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

Percentage Accurate: 92.7% → 99.0%

Time: 10.0s

Alternatives: 12

Speedup: 1.0×

• 25.3% 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: 92.7% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+108}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+108)))
     (+ x (/ y (/ a (- t z))))
     (+ x (/ (* y (- t z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+108)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+108)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+108):
		tmp = x + (y / (a / (t - z)))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+108))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	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)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+108)))
		tmp = x + (y / (a / (t - z)));
	else
		tmp = x + ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+108]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $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 (*.f64 y (-.f64 z t)) < -inf.0 or 1e108 < (*.f64 y (-.f64 z t))

   1. Initial program 85.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 1e108

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -\infty \lor \neg \left(\left(z - t\right) \cdot y \leq 10^{+108}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+141}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))))
   (if (<= z -5.3e+141)
     (/ (- z) (/ a y))
     (if (<= z -3.2e+86)
       t_1
       (if (<= z -5.3e+57)
         (* (/ z a) (- y))
         (if (<= z 3.6e+125) t_1 (* (- z) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -5.3e+141) {
		tmp = -z / (a / y);
	} else if (z <= -3.2e+86) {
		tmp = t_1;
	} else if (z <= -5.3e+57) {
		tmp = (z / a) * -y;
	} else if (z <= 3.6e+125) {
		tmp = t_1;
	} else {
		tmp = -z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    if (z <= (-5.3d+141)) then
        tmp = -z / (a / y)
    else if (z <= (-3.2d+86)) then
        tmp = t_1
    else if (z <= (-5.3d+57)) then
        tmp = (z / a) * -y
    else if (z <= 3.6d+125) then
        tmp = t_1
    else
        tmp = -z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double tmp;
	if (z <= -5.3e+141) {
		tmp = -z / (a / y);
	} else if (z <= -3.2e+86) {
		tmp = t_1;
	} else if (z <= -5.3e+57) {
		tmp = (z / a) * -y;
	} else if (z <= 3.6e+125) {
		tmp = t_1;
	} else {
		tmp = -z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	tmp = 0
	if z <= -5.3e+141:
		tmp = -z / (a / y)
	elif z <= -3.2e+86:
		tmp = t_1
	elif z <= -5.3e+57:
		tmp = (z / a) * -y
	elif z <= 3.6e+125:
		tmp = t_1
	else:
		tmp = -z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	tmp = 0.0
	if (z <= -5.3e+141)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= -3.2e+86)
		tmp = t_1;
	elseif (z <= -5.3e+57)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (z <= 3.6e+125)
		tmp = t_1;
	else
		tmp = Float64(Float64(-z) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	tmp = 0.0;
	if (z <= -5.3e+141)
		tmp = -z / (a / y);
	elseif (z <= -3.2e+86)
		tmp = t_1;
	elseif (z <= -5.3e+57)
		tmp = (z / a) * -y;
	elseif (z <= 3.6e+125)
		tmp = t_1;
	else
		tmp = -z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.3e+141], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e+86], t$95$1, If[LessEqual[z, -5.3e+57], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 3.6e+125], t$95$1, N[((-z) * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.3e141

   1. Initial program 94.4%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 91.4%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/r/ 94.0%

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

   9. Applied egg-rr 94.0%

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

   10. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 58.4%

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

       2. *-commutative 58.4%

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

       3. associate-*l* 58.4%

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

       4. *-commutative 58.4%

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

       5. associate-*r/ 58.4%

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

       6. neg-mul-1 58.4%

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

   12. Simplified 58.4%

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

       1. distribute-frac-neg 58.4%

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

       2. distribute-rgt-neg-out 58.4%

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

       3. *-commutative 58.4%

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

       4. /-rgt-identity 58.4%

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

       5. associate-/r/ 58.3%

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

       6. associate-/l/ 66.4%

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

       7. distribute-neg-frac2 66.4%

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

       8. associate-*l/ 66.5%

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

       9. *-un-lft-identity 66.5%

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

   14. Applied egg-rr 66.5%

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

   if -5.3e141 < z < -3.2e86 or -5.29999999999999986e57 < z < 3.6000000000000003e125

   1. Initial program 97.2%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 88.2%

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

      1. mul-1-neg 88.2%

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

      2. associate-/l* 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

      4. distribute-neg-frac2 90.2%

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

   7. Simplified 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. associate-*r/ 88.2%

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

      3. *-commutative 88.2%

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

      4. add-sqr-sqrt 48.6%

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

      5. sqrt-unprod 64.9%

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

      6. sqr-neg 64.9%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 50.8%

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

      9. associate-/l* 50.8%

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

      10. add-sqr-sqrt 21.9%

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

      11. sqrt-unprod 58.7%

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

      12. sqr-neg 58.7%

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

      13. sqrt-unprod 48.9%

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

      14. add-sqr-sqrt 84.4%

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

   9. Applied egg-rr 84.4%

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

   if -3.2e86 < z < -5.29999999999999986e57

   1. Initial program 72.4%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. associate-/l* 85.7%

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

   7. Simplified 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/r/ 85.7%

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

   9. Applied egg-rr 85.7%

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

   10. Taylor expanded in x around 0 58.1%

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

       1. associate-*r/ 85.7%

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

       2. *-commutative 85.7%

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

       3. associate-*l* 85.7%

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

       4. *-commutative 85.7%

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

       5. associate-*r/ 85.7%

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

       6. neg-mul-1 85.7%

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

   12. Simplified 85.7%

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

   if 3.6000000000000003e125 < z

   1. Initial program 89.4%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 79.2%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in x around 0 60.5%

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

      1. associate-*r/ 60.5%

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

      2. *-commutative 60.5%

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

      3. neg-mul-1 60.5%

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

      4. distribute-rgt-neg-out 60.5%

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

      5. associate-/l* 65.5%

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

   10. Simplified 65.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+141}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+86}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t}}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a t)))))
   (if (<= z -4.4e+142)
     (/ (- z) (/ a y))
     (if (<= z -1.7e+86)
       t_1
       (if (<= z -1.5e+58)
         (* (/ z a) (- y))
         (if (<= z 2.6e+125) t_1 (* (- z) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -4.4e+142) {
		tmp = -z / (a / y);
	} else if (z <= -1.7e+86) {
		tmp = t_1;
	} else if (z <= -1.5e+58) {
		tmp = (z / a) * -y;
	} else if (z <= 2.6e+125) {
		tmp = t_1;
	} else {
		tmp = -z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / t))
    if (z <= (-4.4d+142)) then
        tmp = -z / (a / y)
    else if (z <= (-1.7d+86)) then
        tmp = t_1
    else if (z <= (-1.5d+58)) then
        tmp = (z / a) * -y
    else if (z <= 2.6d+125) then
        tmp = t_1
    else
        tmp = -z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / t));
	double tmp;
	if (z <= -4.4e+142) {
		tmp = -z / (a / y);
	} else if (z <= -1.7e+86) {
		tmp = t_1;
	} else if (z <= -1.5e+58) {
		tmp = (z / a) * -y;
	} else if (z <= 2.6e+125) {
		tmp = t_1;
	} else {
		tmp = -z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / t))
	tmp = 0
	if z <= -4.4e+142:
		tmp = -z / (a / y)
	elif z <= -1.7e+86:
		tmp = t_1
	elif z <= -1.5e+58:
		tmp = (z / a) * -y
	elif z <= 2.6e+125:
		tmp = t_1
	else:
		tmp = -z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / t)))
	tmp = 0.0
	if (z <= -4.4e+142)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= -1.7e+86)
		tmp = t_1;
	elseif (z <= -1.5e+58)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (z <= 2.6e+125)
		tmp = t_1;
	else
		tmp = Float64(Float64(-z) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / t));
	tmp = 0.0;
	if (z <= -4.4e+142)
		tmp = -z / (a / y);
	elseif (z <= -1.7e+86)
		tmp = t_1;
	elseif (z <= -1.5e+58)
		tmp = (z / a) * -y;
	elseif (z <= 2.6e+125)
		tmp = t_1;
	else
		tmp = -z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+142], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e+86], t$95$1, If[LessEqual[z, -1.5e+58], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 2.6e+125], t$95$1, N[((-z) * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.39999999999999974e142

   1. Initial program 94.4%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 91.4%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/r/ 94.0%

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

   9. Applied egg-rr 94.0%

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

   10. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 58.4%

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

       2. *-commutative 58.4%

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

       3. associate-*l* 58.4%

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

       4. *-commutative 58.4%

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

       5. associate-*r/ 58.4%

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

       6. neg-mul-1 58.4%

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

   12. Simplified 58.4%

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

       1. distribute-frac-neg 58.4%

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

       2. distribute-rgt-neg-out 58.4%

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

       3. *-commutative 58.4%

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

       4. /-rgt-identity 58.4%

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

       5. associate-/r/ 58.3%

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

       6. associate-/l/ 66.4%

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

       7. distribute-neg-frac2 66.4%

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

       8. associate-*l/ 66.5%

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

       9. *-un-lft-identity 66.5%

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

   14. Applied egg-rr 66.5%

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

   if -4.39999999999999974e142 < z < -1.6999999999999999e86 or -1.5000000000000001e58 < z < 2.60000000000000003e125

   1. Initial program 97.2%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 88.2%

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

      1. mul-1-neg 88.2%

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

      2. associate-/l* 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

      4. distribute-neg-frac2 90.2%

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

   7. Simplified 90.2%

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

      1. cancel-sign-sub-inv 90.2%

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

      2. associate-*r/ 88.2%

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

      3. *-commutative 88.2%

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

      4. add-sqr-sqrt 48.6%

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

      5. sqrt-unprod 64.9%

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

      6. sqr-neg 64.9%

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

      7. sqrt-unprod 26.1%

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

      8. add-sqr-sqrt 50.8%

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

      9. associate-/l* 50.8%

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

      10. add-sqr-sqrt 21.9%

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

      11. sqrt-unprod 58.7%

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

      12. sqr-neg 58.7%

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

      13. sqrt-unprod 48.9%

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

      14. add-sqr-sqrt 84.4%

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

   9. Applied egg-rr 84.4%

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

       1. clear-num 84.4%

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

       2. un-div-inv 84.5%

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

   11. Applied egg-rr 84.5%

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

   if -1.6999999999999999e86 < z < -1.5000000000000001e58

   1. Initial program 72.4%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. associate-/l* 85.7%

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

   7. Simplified 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/r/ 85.7%

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

   9. Applied egg-rr 85.7%

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

   10. Taylor expanded in x around 0 58.1%

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

       1. associate-*r/ 85.7%

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

       2. *-commutative 85.7%

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

       3. associate-*l* 85.7%

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

       4. *-commutative 85.7%

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

       5. associate-*r/ 85.7%

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

       6. neg-mul-1 85.7%

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

   12. Simplified 85.7%

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

   if 2.60000000000000003e125 < z

   1. Initial program 89.4%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 79.2%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in x around 0 60.5%

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

      1. associate-*r/ 60.5%

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

      2. *-commutative 60.5%

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

      3. neg-mul-1 60.5%

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

      4. distribute-rgt-neg-out 60.5%

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

      5. associate-/l* 65.5%

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

   10. Simplified 65.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+142}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+141}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+141)
   (/ (- z) (/ a y))
   (if (<= z -1.8e+86)
     (+ x (/ y (/ a t)))
     (if (<= z -1.52e+58)
       (* (/ z a) (- y))
       (if (<= z 3.4e+125) (+ x (/ (* t y) a)) (* (- z) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+141) {
		tmp = -z / (a / y);
	} else if (z <= -1.8e+86) {
		tmp = x + (y / (a / t));
	} else if (z <= -1.52e+58) {
		tmp = (z / a) * -y;
	} else if (z <= 3.4e+125) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = -z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+141)) then
        tmp = -z / (a / y)
    else if (z <= (-1.8d+86)) then
        tmp = x + (y / (a / t))
    else if (z <= (-1.52d+58)) then
        tmp = (z / a) * -y
    else if (z <= 3.4d+125) then
        tmp = x + ((t * y) / a)
    else
        tmp = -z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+141) {
		tmp = -z / (a / y);
	} else if (z <= -1.8e+86) {
		tmp = x + (y / (a / t));
	} else if (z <= -1.52e+58) {
		tmp = (z / a) * -y;
	} else if (z <= 3.4e+125) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = -z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+141:
		tmp = -z / (a / y)
	elif z <= -1.8e+86:
		tmp = x + (y / (a / t))
	elif z <= -1.52e+58:
		tmp = (z / a) * -y
	elif z <= 3.4e+125:
		tmp = x + ((t * y) / a)
	else:
		tmp = -z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+141)
		tmp = Float64(Float64(-z) / Float64(a / y));
	elseif (z <= -1.8e+86)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (z <= -1.52e+58)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (z <= 3.4e+125)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(Float64(-z) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+141)
		tmp = -z / (a / y);
	elseif (z <= -1.8e+86)
		tmp = x + (y / (a / t));
	elseif (z <= -1.52e+58)
		tmp = (z / a) * -y;
	elseif (z <= 3.4e+125)
		tmp = x + ((t * y) / a);
	else
		tmp = -z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+141], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e+86], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.52e+58], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[z, 3.4e+125], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[((-z) * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.4000000000000002e141

   1. Initial program 94.4%

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

      1. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 91.4%

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

      1. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/r/ 94.0%

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

   9. Applied egg-rr 94.0%

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

   10. Taylor expanded in x around 0 66.3%

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

       1. associate-*r/ 58.4%

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

       2. *-commutative 58.4%

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

       3. associate-*l* 58.4%

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

       4. *-commutative 58.4%

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

       5. associate-*r/ 58.4%

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

       6. neg-mul-1 58.4%

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

   12. Simplified 58.4%

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

       1. distribute-frac-neg 58.4%

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

       2. distribute-rgt-neg-out 58.4%

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

       3. *-commutative 58.4%

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

       4. /-rgt-identity 58.4%

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

       5. associate-/r/ 58.3%

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

       6. associate-/l/ 66.4%

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

       7. distribute-neg-frac2 66.4%

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

       8. associate-*l/ 66.5%

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

       9. *-un-lft-identity 66.5%

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

   14. Applied egg-rr 66.5%

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

   if -5.4000000000000002e141 < z < -1.80000000000000003e86

   1. Initial program 78.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. associate-/l* 89.9%

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

      3. distribute-rgt-neg-in 89.9%

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

      4. distribute-neg-frac2 89.9%

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

   7. Simplified 89.9%

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

      1. cancel-sign-sub-inv 89.9%

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

      2. associate-*r/ 68.2%

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

      3. *-commutative 68.2%

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

      4. add-sqr-sqrt 44.8%

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

      5. sqrt-unprod 66.7%

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

      6. sqr-neg 66.7%

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

      7. sqrt-unprod 23.1%

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

      8. add-sqr-sqrt 45.4%

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

      9. associate-/l* 55.6%

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

      10. add-sqr-sqrt 22.3%

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

      11. sqrt-unprod 57.3%

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

      12. sqr-neg 57.3%

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

      13. sqrt-unprod 45.4%

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

      14. add-sqr-sqrt 89.7%

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

   9. Applied egg-rr 89.7%

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

       1. clear-num 89.9%

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

       2. un-div-inv 89.9%

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

   11. Applied egg-rr 89.9%

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

   if -1.80000000000000003e86 < z < -1.5199999999999999e58

   1. Initial program 72.4%

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

   5. Taylor expanded in z around inf 58.1%

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

      1. associate-/l* 85.7%

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

   7. Simplified 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/r/ 85.7%

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

   9. Applied egg-rr 85.7%

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

   10. Taylor expanded in x around 0 58.1%

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

       1. associate-*r/ 85.7%

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

       2. *-commutative 85.7%

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

       3. associate-*l* 85.7%

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

       4. *-commutative 85.7%

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

       5. associate-*r/ 85.7%

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

       6. neg-mul-1 85.7%

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

   12. Simplified 85.7%

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

   if -1.5199999999999999e58 < z < 3.3999999999999999e125

   1. Initial program 98.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 89.3%

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

      1. mul-1-neg 89.3%

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

      2. associate-/l* 90.2%

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

      3. distribute-rgt-neg-in 90.2%

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

      4. distribute-neg-frac2 90.2%

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

   7. Simplified 90.2%

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

   8. Taylor expanded in t around 0 89.3%

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

   if 3.3999999999999999e125 < z

   1. Initial program 89.4%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in z around inf 79.2%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in x around 0 60.5%

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

      1. associate-*r/ 60.5%

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

      2. *-commutative 60.5%

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

      3. neg-mul-1 60.5%

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

      4. distribute-rgt-neg-out 60.5%

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

      5. associate-/l* 65.5%

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

   10. Simplified 65.5%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+141}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+86}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+125}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+22} \lor \neg \left(t \leq 7.2 \cdot 10^{-12}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.9e+22) (not (<= t 7.2e-12)))
   (+ 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 <= -3.9e+22) || !(t <= 7.2e-12)) {
		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 <= (-3.9d+22)) .or. (.not. (t <= 7.2d-12))) 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 <= -3.9e+22) || !(t <= 7.2e-12)) {
		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 <= -3.9e+22) or not (t <= 7.2e-12):
		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 <= -3.9e+22) || !(t <= 7.2e-12))
		tmp = Float64(x + Float64(Float64(t * 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 <= -3.9e+22) || ~((t <= 7.2e-12)))
		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, -3.9e+22], N[Not[LessEqual[t, 7.2e-12]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.90000000000000021e22 or 7.2e-12 < t

   1. Initial program 94.4%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

      4. distribute-neg-frac2 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in t around 0 87.0%

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

   if -3.90000000000000021e22 < t < 7.2e-12

   1. Initial program 95.6%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+22} \lor \neg \left(t \leq 7.2 \cdot 10^{-12}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+23} \lor \neg \left(t \leq 9.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+23) (not (<= t 9.5e-13)))
   (+ x (/ (* t y) a))
   (- x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+23) || !(t <= 9.5e-13)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (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 <= (-8.2d+23)) .or. (.not. (t <= 9.5d-13))) then
        tmp = x + ((t * y) / a)
    else
        tmp = x - (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 <= -8.2e+23) || !(t <= 9.5e-13)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+23) or not (t <= 9.5e-13):
		tmp = x + ((t * y) / a)
	else:
		tmp = x - (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+23) || !(t <= 9.5e-13))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x - Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+23) || ~((t <= 9.5e-13)))
		tmp = x + ((t * y) / a);
	else
		tmp = x - (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+23], N[Not[LessEqual[t, 9.5e-13]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.19999999999999992e23 or 9.49999999999999991e-13 < t

   1. Initial program 94.4%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

      4. distribute-neg-frac2 89.2%

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

   7. Simplified 89.2%

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

   8. Taylor expanded in t around 0 87.0%

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

   if -8.19999999999999992e23 < t < 9.49999999999999991e-13

   1. Initial program 95.6%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+23} \lor \neg \left(t \leq 9.5 \cdot 10^{-13}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+23} \lor \neg \left(t \leq 2.15 \cdot 10^{-12}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.6e+23) (not (<= t 2.15e-12)))
   (+ x (* t (/ y a)))
   (- x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.6e+23) || !(t <= 2.15e-12)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (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 <= (-4.6d+23)) .or. (.not. (t <= 2.15d-12))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (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 <= -4.6e+23) || !(t <= 2.15e-12)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.6e+23) or not (t <= 2.15e-12):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.6e+23) || !(t <= 2.15e-12))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.6e+23) || ~((t <= 2.15e-12)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.6e+23], N[Not[LessEqual[t, 2.15e-12]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6000000000000001e23 or 2.14999999999999993e-12 < t

   1. Initial program 94.4%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 89.2%

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

      3. distribute-rgt-neg-in 89.2%

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

      4. distribute-neg-frac2 89.2%

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

   7. Simplified 89.2%

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

   if -4.6000000000000001e23 < t < 2.14999999999999993e-12

   1. Initial program 95.6%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 89.8%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+23} \lor \neg \left(t \leq 2.15 \cdot 10^{-12}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e+20) x (if (<= a 5.2e-40) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.45e+20) {
		tmp = x;
	} else if (a <= 5.2e-40) {
		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 (a <= (-1.45d+20)) then
        tmp = x
    else if (a <= 5.2d-40) 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 (a <= -1.45e+20) {
		tmp = x;
	} else if (a <= 5.2e-40) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.45e+20:
		tmp = x
	elif a <= 5.2e-40:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.45e+20)
		tmp = x;
	elseif (a <= 5.2e-40)
		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 (a <= -1.45e+20)
		tmp = x;
	elseif (a <= 5.2e-40)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.45e+20], x, If[LessEqual[a, 5.2e-40], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45e20 or 5.2000000000000003e-40 < a

   1. Initial program 91.6%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in x around inf 63.0%

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

   if -1.45e20 < a < 5.2000000000000003e-40

   1. Initial program 99.0%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in z around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. associate-/l* 74.9%

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

      3. distribute-rgt-neg-in 74.9%

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

      4. distribute-neg-frac2 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in x around 0 50.4%

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

      1. associate-*r/ 56.6%

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

   10. Simplified 56.6%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{+90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -7.1e+90) (+ x (* t (/ y a))) (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -7.1e+90) {
		tmp = x + (t * (y / 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 (t <= (-7.1d+90)) then
        tmp = x + (t * (y / 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 (t <= -7.1e+90) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -7.1e+90:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -7.1e+90)
		tmp = Float64(x + Float64(t * Float64(y / 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 (t <= -7.1e+90)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -7.1e+90], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.09999999999999975e90

   1. Initial program 95.1%

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

      1. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 87.6%

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

      3. distribute-rgt-neg-in 87.6%

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

      4. distribute-neg-frac2 87.6%

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

   7. Simplified 87.6%

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

   if -7.09999999999999975e90 < t

   1. Initial program 95.0%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{+90}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{+91}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.62e+91) (+ x (* t (/ y a))) (+ x (/ y (/ a (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.62e+91) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (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 (t <= (-1.62d+91)) then
        tmp = x + (t * (y / a))
    else
        tmp = x + (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 (t <= -1.62e+91) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + (y / (a / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.62e+91:
		tmp = x + (t * (y / a))
	else:
		tmp = x + (y / (a / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.62e+91)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.62e+91)
		tmp = x + (t * (y / a));
	else
		tmp = x + (y / (a / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.62e+91], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.62e91

   1. Initial program 95.1%

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

      1. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 87.6%

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

      3. distribute-rgt-neg-in 87.6%

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

      4. distribute-neg-frac2 87.6%

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

   7. Simplified 87.6%

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

   if -1.62e91 < t

   1. Initial program 95.0%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. clear-num 95.5%

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

      2. un-div-inv 95.6%

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

   6. Applied egg-rr 95.6%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.62 \cdot 10^{+91}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-/l* 92.6%

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

3. Simplified 92.6%

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

5. Taylor expanded in y around 0 95.0%

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

   1. *-lft-identity 95.0%

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

   2. associate-*l/ 95.0%

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

   3. associate-*r* 97.9%

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

   4. associate-/r/ 97.8%

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

   5. associate-*l/ 98.3%

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

   6. *-lft-identity 98.3%

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

7. Simplified 98.3%

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

8. Final simplification 98.3%

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

Alternative 12: 38.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-/l* 92.6%

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

3. Simplified 92.6%

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

5. Taylor expanded in z around inf 69.3%

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

   1. associate-/l* 69.4%

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

7. Simplified 69.4%

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

8. Taylor expanded in x around inf 42.8%

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

9. Final simplification 42.8%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 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 2024055 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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