + (t / (a / y));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -0.00026], N[Not[LessEqual[x, 3.25e+91]], $MachinePrecision]], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.59999999999999977e-4 or 3.2499999999999999e91 < x

   1. Initial program 92.1%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

      1. clear-num 90.5%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. clear-num 90.5%

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

      2. associate-/r/ 91.4%

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

   8. Applied egg-rr 91.4%

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

   9. Taylor expanded in z around 0 80.9%

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

       1. sub-neg 80.9%

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

       2. mul-1-neg 80.9%

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

       3. associate-*l/ 80.2%

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

       4. distribute-rgt-neg-in 80.2%

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

       5. distribute-rgt-neg-out 80.2%

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

       6. remove-double-neg 80.2%

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

       7. associate-/r/ 84.4%

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

   11. Simplified 84.4%

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

   if -2.59999999999999977e-4 < x < 3.2499999999999999e91

   1. Initial program 91.3%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.6%

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

      2. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in x around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-*r/ 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. neg-sub0 78.6%

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

      5. div-sub 76.6%

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

      6. associate--r- 76.6%

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

      7. neg-sub0 76.6%

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

      8. +-commutative 76.6%

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

      9. sub-neg 76.6%

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

      10. distribute-lft-out-- 75.9%

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

      11. associate-/l* 75.8%

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

      12. *-commutative 75.8%

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

      13. associate-/l* 74.6%

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

      14. *-commutative 74.6%

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

      15. associate-*l/ 70.9%

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

      16. associate-*r/ 76.4%

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

      17. distribute-rgt-out-- 81.3%

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

   9. Simplified 81.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00026 \lor \neg \left(x \leq 3.25 \cdot 10^{+91}\right):\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-164}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.8e-164)
   (* (- t z) (/ y a))
   (if (<= y 2.1e-83) x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.8e-164) {
		tmp = (t - z) * (y / a);
	} else if (y <= 2.1e-83) {
		tmp = x;
	} else {
		tmp = y * ((t - 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 (y <= (-5.8d-164)) then
        tmp = (t - z) * (y / a)
    else if (y <= 2.1d-83) then
        tmp = x
    else
        tmp = y * ((t - 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 (y <= -5.8e-164) {
		tmp = (t - z) * (y / a);
	} else if (y <= 2.1e-83) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.8e-164:
		tmp = (t - z) * (y / a)
	elif y <= 2.1e-83:
		tmp = x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.8e-164)
		tmp = Float64(Float64(t - z) * Float64(y / a));
	elseif (y <= 2.1e-83)
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.8e-164)
		tmp = (t - z) * (y / a);
	elseif (y <= 2.1e-83)
		tmp = x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.8e-164], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-83], x, N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e-164

   1. Initial program 91.6%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. clear-num 90.9%

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

      2. un-div-inv 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in x around 0 69.4%

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

      1. mul-1-neg 69.4%

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

      2. associate-*r/ 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

      4. neg-sub0 70.7%

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

      5. div-sub 69.7%

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

      6. associate--r- 69.7%

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

      7. neg-sub0 69.7%

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

      8. +-commutative 69.7%

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

      9. sub-neg 69.7%

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

      10. distribute-lft-out-- 67.8%

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

      11. associate-/l* 63.8%

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

      12. *-commutative 63.8%

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

      13. associate-/l* 66.8%

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

      14. *-commutative 66.8%

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

      15. associate-*l/ 65.2%

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

      16. associate-*r/ 66.5%

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

      17. distribute-rgt-out-- 75.1%

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

   9. Simplified 75.1%

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

   if -5.8e-164 < y < 2.0999999999999999e-83

   1. Initial program 98.5%

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

      1. associate-/l* 83.9%

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

   3. Simplified 83.9%

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

   5. Taylor expanded in x around inf 66.9%

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

   if 2.0999999999999999e-83 < y

   1. Initial program 85.4%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in x around 0 72.7%

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

       1. mul-1-neg 72.7%

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

       2. associate-*l/ 80.0%

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

       3. distribute-rgt-neg-in 80.0%

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

       4. sub-neg 80.0%

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

       5. distribute-neg-in 80.0%

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

       6. remove-double-neg 80.0%

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

       7. +-commutative 80.0%

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

       8. sub-neg 80.0%

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

       9. associate-*l/ 72.7%

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

       10. associate-/l* 82.1%

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

   11. Simplified 82.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-164}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-38}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.8e-11)
   (+ x (/ t (/ a y)))
   (if (<= t 3.8e-38) (- x (* y (/ z a))) (* (- t z) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.8e-11) {
		tmp = x + (t / (a / y));
	} else if (t <= 3.8e-38) {
		tmp = x - (y * (z / a));
	} else {
		tmp = (t - 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 <= (-4.8d-11)) then
        tmp = x + (t / (a / y))
    else if (t <= 3.8d-38) then
        tmp = x - (y * (z / a))
    else
        tmp = (t - 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 <= -4.8e-11) {
		tmp = x + (t / (a / y));
	} else if (t <= 3.8e-38) {
		tmp = x - (y * (z / a));
	} else {
		tmp = (t - z) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.8e-11:
		tmp = x + (t / (a / y))
	elif t <= 3.8e-38:
		tmp = x - (y * (z / a))
	else:
		tmp = (t - z) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.8e-11)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t <= 3.8e-38)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(t - z) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.8e-11)
		tmp = x + (t / (a / y));
	elseif (t <= 3.8e-38)
		tmp = x - (y * (z / a));
	else
		tmp = (t - z) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.8e-11], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-38], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8000000000000002e-11

   1. Initial program 91.2%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

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

      2. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 93.0%

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

   8. Applied egg-rr 93.0%

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

   9. Taylor expanded in z around 0 79.7%

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

       1. sub-neg 79.7%

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

       2. mul-1-neg 79.7%

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

       3. associate-*l/ 81.7%

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

       4. distribute-rgt-neg-in 81.7%

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

       5. distribute-rgt-neg-out 81.7%

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

       6. remove-double-neg 81.7%

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

       7. associate-/r/ 83.2%

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

   11. Simplified 83.2%

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

   if -4.8000000000000002e-11 < t < 3.8e-38

   1. Initial program 93.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 84.7%

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

      1. associate-/l* 87.0%

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

   7. Simplified 87.0%

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

   if 3.8e-38 < t

   1. Initial program 89.4%

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

      1. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

      1. clear-num 82.9%

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

      2. un-div-inv 84.3%

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

   6. Applied egg-rr 84.3%

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

   7. Taylor expanded in x around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-*r/ 70.1%

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

      3. distribute-rgt-neg-in 70.1%

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

      4. neg-sub0 70.1%

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

      5. div-sub 64.4%

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

      6. associate--r- 64.4%

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

      7. neg-sub0 64.4%

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

      8. +-commutative 64.4%

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

      9. sub-neg 64.4%

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

      10. distribute-lft-out-- 64.4%

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

      11. associate-/l* 64.3%

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

      12. *-commutative 64.3%

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

      13. associate-/l* 68.4%

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

      14. *-commutative 68.4%

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

      15. associate-*l/ 69.8%

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

      16. associate-*r/ 73.4%

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

      17. distribute-rgt-out-- 81.8%

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

   9. Simplified 81.8%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-38}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-39}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.8e-12)
   (+ x (/ t (/ a y)))
   (if (<= t 1.05e-39) (- x (* y (/ z a))) (/ (- t z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e-12) {
		tmp = x + (t / (a / y));
	} else if (t <= 1.05e-39) {
		tmp = x - (y * (z / a));
	} else {
		tmp = (t - z) / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.8d-12)) then
        tmp = x + (t / (a / y))
    else if (t <= 1.05d-39) then
        tmp = x - (y * (z / a))
    else
        tmp = (t - z) / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.8e-12) {
		tmp = x + (t / (a / y));
	} else if (t <= 1.05e-39) {
		tmp = x - (y * (z / a));
	} else {
		tmp = (t - z) / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.8e-12:
		tmp = x + (t / (a / y))
	elif t <= 1.05e-39:
		tmp = x - (y * (z / a))
	else:
		tmp = (t - z) / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.8e-12)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	elseif (t <= 1.05e-39)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(Float64(t - z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.8e-12)
		tmp = x + (t / (a / y));
	elseif (t <= 1.05e-39)
		tmp = x - (y * (z / a));
	else
		tmp = (t - z) / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.8e-12], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e-39], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8000000000000001e-12

   1. Initial program 91.2%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

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

      2. un-div-inv 93.1%

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

   6. Applied egg-rr 93.1%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 93.0%

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

   8. Applied egg-rr 93.0%

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

   9. Taylor expanded in z around 0 79.7%

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

       1. sub-neg 79.7%

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

       2. mul-1-neg 79.7%

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

       3. associate-*l/ 81.7%

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

       4. distribute-rgt-neg-in 81.7%

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

       5. distribute-rgt-neg-out 81.7%

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

       6. remove-double-neg 81.7%

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

       7. associate-/r/ 83.2%

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

   11. Simplified 83.2%

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

   if -6.8000000000000001e-12 < t < 1.04999999999999997e-39

   1. Initial program 93.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 85.2%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

   if 1.04999999999999997e-39 < t

   1. Initial program 89.7%

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

      1. associate-/l* 83.4%

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

   3. Simplified 83.4%

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

      1. clear-num 83.4%

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

      2. un-div-inv 84.7%

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

   6. Applied egg-rr 84.7%

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

   7. Taylor expanded in x around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*r/ 69.6%

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

      3. distribute-rgt-neg-in 69.6%

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

      4. neg-sub0 69.6%

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

      5. div-sub 64.0%

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

      6. associate--r- 64.0%

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

      7. neg-sub0 64.0%

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

      8. +-commutative 64.0%

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

      9. sub-neg 64.0%

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

      10. distribute-lft-out-- 64.0%

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

      11. associate-/l* 63.9%

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

      12. *-commutative 63.9%

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

      13. associate-/l* 67.9%

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

      14. *-commutative 67.9%

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

      15. associate-*l/ 69.3%

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

      16. associate-*r/ 72.8%

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

      17. distribute-rgt-out-- 80.9%

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

   9. Simplified 80.9%

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

       1. *-commutative 80.9%

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

       2. clear-num 80.9%

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

       3. un-div-inv 81.0%

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

   11. Applied egg-rr 81.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-39}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{-21} \lor \neg \left(t \leq 3.5 \cdot 10^{-70}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.52e-21) (not (<= t 3.5e-70))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.52e-21) || !(t <= 3.5e-70)) {
		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 <= (-1.52d-21)) .or. (.not. (t <= 3.5d-70))) 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 <= -1.52e-21) || !(t <= 3.5e-70)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.52e-21) or not (t <= 3.5e-70):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.52e-21) || !(t <= 3.5e-70))
		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 <= -1.52e-21) || ~((t <= 3.5e-70)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.52e-21], N[Not[LessEqual[t, 3.5e-70]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -1.52000000000000009e-21 or 3.49999999999999974e-70 < t

   1. Initial program 90.2%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t around inf 58.6%

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

      1. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   if -1.52000000000000009e-21 < t < 3.49999999999999974e-70

   1. Initial program 93.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 46.9%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{-21} \lor \neg \left(t \leq 3.5 \cdot 10^{-70}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.4e-65) (* y (/ t a)) (if (<= t 2.75e-70) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e-65) {
		tmp = y * (t / a);
	} else if (t <= 2.75e-70) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.4d-65)) then
        tmp = y * (t / a)
    else if (t <= 2.75d-70) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e-65) {
		tmp = y * (t / a);
	} else if (t <= 2.75e-70) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.4e-65:
		tmp = y * (t / a)
	elif t <= 2.75e-70:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.4e-65)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 2.75e-70)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.4e-65)
		tmp = y * (t / a);
	elseif (t <= 2.75e-70)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.4e-65], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.75e-70], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4e-65

   1. Initial program 91.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 52.2%

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

   7. Simplified 52.2%

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

   if -1.4e-65 < t < 2.75e-70

   1. Initial program 92.7%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 48.7%

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

   if 2.75e-70 < t

   1. Initial program 90.4%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 59.5%

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

   7. Simplified 59.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e-67) (/ y (/ a t)) (if (<= t 3.5e-70) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e-67) {
		tmp = y / (a / t);
	} else if (t <= 3.5e-70) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.6d-67)) then
        tmp = y / (a / t)
    else if (t <= 3.5d-70) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e-67) {
		tmp = y / (a / t);
	} else if (t <= 3.5e-70) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e-67:
		tmp = y / (a / t)
	elif t <= 3.5e-70:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e-67)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 3.5e-70)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e-67)
		tmp = y / (a / t);
	elseif (t <= 3.5e-70)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e-67], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-70], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.59999999999999999e-67

   1. Initial program 91.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 52.2%

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

   7. Simplified 52.2%

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

      1. clear-num 52.2%

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

      2. un-div-inv 52.2%

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

   9. Applied egg-rr 52.2%

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

   if -3.59999999999999999e-67 < t < 3.49999999999999974e-70

   1. Initial program 92.7%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 48.7%

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

   if 3.49999999999999974e-70 < t

   1. Initial program 90.4%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 59.5%

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

   7. Simplified 59.5%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.25e-64) (/ y (/ a t)) (if (<= t 3.5e-70) x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.25e-64) {
		tmp = y / (a / t);
	} else if (t <= 3.5e-70) {
		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 (t <= (-2.25d-64)) then
        tmp = y / (a / t)
    else if (t <= 3.5d-70) 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 (t <= -2.25e-64) {
		tmp = y / (a / t);
	} else if (t <= 3.5e-70) {
		tmp = x;
	} else {
		tmp = (y * t) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.25e-64:
		tmp = y / (a / t)
	elif t <= 3.5e-70:
		tmp = x
	else:
		tmp = (y * t) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.25e-64)
		tmp = Float64(y / Float64(a / t));
	elseif (t <= 3.5e-70)
		tmp = x;
	else
		tmp = Float64(Float64(y * t) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.25e-64)
		tmp = y / (a / t);
	elseif (t <= 3.5e-70)
		tmp = x;
	else
		tmp = (y * t) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.25e-64], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-70], x, N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.25000000000000005e-64

   1. Initial program 91.6%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. associate-/l* 52.2%

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

   7. Simplified 52.2%

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

      1. clear-num 52.2%

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

      2. un-div-inv 52.2%

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

   9. Applied egg-rr 52.2%

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

   if -2.25000000000000005e-64 < t < 3.49999999999999974e-70

   1. Initial program 92.7%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 48.7%

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

   if 3.49999999999999974e-70 < t

   1. Initial program 90.4%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

   5. Taylor expanded in t around inf 60.7%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-64}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+231}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.5e+231) (- x (/ (* y z) a)) (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.5e+231) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y * ((t - 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 (x <= (-2.5d+231)) then
        tmp = x - ((y * z) / a)
    else
        tmp = x + (y * ((t - 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 (x <= -2.5e+231) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.5e+231:
		tmp = x - ((y * z) / a)
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.5e+231)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.5e+231)
		tmp = x - ((y * z) / a);
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.5e+231], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.50000000000000014e231

   1. Initial program 94.4%

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

      1. associate-/l* 73.1%

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

   3. Simplified 73.1%

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

   5. Taylor expanded in z around inf 100.0%

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

   if -2.50000000000000014e231 < x

   1. Initial program 91.4%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+231}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.6%

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

   1. associate-/l* 91.7%

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

3. Simplified 91.7%

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

   1. clear-num 91.7%

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

   2. un-div-inv 92.1%

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

6. Applied egg-rr 92.1%

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

7. Final simplification 92.1%

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

Alternative 16: 39.4% 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 91.6%

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

   1. associate-/l* 91.7%

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

3. Simplified 91.7%

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

5. Taylor expanded in x around inf 34.0%

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

6. Final simplification 34.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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