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

Percentage Accurate: 93.0% → 97.2%

Time: 9.2s

Alternatives: 13

Speedup: 1.0×

• 24.2% 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: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% 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 91.8%

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

   1. *-commutative 91.8%

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

   2. associate-/l* 97.2%

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

4. Applied egg-rr 97.2%

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

   1. clear-num 97.2%

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

   2. un-div-inv 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

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

Alternative 2: 50.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= z -3.1e+79)
     (* (/ y a) (- z))
     (if (<= z -9.4e-67)
       t_1
       (if (<= z -1.75e-184)
         x
         (if (<= z -3e-196)
           (* y (/ t a))
           (if (<= z 1.3e-108)
             x
             (if (<= z 5.2e-55)
               t_1
               (if (<= z 1.65e-53)
                 x
                 (if (<= z 9e-11)
                   (/ y (/ a t))
                   (if (<= z 7e+31) x (/ z (/ a (- y))))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (z <= -3.1e+79) {
		tmp = (y / a) * -z;
	} else if (z <= -9.4e-67) {
		tmp = t_1;
	} else if (z <= -1.75e-184) {
		tmp = x;
	} else if (z <= -3e-196) {
		tmp = y * (t / a);
	} else if (z <= 1.3e-108) {
		tmp = x;
	} else if (z <= 5.2e-55) {
		tmp = t_1;
	} else if (z <= 1.65e-53) {
		tmp = x;
	} else if (z <= 9e-11) {
		tmp = y / (a / t);
	} else if (z <= 7e+31) {
		tmp = x;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t / (a / y)
    if (z <= (-3.1d+79)) then
        tmp = (y / a) * -z
    else if (z <= (-9.4d-67)) then
        tmp = t_1
    else if (z <= (-1.75d-184)) then
        tmp = x
    else if (z <= (-3d-196)) then
        tmp = y * (t / a)
    else if (z <= 1.3d-108) then
        tmp = x
    else if (z <= 5.2d-55) then
        tmp = t_1
    else if (z <= 1.65d-53) then
        tmp = x
    else if (z <= 9d-11) then
        tmp = y / (a / t)
    else if (z <= 7d+31) then
        tmp = x
    else
        tmp = 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 t_1 = t / (a / y);
	double tmp;
	if (z <= -3.1e+79) {
		tmp = (y / a) * -z;
	} else if (z <= -9.4e-67) {
		tmp = t_1;
	} else if (z <= -1.75e-184) {
		tmp = x;
	} else if (z <= -3e-196) {
		tmp = y * (t / a);
	} else if (z <= 1.3e-108) {
		tmp = x;
	} else if (z <= 5.2e-55) {
		tmp = t_1;
	} else if (z <= 1.65e-53) {
		tmp = x;
	} else if (z <= 9e-11) {
		tmp = y / (a / t);
	} else if (z <= 7e+31) {
		tmp = x;
	} else {
		tmp = z / (a / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if z <= -3.1e+79:
		tmp = (y / a) * -z
	elif z <= -9.4e-67:
		tmp = t_1
	elif z <= -1.75e-184:
		tmp = x
	elif z <= -3e-196:
		tmp = y * (t / a)
	elif z <= 1.3e-108:
		tmp = x
	elif z <= 5.2e-55:
		tmp = t_1
	elif z <= 1.65e-53:
		tmp = x
	elif z <= 9e-11:
		tmp = y / (a / t)
	elif z <= 7e+31:
		tmp = x
	else:
		tmp = z / (a / -y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (z <= -3.1e+79)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (z <= -9.4e-67)
		tmp = t_1;
	elseif (z <= -1.75e-184)
		tmp = x;
	elseif (z <= -3e-196)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 1.3e-108)
		tmp = x;
	elseif (z <= 5.2e-55)
		tmp = t_1;
	elseif (z <= 1.65e-53)
		tmp = x;
	elseif (z <= 9e-11)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 7e+31)
		tmp = x;
	else
		tmp = Float64(z / Float64(a / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (z <= -3.1e+79)
		tmp = (y / a) * -z;
	elseif (z <= -9.4e-67)
		tmp = t_1;
	elseif (z <= -1.75e-184)
		tmp = x;
	elseif (z <= -3e-196)
		tmp = y * (t / a);
	elseif (z <= 1.3e-108)
		tmp = x;
	elseif (z <= 5.2e-55)
		tmp = t_1;
	elseif (z <= 1.65e-53)
		tmp = x;
	elseif (z <= 9e-11)
		tmp = y / (a / t);
	elseif (z <= 7e+31)
		tmp = x;
	else
		tmp = z / (a / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+79], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, -9.4e-67], t$95$1, If[LessEqual[z, -1.75e-184], x, If[LessEqual[z, -3e-196], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-108], x, If[LessEqual[z, 5.2e-55], t$95$1, If[LessEqual[z, 1.65e-53], x, If[LessEqual[z, 9e-11], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7e+31], x, N[(z / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.0999999999999999e79

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

      2. associate-/l* 95.9%

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

   4. Applied egg-rr 95.9%

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

   5. Taylor expanded in z around inf 63.0%

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

      1. mul-1-neg 63.0%

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

      2. distribute-neg-frac2 63.0%

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

      3. *-commutative 63.0%

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

      4. associate-*r/ 73.7%

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

   7. Simplified 73.7%

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

   if -3.0999999999999999e79 < z < -9.40000000000000009e-67 or 1.29999999999999992e-108 < z < 5.1999999999999998e-55

   1. Initial program 88.0%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around inf 42.6%

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

      1. *-commutative 42.6%

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

   7. Simplified 42.6%

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

      1. associate-/l* 49.8%

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

      2. *-commutative 49.8%

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

   9. Applied egg-rr 49.8%

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

       1. associate-/r/ 57.0%

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

   11. Applied egg-rr 57.0%

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

   if -9.40000000000000009e-67 < z < -1.74999999999999991e-184 or -3e-196 < z < 1.29999999999999992e-108 or 5.1999999999999998e-55 < z < 1.65000000000000002e-53 or 8.9999999999999999e-11 < z < 7e31

   1. Initial program 96.2%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around inf 60.8%

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

   if -1.74999999999999991e-184 < z < -3e-196

   1. Initial program 81.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

   if 1.65000000000000002e-53 < z < 8.9999999999999999e-11

   1. Initial program 89.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 44.6%

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

      1. *-commutative 44.6%

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

   7. Simplified 44.6%

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

      1. associate-/l* 54.5%

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

      2. *-commutative 54.5%

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

   9. Applied egg-rr 54.5%

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

       1. *-commutative 54.5%

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

       2. clear-num 54.5%

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

       3. un-div-inv 54.7%

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

   11. Applied egg-rr 54.7%

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

   if 7e31 < z

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. associate-*r/ 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l/ 62.1%

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

      5. associate-*r/ 68.0%

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

      6. distribute-lft-neg-in 68.0%

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

   9. Simplified 68.0%

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

       1. clear-num 68.1%

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

       2. un-div-inv 68.2%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 3.3%

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

       5. sqr-neg 3.3%

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

       6. sqrt-unprod 3.4%

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

       7. add-sqr-sqrt 3.4%

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

       8. frac-2neg 3.4%

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

       9. add-sqr-sqrt 0.0%

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

       10. sqrt-unprod 44.9%

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

       11. sqr-neg 44.9%

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

       12. sqrt-unprod 68.0%

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

       13. add-sqr-sqrt 68.2%

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

       14. distribute-neg-frac2 68.2%

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

   11. Applied egg-rr 68.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{a}{-y}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-196}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ t_2 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-185}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))) (t_2 (* (/ y a) (- z))))
   (if (<= z -3.1e+79)
     t_2
     (if (<= z -4.7e-67)
       t_1
       (if (<= z -1.8e-185)
         x
         (if (<= z -5.9e-198)
           (* y (/ t a))
           (if (<= z 4.3e-108)
             x
             (if (<= z 5.4e-55)
               t_1
               (if (<= z 5e-53)
                 x
                 (if (<= z 1.45e-8)
                   (/ y (/ a t))
                   (if (<= z 5.5e+20) x t_2)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -3.1e+79) {
		tmp = t_2;
	} else if (z <= -4.7e-67) {
		tmp = t_1;
	} else if (z <= -1.8e-185) {
		tmp = x;
	} else if (z <= -5.9e-198) {
		tmp = y * (t / a);
	} else if (z <= 4.3e-108) {
		tmp = x;
	} else if (z <= 5.4e-55) {
		tmp = t_1;
	} else if (z <= 5e-53) {
		tmp = x;
	} else if (z <= 1.45e-8) {
		tmp = y / (a / t);
	} else if (z <= 5.5e+20) {
		tmp = x;
	} 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 / (a / y)
    t_2 = (y / a) * -z
    if (z <= (-3.1d+79)) then
        tmp = t_2
    else if (z <= (-4.7d-67)) then
        tmp = t_1
    else if (z <= (-1.8d-185)) then
        tmp = x
    else if (z <= (-5.9d-198)) then
        tmp = y * (t / a)
    else if (z <= 4.3d-108) then
        tmp = x
    else if (z <= 5.4d-55) then
        tmp = t_1
    else if (z <= 5d-53) then
        tmp = x
    else if (z <= 1.45d-8) then
        tmp = y / (a / t)
    else if (z <= 5.5d+20) then
        tmp = x
    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 / (a / y);
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -3.1e+79) {
		tmp = t_2;
	} else if (z <= -4.7e-67) {
		tmp = t_1;
	} else if (z <= -1.8e-185) {
		tmp = x;
	} else if (z <= -5.9e-198) {
		tmp = y * (t / a);
	} else if (z <= 4.3e-108) {
		tmp = x;
	} else if (z <= 5.4e-55) {
		tmp = t_1;
	} else if (z <= 5e-53) {
		tmp = x;
	} else if (z <= 1.45e-8) {
		tmp = y / (a / t);
	} else if (z <= 5.5e+20) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	t_2 = (y / a) * -z
	tmp = 0
	if z <= -3.1e+79:
		tmp = t_2
	elif z <= -4.7e-67:
		tmp = t_1
	elif z <= -1.8e-185:
		tmp = x
	elif z <= -5.9e-198:
		tmp = y * (t / a)
	elif z <= 4.3e-108:
		tmp = x
	elif z <= 5.4e-55:
		tmp = t_1
	elif z <= 5e-53:
		tmp = x
	elif z <= 1.45e-8:
		tmp = y / (a / t)
	elif z <= 5.5e+20:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	t_2 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (z <= -3.1e+79)
		tmp = t_2;
	elseif (z <= -4.7e-67)
		tmp = t_1;
	elseif (z <= -1.8e-185)
		tmp = x;
	elseif (z <= -5.9e-198)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 4.3e-108)
		tmp = x;
	elseif (z <= 5.4e-55)
		tmp = t_1;
	elseif (z <= 5e-53)
		tmp = x;
	elseif (z <= 1.45e-8)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 5.5e+20)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	t_2 = (y / a) * -z;
	tmp = 0.0;
	if (z <= -3.1e+79)
		tmp = t_2;
	elseif (z <= -4.7e-67)
		tmp = t_1;
	elseif (z <= -1.8e-185)
		tmp = x;
	elseif (z <= -5.9e-198)
		tmp = y * (t / a);
	elseif (z <= 4.3e-108)
		tmp = x;
	elseif (z <= 5.4e-55)
		tmp = t_1;
	elseif (z <= 5e-53)
		tmp = x;
	elseif (z <= 1.45e-8)
		tmp = y / (a / t);
	elseif (z <= 5.5e+20)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -3.1e+79], t$95$2, If[LessEqual[z, -4.7e-67], t$95$1, If[LessEqual[z, -1.8e-185], x, If[LessEqual[z, -5.9e-198], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e-108], x, If[LessEqual[z, 5.4e-55], t$95$1, If[LessEqual[z, 5e-53], x, If[LessEqual[z, 1.45e-8], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+20], x, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.0999999999999999e79 or 5.5e20 < z

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-/l* 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in z around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. distribute-neg-frac2 62.6%

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

      3. *-commutative 62.6%

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

      4. associate-*r/ 71.0%

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

   7. Simplified 71.0%

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

   if -3.0999999999999999e79 < z < -4.70000000000000004e-67 or 4.3e-108 < z < 5.40000000000000008e-55

   1. Initial program 88.0%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in t around inf 42.6%

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

      1. *-commutative 42.6%

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

   7. Simplified 42.6%

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

      1. associate-/l* 49.8%

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

      2. *-commutative 49.8%

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

   9. Applied egg-rr 49.8%

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

       1. associate-/r/ 57.0%

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

   11. Applied egg-rr 57.0%

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

   if -4.70000000000000004e-67 < z < -1.7999999999999999e-185 or -5.89999999999999974e-198 < z < 4.3e-108 or 5.40000000000000008e-55 < z < 5e-53 or 1.4500000000000001e-8 < z < 5.5e20

   1. Initial program 96.2%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around inf 60.8%

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

   if -1.7999999999999999e-185 < z < -5.89999999999999974e-198

   1. Initial program 81.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

   if 5e-53 < z < 1.4500000000000001e-8

   1. Initial program 89.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 44.6%

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

      1. *-commutative 44.6%

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

   7. Simplified 44.6%

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

      1. associate-/l* 54.5%

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

      2. *-commutative 54.5%

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

   9. Applied egg-rr 54.5%

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

       1. *-commutative 54.5%

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

       2. clear-num 54.5%

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

       3. un-div-inv 54.7%

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

   11. Applied egg-rr 54.7%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-185}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ t_2 := y \cdot \frac{z}{-a}\\ \mathbf{if}\;y \leq -4.75 \cdot 10^{+58}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 380:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+226}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))) (t_2 (* y (/ z (- a)))))
   (if (<= y -4.75e+58)
     t_2
     (if (<= y -4.5e-21)
       t_1
       (if (<= y 380.0)
         x
         (if (<= y 2.8e+49)
           (* y (/ t a))
           (if (<= y 3.2e+161)
             t_2
             (if (<= y 7.8e+191)
               (/ t (/ a y))
               (if (<= y 8e+191) x (if (<= y 5.8e+226) t_2 t_1))))))))))

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 (y <= -4.75e+58) {
		tmp = t_2;
	} else if (y <= -4.5e-21) {
		tmp = t_1;
	} else if (y <= 380.0) {
		tmp = x;
	} else if (y <= 2.8e+49) {
		tmp = y * (t / a);
	} else if (y <= 3.2e+161) {
		tmp = t_2;
	} else if (y <= 7.8e+191) {
		tmp = t / (a / y);
	} else if (y <= 8e+191) {
		tmp = x;
	} else if (y <= 5.8e+226) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (y / a)
    t_2 = y * (z / -a)
    if (y <= (-4.75d+58)) then
        tmp = t_2
    else if (y <= (-4.5d-21)) then
        tmp = t_1
    else if (y <= 380.0d0) then
        tmp = x
    else if (y <= 2.8d+49) then
        tmp = y * (t / a)
    else if (y <= 3.2d+161) then
        tmp = t_2
    else if (y <= 7.8d+191) then
        tmp = t / (a / y)
    else if (y <= 8d+191) then
        tmp = x
    else if (y <= 5.8d+226) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double t_2 = y * (z / -a);
	double tmp;
	if (y <= -4.75e+58) {
		tmp = t_2;
	} else if (y <= -4.5e-21) {
		tmp = t_1;
	} else if (y <= 380.0) {
		tmp = x;
	} else if (y <= 2.8e+49) {
		tmp = y * (t / a);
	} else if (y <= 3.2e+161) {
		tmp = t_2;
	} else if (y <= 7.8e+191) {
		tmp = t / (a / y);
	} else if (y <= 8e+191) {
		tmp = x;
	} else if (y <= 5.8e+226) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	t_2 = y * (z / -a)
	tmp = 0
	if y <= -4.75e+58:
		tmp = t_2
	elif y <= -4.5e-21:
		tmp = t_1
	elif y <= 380.0:
		tmp = x
	elif y <= 2.8e+49:
		tmp = y * (t / a)
	elif y <= 3.2e+161:
		tmp = t_2
	elif y <= 7.8e+191:
		tmp = t / (a / y)
	elif y <= 8e+191:
		tmp = x
	elif y <= 5.8e+226:
		tmp = t_2
	else:
		tmp = t_1
	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 (y <= -4.75e+58)
		tmp = t_2;
	elseif (y <= -4.5e-21)
		tmp = t_1;
	elseif (y <= 380.0)
		tmp = x;
	elseif (y <= 2.8e+49)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 3.2e+161)
		tmp = t_2;
	elseif (y <= 7.8e+191)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 8e+191)
		tmp = x;
	elseif (y <= 5.8e+226)
		tmp = t_2;
	else
		tmp = t_1;
	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 (y <= -4.75e+58)
		tmp = t_2;
	elseif (y <= -4.5e-21)
		tmp = t_1;
	elseif (y <= 380.0)
		tmp = x;
	elseif (y <= 2.8e+49)
		tmp = y * (t / a);
	elseif (y <= 3.2e+161)
		tmp = t_2;
	elseif (y <= 7.8e+191)
		tmp = t / (a / y);
	elseif (y <= 8e+191)
		tmp = x;
	elseif (y <= 5.8e+226)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.75e+58], t$95$2, If[LessEqual[y, -4.5e-21], t$95$1, If[LessEqual[y, 380.0], x, If[LessEqual[y, 2.8e+49], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+161], t$95$2, If[LessEqual[y, 7.8e+191], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+191], x, If[LessEqual[y, 5.8e+226], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.7500000000000001e58 or 2.7999999999999998e49 < y < 3.20000000000000002e161 or 8.00000000000000058e191 < y < 5.79999999999999949e226

   1. Initial program 85.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. associate-/l* 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

      4. distribute-neg-frac2 59.1%

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

   7. Simplified 59.1%

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

   if -4.7500000000000001e58 < y < -4.49999999999999968e-21 or 5.79999999999999949e226 < y

   1. Initial program 90.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 47.5%

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

      1. *-commutative 47.5%

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

   7. Simplified 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/l* 57.2%

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

      3. *-commutative 57.2%

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

   9. Applied egg-rr 57.2%

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

   if -4.49999999999999968e-21 < y < 380 or 7.8000000000000001e191 < y < 8.00000000000000058e191

   1. Initial program 99.9%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in x around inf 61.2%

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

   if 380 < y < 2.7999999999999998e49

   1. Initial program 82.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 46.4%

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

      1. *-commutative 46.4%

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

      2. associate-/l* 55.3%

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

   7. Simplified 55.3%

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

   if 3.20000000000000002e161 < y < 7.8000000000000001e191

   1. Initial program 47.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 46.7%

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

      1. *-commutative 46.7%

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

   7. Simplified 46.7%

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

      1. associate-/l* 67.8%

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

      2. *-commutative 67.8%

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

   9. Applied egg-rr 67.8%

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

       1. associate-/r/ 68.0%

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

   11. Applied egg-rr 68.0%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.75 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 380:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+191}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+191}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+226}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+173} \lor \neg \left(t \leq 1.45 \cdot 10^{-35}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e+173) (not (<= t 1.45e-35)))
   (+ x (/ (* t y) a))
   (- x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e+173) || !(t <= 1.45e-35)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1d+173)) .or. (.not. (t <= 1.45d-35))) then
        tmp = x + ((t * y) / a)
    else
        tmp = x - ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e+173) || !(t <= 1.45e-35)) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e+173) or not (t <= 1.45e-35):
		tmp = x + ((t * y) / a)
	else:
		tmp = x - ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e+173) || !(t <= 1.45e-35))
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1e+173) || ~((t <= 1.45e-35)))
		tmp = x + ((t * y) / a);
	else
		tmp = x - ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e+173], N[Not[LessEqual[t, 1.45e-35]], $MachinePrecision]], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1e173 or 1.4500000000000001e-35 < t

   1. Initial program 87.4%

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

      1. sub-neg 87.4%

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

      2. distribute-frac-neg2 87.4%

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

      3. +-commutative 87.4%

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

      4. associate-/l* 94.7%

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

      5. fma-define 94.7%

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

      6. distribute-frac-neg2 94.7%

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

      7. distribute-neg-frac 94.7%

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

      8. sub-neg 94.7%

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

      9. distribute-neg-in 94.7%

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

      10. remove-double-neg 94.7%

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

      11. +-commutative 94.7%

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

      12. sub-neg 94.7%

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

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.7%

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

   if -1e173 < t < 1.4500000000000001e-35

   1. Initial program 94.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 84.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+173} \lor \neg \left(t \leq 1.45 \cdot 10^{-35}\right):\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+163}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.14e+163)
   (* (/ y a) (- z))
   (if (<= z 1.7e+35) (+ x (/ (* t y) a)) (/ z (/ a (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.14e+163) {
		tmp = (y / a) * -z;
	} else if (z <= 1.7e+35) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = 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 (z <= (-1.14d+163)) then
        tmp = (y / a) * -z
    else if (z <= 1.7d+35) then
        tmp = x + ((t * y) / a)
    else
        tmp = 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 (z <= -1.14e+163) {
		tmp = (y / a) * -z;
	} else if (z <= 1.7e+35) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = z / (a / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.14e+163:
		tmp = (y / a) * -z
	elif z <= 1.7e+35:
		tmp = x + ((t * y) / a)
	else:
		tmp = z / (a / -y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.14e+163)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (z <= 1.7e+35)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(z / Float64(a / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.14e+163)
		tmp = (y / a) * -z;
	elseif (z <= 1.7e+35)
		tmp = x + ((t * y) / a);
	else
		tmp = z / (a / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.14e+163], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, 1.7e+35], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(z / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.13999999999999999e163

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-/l* 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-neg-frac2 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*r/ 89.0%

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

   7. Simplified 89.0%

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

   if -1.13999999999999999e163 < z < 1.7000000000000001e35

   1. Initial program 93.9%

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

      1. sub-neg 93.9%

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

      2. distribute-frac-neg2 93.9%

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

      3. +-commutative 93.9%

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

      4. associate-/l* 97.7%

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

      5. fma-define 97.7%

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

      6. distribute-frac-neg2 97.7%

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

      7. distribute-neg-frac 97.7%

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

      8. sub-neg 97.7%

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

      9. distribute-neg-in 97.7%

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

      10. remove-double-neg 97.7%

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

      11. +-commutative 97.7%

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

      12. sub-neg 97.7%

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

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 79.9%

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

   if 1.7000000000000001e35 < z

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 62.1%

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

      1. mul-1-neg 62.1%

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

      2. associate-*r/ 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-*l/ 62.1%

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

      5. associate-*r/ 68.0%

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

      6. distribute-lft-neg-in 68.0%

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

   9. Simplified 68.0%

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

       1. clear-num 68.1%

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

       2. un-div-inv 68.2%

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

       3. add-sqr-sqrt 0.0%

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

       4. sqrt-unprod 3.3%

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

       5. sqr-neg 3.3%

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

       6. sqrt-unprod 3.4%

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

       7. add-sqr-sqrt 3.4%

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

       8. frac-2neg 3.4%

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

       9. add-sqr-sqrt 0.0%

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

       10. sqrt-unprod 44.9%

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

       11. sqr-neg 44.9%

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

       12. sqrt-unprod 68.0%

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

       13. add-sqr-sqrt 68.2%

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

       14. distribute-neg-frac2 68.2%

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

   11. Applied egg-rr 68.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.14 \cdot 10^{+163}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -175000000000 \lor \neg \left(y \leq 88000\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -175000000000.0) (not (<= y 88000.0))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -175000000000.0) || !(y <= 88000.0)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-175000000000.0d0)) .or. (.not. (y <= 88000.0d0))) then
        tmp = y * (t / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -175000000000.0) || !(y <= 88000.0)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -175000000000.0) or not (y <= 88000.0):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -175000000000.0) || !(y <= 88000.0))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -175000000000.0) || ~((y <= 88000.0)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -175000000000.0], N[Not[LessEqual[y, 88000.0]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e11 or 88000 < y

   1. Initial program 83.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 38.5%

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

      1. *-commutative 38.5%

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

      2. associate-/l* 43.9%

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

   7. Simplified 43.9%

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

   if -1.75e11 < y < 88000

   1. Initial program 99.9%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 59.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -175000000000 \lor \neg \left(y \leq 88000\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 39:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.45e+24) (/ y (/ a t)) (if (<= y 39.0) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.45e+24) {
		tmp = y / (a / t);
	} else if (y <= 39.0) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.45d+24)) then
        tmp = y / (a / t)
    else if (y <= 39.0d0) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.45e+24) {
		tmp = y / (a / t);
	} else if (y <= 39.0) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.45e+24:
		tmp = y / (a / t)
	elif y <= 39.0:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.45e+24)
		tmp = Float64(y / Float64(a / t));
	elseif (y <= 39.0)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.45e+24)
		tmp = y / (a / t);
	elseif (y <= 39.0)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.45e+24], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 39.0], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4499999999999999e24

   1. Initial program 85.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 36.6%

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

      1. *-commutative 36.6%

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

   7. Simplified 36.6%

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

      1. associate-/l* 39.7%

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

      2. *-commutative 39.7%

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

   9. Applied egg-rr 39.7%

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

       1. *-commutative 39.7%

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

       2. clear-num 39.7%

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

       3. un-div-inv 39.8%

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

   11. Applied egg-rr 39.8%

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

   if -1.4499999999999999e24 < y < 39

   1. Initial program 99.9%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in x around inf 58.2%

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

   if 39 < y

   1. Initial program 79.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 40.6%

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

      1. *-commutative 40.6%

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

   7. Simplified 40.6%

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

      1. associate-/l* 48.6%

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

      2. *-commutative 48.6%

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

   9. Applied egg-rr 48.6%

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

       1. associate-/r/ 54.9%

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

   11. Applied egg-rr 54.9%

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

Alternative 9: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -340000000000:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 68:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -340000000000.0) (* y (/ t a)) (if (<= y 68.0) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -340000000000.0) {
		tmp = y * (t / a);
	} else if (y <= 68.0) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-340000000000.0d0)) then
        tmp = y * (t / a)
    else if (y <= 68.0d0) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -340000000000.0) {
		tmp = y * (t / a);
	} else if (y <= 68.0) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -340000000000.0:
		tmp = y * (t / a)
	elif y <= 68.0:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -340000000000.0)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 68.0)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -340000000000.0)
		tmp = y * (t / a);
	elseif (y <= 68.0)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -340000000000.0], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 68.0], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e11

   1. Initial program 86.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-/l* 39.5%

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

   7. Simplified 39.5%

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

   if -3.4e11 < y < 68

   1. Initial program 99.9%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 59.4%

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

   if 68 < y

   1. Initial program 79.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 40.6%

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

      1. *-commutative 40.6%

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

   7. Simplified 40.6%

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

      1. associate-/l* 48.6%

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

      2. *-commutative 48.6%

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

   9. Applied egg-rr 48.6%

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

       1. associate-/r/ 54.9%

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

   11. Applied egg-rr 54.9%

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

Alternative 10: 50.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 240000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.4e+14) (* y (/ t a)) (if (<= y 240000.0) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.4e+14) {
		tmp = y * (t / a);
	} else if (y <= 240000.0) {
		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 (y <= (-4.4d+14)) then
        tmp = y * (t / a)
    else if (y <= 240000.0d0) 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 (y <= -4.4e+14) {
		tmp = y * (t / a);
	} else if (y <= 240000.0) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.4e+14:
		tmp = y * (t / a)
	elif y <= 240000.0:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.4e+14)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= 240000.0)
		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 (y <= -4.4e+14)
		tmp = y * (t / a);
	elseif (y <= 240000.0)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.4e+14], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 240000.0], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4e14

   1. Initial program 86.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 36.4%

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

      1. *-commutative 36.4%

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

      2. associate-/l* 39.5%

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

   7. Simplified 39.5%

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

   if -4.4e14 < y < 2.4e5

   1. Initial program 99.9%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 59.4%

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

   if 2.4e5 < y

   1. Initial program 79.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 40.6%

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

      1. *-commutative 40.6%

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

   7. Simplified 40.6%

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

      1. *-commutative 40.6%

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

      2. associate-/l* 54.9%

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

      3. *-commutative 54.9%

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

   9. Applied egg-rr 54.9%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+14}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 240000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. *-commutative 91.8%

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

   2. associate-/l* 97.2%

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

4. Applied egg-rr 97.2%

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

5. Final simplification 97.2%

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

Alternative 12: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 95.8%

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

Alternative 13: 39.9% 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 91.8%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 38.8%

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

Developer target: 99.3% 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 2024107 
(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)))