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

Percentage Accurate: 93.2% → 97.6%

Time: 13.6s

Alternatives: 12

Speedup: 1.0×

• 25.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% 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. 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. Add Preprocessing

5. Taylor expanded in y around 0 91.8%

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

   1. *-commutative 91.8%

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

   2. associate-/l* 97.6%

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

7. Simplified 97.6%

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

8. Final simplification 97.6%

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

Alternative 2: 50.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+128}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+14} \lor \neg \left(y \leq -2.4 \cdot 10^{-45}\right) \land y \leq 6500000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= y -2.25e+206)
     t_1
     (if (<= y -1.9e+128)
       (/ t (/ a y))
       (if (or (<= y -5.3e+14) (and (not (<= y -2.4e-45)) (<= y 6500000000.0)))
         x
         t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (y <= -2.25e+206) {
		tmp = t_1;
	} else if (y <= -1.9e+128) {
		tmp = t / (a / y);
	} else if ((y <= -5.3e+14) || (!(y <= -2.4e-45) && (y <= 6500000000.0))) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / -a)
    if (y <= (-2.25d+206)) then
        tmp = t_1
    else if (y <= (-1.9d+128)) then
        tmp = t / (a / y)
    else if ((y <= (-5.3d+14)) .or. (.not. (y <= (-2.4d-45))) .and. (y <= 6500000000.0d0)) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (y <= -2.25e+206) {
		tmp = t_1;
	} else if (y <= -1.9e+128) {
		tmp = t / (a / y);
	} else if ((y <= -5.3e+14) || (!(y <= -2.4e-45) && (y <= 6500000000.0))) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if y <= -2.25e+206:
		tmp = t_1
	elif y <= -1.9e+128:
		tmp = t / (a / y)
	elif (y <= -5.3e+14) or (not (y <= -2.4e-45) and (y <= 6500000000.0)):
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (y <= -2.25e+206)
		tmp = t_1;
	elseif (y <= -1.9e+128)
		tmp = Float64(t / Float64(a / y));
	elseif ((y <= -5.3e+14) || (!(y <= -2.4e-45) && (y <= 6500000000.0)))
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (y <= -2.25e+206)
		tmp = t_1;
	elseif (y <= -1.9e+128)
		tmp = t / (a / y);
	elseif ((y <= -5.3e+14) || (~((y <= -2.4e-45)) && (y <= 6500000000.0)))
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e+206], t$95$1, If[LessEqual[y, -1.9e+128], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.3e+14], And[N[Not[LessEqual[y, -2.4e-45]], $MachinePrecision], LessEqual[y, 6500000000.0]]], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.25000000000000009e206 or -5.3e14 < y < -2.3999999999999999e-45 or 6.5e9 < y

   1. Initial program 86.3%

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

   5. Taylor expanded in z around inf 52.2%

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

      1. mul-1-neg 52.2%

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

      2. associate-*l/ 57.5%

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

      3. *-commutative 57.5%

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

      4. distribute-rgt-neg-in 57.5%

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

      5. *-lft-identity 57.5%

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

      6. associate-*l/ 57.4%

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

      7. remove-double-neg 57.4%

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

      8. neg-mul-1 57.4%

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

      9. associate-*r* 57.4%

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

      10. *-commutative 57.4%

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

      11. neg-mul-1 57.4%

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

      12. *-commutative 57.4%

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

      13. distribute-neg-frac 57.4%

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

      14. metadata-eval 57.4%

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

      15. metadata-eval 57.4%

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

      16. associate-/r* 57.4%

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

      17. neg-mul-1 57.4%

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

      18. associate-*r/ 57.5%

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

      19. *-rgt-identity 57.5%

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

      20. distribute-frac-neg 57.5%

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

      21. remove-double-neg 57.5%

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

   7. Simplified 57.5%

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

   if -2.25000000000000009e206 < y < -1.89999999999999995e128

   1. Initial program 84.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 69.3%

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

   7. Simplified 69.3%

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

      1. clear-num 69.3%

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

      2. div-inv 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -1.89999999999999995e128 < y < -5.3e14 or -2.3999999999999999e-45 < y < 6.5e9

   1. Initial program 97.1%

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

   5. Taylor expanded in x around inf 61.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+206}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+128}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{+14} \lor \neg \left(y \leq -2.4 \cdot 10^{-45}\right) \land y \leq 6500000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+206}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -19500000000000 \lor \neg \left(y \leq -2.05 \cdot 10^{-45}\right) \land y \leq 42000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.3e+206)
   (/ y (/ a (- z)))
   (if (<= y -7.5e+127)
     (/ t (/ a y))
     (if (or (<= y -19500000000000.0)
             (and (not (<= y -2.05e-45)) (<= y 42000000.0)))
       x
       (* z (/ y (- a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.3e+206) {
		tmp = y / (a / -z);
	} else if (y <= -7.5e+127) {
		tmp = t / (a / y);
	} else if ((y <= -19500000000000.0) || (!(y <= -2.05e-45) && (y <= 42000000.0))) {
		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 (y <= (-1.3d+206)) then
        tmp = y / (a / -z)
    else if (y <= (-7.5d+127)) then
        tmp = t / (a / y)
    else if ((y <= (-19500000000000.0d0)) .or. (.not. (y <= (-2.05d-45))) .and. (y <= 42000000.0d0)) 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 (y <= -1.3e+206) {
		tmp = y / (a / -z);
	} else if (y <= -7.5e+127) {
		tmp = t / (a / y);
	} else if ((y <= -19500000000000.0) || (!(y <= -2.05e-45) && (y <= 42000000.0))) {
		tmp = x;
	} else {
		tmp = z * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.3e+206:
		tmp = y / (a / -z)
	elif y <= -7.5e+127:
		tmp = t / (a / y)
	elif (y <= -19500000000000.0) or (not (y <= -2.05e-45) and (y <= 42000000.0)):
		tmp = x
	else:
		tmp = z * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.3e+206)
		tmp = Float64(y / Float64(a / Float64(-z)));
	elseif (y <= -7.5e+127)
		tmp = Float64(t / Float64(a / y));
	elseif ((y <= -19500000000000.0) || (!(y <= -2.05e-45) && (y <= 42000000.0)))
		tmp = x;
	else
		tmp = Float64(z * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.3e+206)
		tmp = y / (a / -z);
	elseif (y <= -7.5e+127)
		tmp = t / (a / y);
	elseif ((y <= -19500000000000.0) || (~((y <= -2.05e-45)) && (y <= 42000000.0)))
		tmp = x;
	else
		tmp = z * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.3e+206], N[(y / N[(a / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e+127], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -19500000000000.0], And[N[Not[LessEqual[y, -2.05e-45]], $MachinePrecision], LessEqual[y, 42000000.0]]], x, N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.29999999999999994e206

   1. Initial program 95.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0 95.1%

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

      1. *-commutative 95.1%

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

      2. associate-/l* 95.2%

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

   7. Simplified 95.2%

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

   8. Taylor expanded in z around inf 62.3%

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

      1. associate-*r/ 62.3%

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

      2. mul-1-neg 62.3%

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

      3. distribute-rgt-neg-out 62.3%

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

      4. associate-/l* 66.9%

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

   10. Simplified 66.9%

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

   if -1.29999999999999994e206 < y < -7.4999999999999996e127

   1. Initial program 84.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 69.3%

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

   7. Simplified 69.3%

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

      1. clear-num 69.3%

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

      2. div-inv 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -7.4999999999999996e127 < y < -1.95e13 or -2.05e-45 < y < 4.2e7

   1. Initial program 97.1%

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

   5. Taylor expanded in x around inf 61.1%

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

   if -1.95e13 < y < -2.05e-45 or 4.2e7 < y

   1. Initial program 84.2%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 49.8%

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

      1. mul-1-neg 49.8%

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

      2. associate-*l/ 55.4%

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

      3. *-commutative 55.4%

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

      4. distribute-rgt-neg-in 55.4%

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

      5. *-lft-identity 55.4%

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

      6. associate-*l/ 55.4%

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

      7. remove-double-neg 55.4%

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

      8. neg-mul-1 55.4%

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

      9. associate-*r* 55.4%

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

      10. *-commutative 55.4%

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

      11. neg-mul-1 55.4%

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

      12. *-commutative 55.4%

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

      13. distribute-neg-frac 55.4%

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

      14. metadata-eval 55.4%

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

      15. metadata-eval 55.4%

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

      16. associate-/r* 55.4%

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

      17. neg-mul-1 55.4%

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

      18. associate-*r/ 55.4%

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

      19. *-rgt-identity 55.4%

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

      20. distribute-frac-neg 55.4%

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

      21. remove-double-neg 55.4%

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

   7. Simplified 55.4%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+206}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+127}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -19500000000000 \lor \neg \left(y \leq -2.05 \cdot 10^{-45}\right) \land y \leq 42000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+206}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+128}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+14} \lor \neg \left(y \leq -7 \cdot 10^{-46}\right) \land y \leq 38000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.95e+206)
   (/ y (/ a (- z)))
   (if (<= y -2.7e+128)
     (/ t (/ a y))
     (if (or (<= y -2.35e+14) (and (not (<= y -7e-46)) (<= y 38000000.0)))
       x
       (/ (- z) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.95e+206) {
		tmp = y / (a / -z);
	} else if (y <= -2.7e+128) {
		tmp = t / (a / y);
	} else if ((y <= -2.35e+14) || (!(y <= -7e-46) && (y <= 38000000.0))) {
		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) :: tmp
    if (y <= (-2.95d+206)) then
        tmp = y / (a / -z)
    else if (y <= (-2.7d+128)) then
        tmp = t / (a / y)
    else if ((y <= (-2.35d+14)) .or. (.not. (y <= (-7d-46))) .and. (y <= 38000000.0d0)) 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 tmp;
	if (y <= -2.95e+206) {
		tmp = y / (a / -z);
	} else if (y <= -2.7e+128) {
		tmp = t / (a / y);
	} else if ((y <= -2.35e+14) || (!(y <= -7e-46) && (y <= 38000000.0))) {
		tmp = x;
	} else {
		tmp = -z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.95e+206:
		tmp = y / (a / -z)
	elif y <= -2.7e+128:
		tmp = t / (a / y)
	elif (y <= -2.35e+14) or (not (y <= -7e-46) and (y <= 38000000.0)):
		tmp = x
	else:
		tmp = -z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.95e+206)
		tmp = Float64(y / Float64(a / Float64(-z)));
	elseif (y <= -2.7e+128)
		tmp = Float64(t / Float64(a / y));
	elseif ((y <= -2.35e+14) || (!(y <= -7e-46) && (y <= 38000000.0)))
		tmp = x;
	else
		tmp = Float64(Float64(-z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.95e+206)
		tmp = y / (a / -z);
	elseif (y <= -2.7e+128)
		tmp = t / (a / y);
	elseif ((y <= -2.35e+14) || (~((y <= -7e-46)) && (y <= 38000000.0)))
		tmp = x;
	else
		tmp = -z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.95e+206], N[(y / N[(a / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e+128], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.35e+14], And[N[Not[LessEqual[y, -7e-46]], $MachinePrecision], LessEqual[y, 38000000.0]]], x, N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.95e206

   1. Initial program 95.1%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in y around 0 95.1%

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

      1. *-commutative 95.1%

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

      2. associate-/l* 95.2%

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

   7. Simplified 95.2%

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

   8. Taylor expanded in z around inf 62.3%

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

      1. associate-*r/ 62.3%

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

      2. mul-1-neg 62.3%

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

      3. distribute-rgt-neg-out 62.3%

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

      4. associate-/l* 66.9%

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

   10. Simplified 66.9%

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

   if -2.95e206 < y < -2.70000000000000001e128

   1. Initial program 84.8%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 69.3%

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

   7. Simplified 69.3%

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

      1. clear-num 69.3%

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

      2. div-inv 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -2.70000000000000001e128 < y < -2.35e14 or -7.0000000000000004e-46 < y < 3.8e7

   1. Initial program 97.1%

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

   5. Taylor expanded in x around inf 61.1%

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

   if -2.35e14 < y < -7.0000000000000004e-46 or 3.8e7 < y

   1. Initial program 84.2%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around inf 49.8%

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

      1. mul-1-neg 49.8%

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

      2. associate-*l/ 55.4%

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

      3. *-commutative 55.4%

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

      4. distribute-rgt-neg-in 55.4%

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

      5. *-lft-identity 55.4%

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

      6. associate-*l/ 55.4%

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

      7. remove-double-neg 55.4%

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

      8. neg-mul-1 55.4%

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

      9. associate-*r* 55.4%

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

      10. *-commutative 55.4%

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

      11. neg-mul-1 55.4%

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

      12. *-commutative 55.4%

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

      13. distribute-neg-frac 55.4%

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

      14. metadata-eval 55.4%

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

      15. metadata-eval 55.4%

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

      16. associate-/r* 55.4%

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

      17. neg-mul-1 55.4%

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

      18. associate-*r/ 55.4%

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

      19. *-rgt-identity 55.4%

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

      20. distribute-frac-neg 55.4%

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

      21. remove-double-neg 55.4%

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

   7. Simplified 55.4%

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

      1. add-sqr-sqrt 26.4%

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

      2. sqrt-unprod 22.1%

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

      3. sqr-neg 22.1%

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

      4. sqrt-unprod 2.5%

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

      5. add-sqr-sqrt 4.2%

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

      6. clear-num 4.2%

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

      7. div-inv 4.2%

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

      8. frac-2neg 4.2%

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

      9. distribute-frac-neg 4.2%

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

      10. add-sqr-sqrt 1.6%

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

      11. sqrt-unprod 26.1%

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

      12. sqr-neg 26.1%

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

      13. sqrt-unprod 28.9%

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

      14. add-sqr-sqrt 56.0%

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

   9. Applied egg-rr 56.0%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+206}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{+128}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{+14} \lor \neg \left(y \leq -7 \cdot 10^{-46}\right) \land y \leq 38000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+127} \lor \neg \left(y \leq -7.2 \cdot 10^{+115}\right) \land \left(y \leq -1.85 \cdot 10^{-128} \lor \neg \left(y \leq 3.2 \cdot 10^{-50}\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e+127)
         (and (not (<= y -7.2e+115))
              (or (<= y -1.85e-128) (not (<= y 3.2e-50)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e+127) || (!(y <= -7.2e+115) && ((y <= -1.85e-128) || !(y <= 3.2e-50)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5d+127)) .or. (.not. (y <= (-7.2d+115))) .and. (y <= (-1.85d-128)) .or. (.not. (y <= 3.2d-50))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e+127) || (!(y <= -7.2e+115) && ((y <= -1.85e-128) || !(y <= 3.2e-50)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5e+127) or (not (y <= -7.2e+115) and ((y <= -1.85e-128) or not (y <= 3.2e-50))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e+127) || (!(y <= -7.2e+115) && ((y <= -1.85e-128) || !(y <= 3.2e-50))))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5e+127) || (~((y <= -7.2e+115)) && ((y <= -1.85e-128) || ~((y <= 3.2e-50)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e+127], And[N[Not[LessEqual[y, -7.2e+115]], $MachinePrecision], Or[LessEqual[y, -1.85e-128], N[Not[LessEqual[y, 3.2e-50]], $MachinePrecision]]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000004e127 or -7.2000000000000001e115 < y < -1.85e-128 or 3.2e-50 < y

   1. Initial program 88.0%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 76.9%

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

      3. distribute-rgt-neg-out 76.9%

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

      4. *-rgt-identity 76.9%

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

      5. *-rgt-identity 76.9%

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

      6. distribute-neg-frac 76.9%

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

      7. neg-sub0 76.9%

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

      8. associate--r- 76.9%

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

      9. neg-sub0 76.9%

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

      10. +-commutative 76.9%

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

      11. sub-neg 76.9%

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

   7. Simplified 76.9%

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

   if -5.0000000000000004e127 < y < -7.2000000000000001e115 or -1.85e-128 < y < 3.2e-50

   1. Initial program 98.8%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 70.2%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+127} \lor \neg \left(y \leq -7.2 \cdot 10^{+115}\right) \land \left(y \leq -1.85 \cdot 10^{-128} \lor \neg \left(y \leq 3.2 \cdot 10^{-50}\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.1e-39)
   (+ x (* t (/ y a)))
   (if (<= t 2.65e+57) (- x (/ y (/ a z))) (- x (/ y (/ (- a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e-39) {
		tmp = x + (t * (y / a));
	} else if (t <= 2.65e+57) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3.1d-39)) then
        tmp = x + (t * (y / a))
    else if (t <= 2.65d+57) then
        tmp = x - (y / (a / z))
    else
        tmp = x - (y / (-a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.1e-39) {
		tmp = x + (t * (y / a));
	} else if (t <= 2.65e+57) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.1e-39:
		tmp = x + (t * (y / a))
	elif t <= 2.65e+57:
		tmp = x - (y / (a / z))
	else:
		tmp = x - (y / (-a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.1e-39)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (t <= 2.65e+57)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.1e-39)
		tmp = x + (t * (y / a));
	elseif (t <= 2.65e+57)
		tmp = x - (y / (a / z));
	else
		tmp = x - (y / (-a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.1e-39], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+57], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.0999999999999997e-39

   1. Initial program 90.0%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 74.8%

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

      1. cancel-sign-sub-inv 74.8%

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

      2. metadata-eval 74.8%

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

      3. *-lft-identity 74.8%

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

      4. +-commutative 74.8%

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

      5. associate-*r/ 82.3%

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

   7. Simplified 82.3%

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

   if -3.0999999999999997e-39 < t < 2.64999999999999993e57

   1. Initial program 91.9%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in z around inf 89.6%

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

   if 2.64999999999999993e57 < t

   1. Initial program 94.1%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in z around 0 92.0%

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

      1. associate-*r/ 92.0%

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

      2. neg-mul-1 92.0%

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

   7. Simplified 92.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-39}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+25} \lor \neg \left(x \leq 7 \cdot 10^{-56}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -8.2e+25) (not (<= x 7e-56)))
   (+ x (* t (/ y a)))
   (* y (/ (- t z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e+25) || !(x <= 7e-56)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-8.2d+25)) .or. (.not. (x <= 7d-56))) then
        tmp = x + (t * (y / a))
    else
        tmp = y * ((t - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -8.2e+25) || !(x <= 7e-56)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -8.2e+25) or not (x <= 7e-56):
		tmp = x + (t * (y / a))
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -8.2e+25) || !(x <= 7e-56))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -8.2e+25) || ~((x <= 7e-56)))
		tmp = x + (t * (y / a));
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -8.2e+25], N[Not[LessEqual[x, 7e-56]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.19999999999999933e25 or 6.9999999999999996e-56 < x

   1. Initial program 91.9%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 74.0%

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

      1. cancel-sign-sub-inv 74.0%

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

      2. metadata-eval 74.0%

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

      3. *-lft-identity 74.0%

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

      4. +-commutative 74.0%

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

      5. associate-*r/ 78.9%

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

   7. Simplified 78.9%

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

   if -8.19999999999999933e25 < x < 6.9999999999999996e-56

   1. Initial program 91.6%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in x around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. associate-*r/ 79.4%

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

      3. distribute-rgt-neg-out 79.4%

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

      4. *-rgt-identity 79.4%

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

      5. *-rgt-identity 79.4%

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

      6. distribute-neg-frac 79.4%

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

      7. neg-sub0 79.4%

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

      8. associate--r- 79.4%

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

      9. neg-sub0 79.4%

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

      10. +-commutative 79.4%

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

      11. sub-neg 79.4%

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

   7. Simplified 79.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+25} \lor \neg \left(x \leq 7 \cdot 10^{-56}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -65000000 \lor \neg \left(z \leq 1.2 \cdot 10^{+91}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -65000000.0) (not (<= z 1.2e+91)))
   (- x (/ y (/ a z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -65000000.0) || !(z <= 1.2e+91)) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-65000000.0d0)) .or. (.not. (z <= 1.2d+91))) then
        tmp = x - (y / (a / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -65000000.0) || !(z <= 1.2e+91)) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -65000000.0) or not (z <= 1.2e+91):
		tmp = x - (y / (a / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -65000000.0) || !(z <= 1.2e+91))
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -65000000.0) || ~((z <= 1.2e+91)))
		tmp = x - (y / (a / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -65000000.0], N[Not[LessEqual[z, 1.2e+91]], $MachinePrecision]], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e7 or 1.19999999999999991e91 < z

   1. Initial program 88.1%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 88.9%

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

   if -6.5e7 < z < 1.19999999999999991e91

   1. Initial program 95.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. cancel-sign-sub-inv 80.0%

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

      2. metadata-eval 80.0%

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

      3. *-lft-identity 80.0%

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

      4. +-commutative 80.0%

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

      5. associate-*r/ 86.3%

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

   7. Simplified 86.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -65000000 \lor \neg \left(z \leq 1.2 \cdot 10^{+91}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+127} \lor \neg \left(y \leq 320000000\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5e+127) (not (<= y 320000000.0))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e+127) || !(y <= 320000000.0)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5d+127)) .or. (.not. (y <= 320000000.0d0))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5e+127) || !(y <= 320000000.0)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5e+127) or not (y <= 320000000.0):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5e+127) || !(y <= 320000000.0))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5e+127) || ~((y <= 320000000.0)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5e+127], N[Not[LessEqual[y, 320000000.0]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000004e127 or 3.2e8 < y

   1. Initial program 83.9%

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

   5. Taylor expanded in t around inf 40.0%

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

      1. associate-*r/ 47.8%

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

   7. Simplified 47.8%

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

   if -5.0000000000000004e127 < y < 3.2e8

   1. Initial program 97.4%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 56.4%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+127} \lor \neg \left(y \leq 320000000\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+128} \lor \neg \left(y \leq 2500000000\right):\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e+128) (not (<= y 2500000000.0))) (/ t (/ a y)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e+128) || !(y <= 2500000000.0)) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.9d+128)) .or. (.not. (y <= 2500000000.0d0))) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e+128) || !(y <= 2500000000.0)) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e+128) or not (y <= 2500000000.0):
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e+128) || !(y <= 2500000000.0))
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e+128) || ~((y <= 2500000000.0)))
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e+128], N[Not[LessEqual[y, 2500000000.0]], $MachinePrecision]], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e128 or 2.5e9 < y

   1. Initial program 83.9%

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

   5. Taylor expanded in t around inf 40.0%

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

      1. associate-*r/ 47.8%

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

   7. Simplified 47.8%

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

      1. clear-num 47.8%

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

      2. div-inv 47.9%

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

   9. Applied egg-rr 47.9%

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

   if -2.9e128 < y < 2.5e9

   1. Initial program 97.4%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 56.4%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+128} \lor \neg \left(y \leq 2500000000\right):\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.5% 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. 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. Add Preprocessing

5. Final simplification 97.4%

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

Alternative 12: 39.5% 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/ 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. Add Preprocessing

5. Taylor expanded in x around inf 39.1%

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

6. Final simplification 39.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024014 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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