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

Percentage Accurate: 93.1% → 97.2%

Time: 10.1s

Alternatives: 10

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

   1. *-commutative 97.3%

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

   2. clear-num 97.0%

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

   3. un-div-inv 97.5%

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

5. Applied egg-rr 97.5%

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

6. Final simplification 97.5%

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

Alternative 2: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+134)
   (* y (/ z a))
   (if (<= z -2.3e-201)
     x
     (if (<= z 1.65e-273)
       (* t (/ y (- a)))
       (if (<= z 4.7e+67) x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+134) {
		tmp = y * (z / a);
	} else if (z <= -2.3e-201) {
		tmp = x;
	} else if (z <= 1.65e-273) {
		tmp = t * (y / -a);
	} else if (z <= 4.7e+67) {
		tmp = x;
	} 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+134)) then
        tmp = y * (z / a)
    else if (z <= (-2.3d-201)) then
        tmp = x
    else if (z <= 1.65d-273) then
        tmp = t * (y / -a)
    else if (z <= 4.7d+67) then
        tmp = x
    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+134) {
		tmp = y * (z / a);
	} else if (z <= -2.3e-201) {
		tmp = x;
	} else if (z <= 1.65e-273) {
		tmp = t * (y / -a);
	} else if (z <= 4.7e+67) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+134:
		tmp = y * (z / a)
	elif z <= -2.3e-201:
		tmp = x
	elif z <= 1.65e-273:
		tmp = t * (y / -a)
	elif z <= 4.7e+67:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+134)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= -2.3e-201)
		tmp = x;
	elseif (z <= 1.65e-273)
		tmp = Float64(t * Float64(y / Float64(-a)));
	elseif (z <= 4.7e+67)
		tmp = x;
	else
		tmp = 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+134)
		tmp = y * (z / a);
	elseif (z <= -2.3e-201)
		tmp = x;
	elseif (z <= 1.65e-273)
		tmp = t * (y / -a);
	elseif (z <= 4.7e+67)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+134], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-201], x, If[LessEqual[z, 1.65e-273], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.7e+67], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4e134

   1. Initial program 94.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 62.0%

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

   5. Taylor expanded in z around inf 62.1%

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

   if -5.4e134 < z < -2.29999999999999986e-201 or 1.64999999999999995e-273 < z < 4.70000000000000017e67

   1. Initial program 92.4%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 56.0%

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

   if -2.29999999999999986e-201 < z < 1.64999999999999995e-273

   1. Initial program 91.3%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 62.1%

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

   5. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-frac-neg 62.1%

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

   7. Simplified 62.1%

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

      1. *-commutative 62.1%

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

      2. frac-2neg 62.1%

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

      3. remove-double-neg 62.1%

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

      4. associate-*r/ 57.8%

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

   9. Applied egg-rr 57.8%

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

       1. associate-/l* 62.1%

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

       2. associate-/r/ 59.9%

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

   11. Simplified 59.9%

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

   if 4.70000000000000017e67 < z

   1. Initial program 91.2%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. sub-div 64.9%

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

      2. associate-/r/ 75.7%

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

   6. Applied egg-rr 75.7%

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

   7. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 62.8%

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

   9. Simplified 62.8%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-273}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 50.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+134)
   (* y (/ z a))
   (if (<= z -5e-195)
     x
     (if (<= z 1.58e-273)
       (* y (/ (- t) a))
       (if (<= z 6.8e+67) x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+134) {
		tmp = y * (z / a);
	} else if (z <= -5e-195) {
		tmp = x;
	} else if (z <= 1.58e-273) {
		tmp = y * (-t / a);
	} else if (z <= 6.8e+67) {
		tmp = x;
	} 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 <= (-5.5d+134)) then
        tmp = y * (z / a)
    else if (z <= (-5d-195)) then
        tmp = x
    else if (z <= 1.58d-273) then
        tmp = y * (-t / a)
    else if (z <= 6.8d+67) then
        tmp = x
    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 <= -5.5e+134) {
		tmp = y * (z / a);
	} else if (z <= -5e-195) {
		tmp = x;
	} else if (z <= 1.58e-273) {
		tmp = y * (-t / a);
	} else if (z <= 6.8e+67) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+134:
		tmp = y * (z / a)
	elif z <= -5e-195:
		tmp = x
	elif z <= 1.58e-273:
		tmp = y * (-t / a)
	elif z <= 6.8e+67:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+134)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= -5e-195)
		tmp = x;
	elseif (z <= 1.58e-273)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (z <= 6.8e+67)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+134)
		tmp = y * (z / a);
	elseif (z <= -5e-195)
		tmp = x;
	elseif (z <= 1.58e-273)
		tmp = y * (-t / a);
	elseif (z <= 6.8e+67)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+134], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5e-195], x, If[LessEqual[z, 1.58e-273], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+67], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.4999999999999999e134

   1. Initial program 94.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 62.0%

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

   5. Taylor expanded in z around inf 62.1%

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

   if -5.4999999999999999e134 < z < -5.00000000000000009e-195 or 1.57999999999999994e-273 < z < 6.8000000000000003e67

   1. Initial program 92.4%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 56.0%

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

   if -5.00000000000000009e-195 < z < 1.57999999999999994e-273

   1. Initial program 91.3%

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

      1. associate-*l/ 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 62.1%

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

   5. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-frac-neg 62.1%

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

   7. Simplified 62.1%

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

   if 6.8000000000000003e67 < z

   1. Initial program 91.2%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. sub-div 64.9%

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

      2. associate-/r/ 75.7%

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

   6. Applied egg-rr 75.7%

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

   7. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 62.8%

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

   9. Simplified 62.8%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+134}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-195}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.58 \cdot 10^{-273}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-42} \lor \neg \left(y \leq 1.45 \cdot 10^{-74}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.5e-42) (not (<= y 1.45e-74))) (* (- z t) (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.5e-42) || !(y <= 1.45e-74)) {
		tmp = (z - 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 ((y <= (-3.5d-42)) .or. (.not. (y <= 1.45d-74))) then
        tmp = (z - 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 ((y <= -3.5e-42) || !(y <= 1.45e-74)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.5e-42) or not (y <= 1.45e-74):
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.5e-42) || !(y <= 1.45e-74))
		tmp = Float64(Float64(z - 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 ((y <= -3.5e-42) || ~((y <= 1.45e-74)))
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.5e-42], N[Not[LessEqual[y, 1.45e-74]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.5000000000000002e-42 or 1.45e-74 < y

   1. Initial program 86.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around 0 94.3%

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

   5. Taylor expanded in a around 0 68.0%

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

   6. Taylor expanded in z around 0 59.3%

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

      1. associate-*l/ 60.1%

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

      2. mul-1-neg 60.1%

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

      3. associate-/l* 64.2%

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

      4. fma-def 65.6%

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

      5. fma-neg 64.2%

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

      6. associate-/r/ 62.7%

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

      7. distribute-lft-out-- 74.3%

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

   8. Simplified 74.3%

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

   if -3.5000000000000002e-42 < y < 1.45e-74

   1. Initial program 98.6%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around inf 67.6%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-42} \lor \neg \left(y \leq 1.45 \cdot 10^{-74}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -11.5 \lor \neg \left(t \leq 1.4 \cdot 10^{+145}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -11.5) (not (<= t 1.4e+145)))
   (* (- z t) (/ y a))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -11.5) || !(t <= 1.4e+145)) {
		tmp = (z - 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 <= (-11.5d0)) .or. (.not. (t <= 1.4d+145))) then
        tmp = (z - 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 <= -11.5) || !(t <= 1.4e+145)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -11.5) or not (t <= 1.4e+145):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -11.5) || !(t <= 1.4e+145))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -11.5) || ~((t <= 1.4e+145)))
		tmp = (z - 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, -11.5], N[Not[LessEqual[t, 1.4e+145]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -11.5 or 1.3999999999999999e145 < t

   1. Initial program 87.0%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in y around 0 85.8%

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

   5. Taylor expanded in a around 0 64.0%

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

   6. Taylor expanded in z around 0 56.1%

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

      1. associate-*l/ 57.2%

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

      2. mul-1-neg 57.2%

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

      3. associate-/l* 58.9%

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

      4. fma-def 60.9%

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

      5. fma-neg 58.9%

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

      6. associate-/r/ 62.7%

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

      7. distribute-lft-out-- 70.5%

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

   8. Simplified 70.5%

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

   if -11.5 < t < 1.3999999999999999e145

   1. Initial program 95.7%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around 0 84.9%

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

      1. associate-*l/ 88.0%

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

      2. *-commutative 88.0%

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

   6. Simplified 88.0%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -11.5 \lor \neg \left(t \leq 1.4 \cdot 10^{+145}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \lor \neg \left(t \leq 6.1 \cdot 10^{+72}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.45) (not (<= t 6.1e+72)))
   (- 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 <= -1.45) || !(t <= 6.1e+72)) {
		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 <= (-1.45d0)) .or. (.not. (t <= 6.1d+72))) 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 <= -1.45) || !(t <= 6.1e+72)) {
		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 <= -1.45) or not (t <= 6.1e+72):
		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 <= -1.45) || !(t <= 6.1e+72))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.45) || ~((t <= 6.1e+72)))
		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, -1.45], N[Not[LessEqual[t, 6.1e+72]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999996 or 6.09999999999999991e72 < t

   1. Initial program 86.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. associate-*l/ 88.8%

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

      3. distribute-rgt-neg-out 88.8%

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

      4. +-commutative 88.8%

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

      5. *-commutative 88.8%

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

      6. distribute-lft-neg-out 88.8%

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

      7. unsub-neg 88.8%

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

   6. Simplified 88.8%

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

   if -1.44999999999999996 < t < 6.09999999999999991e72

   1. Initial program 96.2%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in t around 0 84.8%

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

      1. associate-*l/ 87.4%

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

      2. *-commutative 87.4%

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

   6. Simplified 87.4%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \lor \neg \left(t \leq 6.1 \cdot 10^{+72}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 51.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133} \lor \neg \left(z \leq 1.05 \cdot 10^{+68}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+133) (not (<= z 1.05e+68))) (* z (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+133) || !(z <= 1.05e+68)) {
		tmp = z * (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 ((z <= (-3.8d+133)) .or. (.not. (z <= 1.05d+68))) then
        tmp = z * (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 ((z <= -3.8e+133) || !(z <= 1.05e+68)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+133) or not (z <= 1.05e+68):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+133) || !(z <= 1.05e+68))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e+133) || ~((z <= 1.05e+68)))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+133], N[Not[LessEqual[z, 1.05e+68]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e133 or 1.05e68 < z

   1. Initial program 92.4%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 61.1%

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

      1. sub-div 66.3%

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

      2. associate-/r/ 73.6%

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

   6. Applied egg-rr 73.6%

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

   7. Taylor expanded in z around inf 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*r/ 61.9%

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

   9. Simplified 61.9%

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

   if -3.8000000000000002e133 < z < 1.05e68

   1. Initial program 92.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 52.3%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133} \lor \neg \left(z \leq 1.05 \cdot 10^{+68}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+133) (* y (/ z a)) (if (<= z 1.05e+67) x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+133) {
		tmp = y * (z / a);
	} else if (z <= 1.05e+67) {
		tmp = x;
	} 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 <= (-3.8d+133)) then
        tmp = y * (z / a)
    else if (z <= 1.05d+67) then
        tmp = x
    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 <= -3.8e+133) {
		tmp = y * (z / a);
	} else if (z <= 1.05e+67) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+133:
		tmp = y * (z / a)
	elif z <= 1.05e+67:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+133)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= 1.05e+67)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+133)
		tmp = y * (z / a);
	elseif (z <= 1.05e+67)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+133], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+67], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e133

   1. Initial program 94.0%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in y around inf 62.0%

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

   5. Taylor expanded in z around inf 62.1%

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

   if -3.8000000000000002e133 < z < 1.0500000000000001e67

   1. Initial program 92.1%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 52.3%

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

   if 1.0500000000000001e67 < z

   1. Initial program 91.2%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 60.4%

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

      1. sub-div 64.9%

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

      2. associate-/r/ 75.7%

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

   6. Applied egg-rr 75.7%

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

   7. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. associate-*r/ 62.8%

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

   9. Simplified 62.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+133}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 10: 39.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in x around inf 44.0%

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

5. Final simplification 44.0%

   \[\leadsto x \]

Developer target: 99.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

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

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