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

Percentage Accurate: 93.3% → 97.1%

Time: 11.4s

Alternatives: 15

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% 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: 97.1% 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 93.9%

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

   1. *-commutative 93.9%

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

   2. associate-/l* 97.6%

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

4. Applied egg-rr 97.6%

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

   1. clear-num 97.5%

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

   2. un-div-inv 97.8%

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

6. Applied egg-rr 97.8%

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

7. Final simplification 97.8%

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

Alternative 2: 46.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ t_2 := \frac{y}{a} \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167} \lor \neg \left(z \leq 6.5 \cdot 10^{+245}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))) (t_2 (* (/ y a) (- z))))
   (if (<= z -5.2e+76)
     t_2
     (if (<= z 1.6e-227)
       t_1
       (if (<= z 2.6e-183)
         x
         (if (<= z 3e+53)
           t_1
           (if (or (<= z 1.15e+167) (not (<= z 6.5e+245))) t_2 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -5.2e+76) {
		tmp = t_2;
	} else if (z <= 1.6e-227) {
		tmp = t_1;
	} else if (z <= 2.6e-183) {
		tmp = x;
	} else if (z <= 3e+53) {
		tmp = t_1;
	} else if ((z <= 1.15e+167) || !(z <= 6.5e+245)) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (a / y)
    t_2 = (y / a) * -z
    if (z <= (-5.2d+76)) then
        tmp = t_2
    else if (z <= 1.6d-227) then
        tmp = t_1
    else if (z <= 2.6d-183) then
        tmp = x
    else if (z <= 3d+53) then
        tmp = t_1
    else if ((z <= 1.15d+167) .or. (.not. (z <= 6.5d+245))) then
        tmp = t_2
    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 t_1 = t / (a / y);
	double t_2 = (y / a) * -z;
	double tmp;
	if (z <= -5.2e+76) {
		tmp = t_2;
	} else if (z <= 1.6e-227) {
		tmp = t_1;
	} else if (z <= 2.6e-183) {
		tmp = x;
	} else if (z <= 3e+53) {
		tmp = t_1;
	} else if ((z <= 1.15e+167) || !(z <= 6.5e+245)) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	t_2 = (y / a) * -z
	tmp = 0
	if z <= -5.2e+76:
		tmp = t_2
	elif z <= 1.6e-227:
		tmp = t_1
	elif z <= 2.6e-183:
		tmp = x
	elif z <= 3e+53:
		tmp = t_1
	elif (z <= 1.15e+167) or not (z <= 6.5e+245):
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	t_2 = Float64(Float64(y / a) * Float64(-z))
	tmp = 0.0
	if (z <= -5.2e+76)
		tmp = t_2;
	elseif (z <= 1.6e-227)
		tmp = t_1;
	elseif (z <= 2.6e-183)
		tmp = x;
	elseif (z <= 3e+53)
		tmp = t_1;
	elseif ((z <= 1.15e+167) || !(z <= 6.5e+245))
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	t_2 = (y / a) * -z;
	tmp = 0.0;
	if (z <= -5.2e+76)
		tmp = t_2;
	elseif (z <= 1.6e-227)
		tmp = t_1;
	elseif (z <= 2.6e-183)
		tmp = x;
	elseif (z <= 3e+53)
		tmp = t_1;
	elseif ((z <= 1.15e+167) || ~((z <= 6.5e+245)))
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[z, -5.2e+76], t$95$2, If[LessEqual[z, 1.6e-227], t$95$1, If[LessEqual[z, 2.6e-183], x, If[LessEqual[z, 3e+53], t$95$1, If[Or[LessEqual[z, 1.15e+167], N[Not[LessEqual[z, 6.5e+245]], $MachinePrecision]], t$95$2, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999999e76 or 2.99999999999999998e53 < z < 1.14999999999999994e167 or 6.50000000000000035e245 < z

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-/l* 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in z around inf 62.5%

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

      1. associate-*r/ 62.5%

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

      2. *-commutative 62.5%

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

      3. neg-mul-1 62.5%

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

      4. distribute-rgt-neg-in 62.5%

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

      5. associate-*r/ 71.1%

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

   7. Simplified 71.1%

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

   if -5.1999999999999999e76 < z < 1.60000000000000005e-227 or 2.5999999999999999e-183 < z < 2.99999999999999998e53

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-/l* 97.1%

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in t around inf 54.4%

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

      1. associate-/l* 57.5%

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

   7. Simplified 57.5%

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

      1. clear-num 57.6%

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

      2. div-inv 57.9%

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

   9. Applied egg-rr 57.9%

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

   if 1.60000000000000005e-227 < z < 2.5999999999999999e-183 or 1.14999999999999994e167 < z < 6.50000000000000035e245

   1. Initial program 96.0%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in x around inf 80.7%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-227}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+53}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167} \lor \neg \left(z \leq 6.5 \cdot 10^{+245}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := x - y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (- x (* y (/ z a)))))
   (if (<= z -1.65e+18)
     t_2
     (if (<= z 1.75e+50)
       t_1
       (if (<= z 1.15e+167)
         (* (/ y a) (- t z))
         (if (<= z 6.5e+245) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = x - (y * (z / a));
	double tmp;
	if (z <= -1.65e+18) {
		tmp = t_2;
	} else if (z <= 1.75e+50) {
		tmp = t_1;
	} else if (z <= 1.15e+167) {
		tmp = (y / a) * (t - z);
	} else if (z <= 6.5e+245) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    t_2 = x - (y * (z / a))
    if (z <= (-1.65d+18)) then
        tmp = t_2
    else if (z <= 1.75d+50) then
        tmp = t_1
    else if (z <= 1.15d+167) then
        tmp = (y / a) * (t - z)
    else if (z <= 6.5d+245) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = x - (y * (z / a));
	double tmp;
	if (z <= -1.65e+18) {
		tmp = t_2;
	} else if (z <= 1.75e+50) {
		tmp = t_1;
	} else if (z <= 1.15e+167) {
		tmp = (y / a) * (t - z);
	} else if (z <= 6.5e+245) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = x - (y * (z / a))
	tmp = 0
	if z <= -1.65e+18:
		tmp = t_2
	elif z <= 1.75e+50:
		tmp = t_1
	elif z <= 1.15e+167:
		tmp = (y / a) * (t - z)
	elif z <= 6.5e+245:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(x - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (z <= -1.65e+18)
		tmp = t_2;
	elseif (z <= 1.75e+50)
		tmp = t_1;
	elseif (z <= 1.15e+167)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= 6.5e+245)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	t_2 = x - (y * (z / a));
	tmp = 0.0;
	if (z <= -1.65e+18)
		tmp = t_2;
	elseif (z <= 1.75e+50)
		tmp = t_1;
	elseif (z <= 1.15e+167)
		tmp = (y / a) * (t - z);
	elseif (z <= 6.5e+245)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+18], t$95$2, If[LessEqual[z, 1.75e+50], t$95$1, If[LessEqual[z, 1.15e+167], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+245], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e18 or 6.50000000000000035e245 < z

   1. Initial program 88.3%

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

      1. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around inf 80.5%

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

      1. associate-/l* 83.8%

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

   7. Simplified 83.8%

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

   if -1.65e18 < z < 1.75000000000000003e50 or 1.14999999999999994e167 < z < 6.50000000000000035e245

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-/l* 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in z around 0 88.0%

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

      1. mul-1-neg 88.0%

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

      2. associate-/l* 89.7%

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

      3. distribute-lft-neg-out 89.7%

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

      4. *-commutative 89.7%

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

   7. Simplified 89.7%

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

      1. *-commutative 89.7%

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

      2. cancel-sign-sub 89.7%

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

      3. +-commutative 89.7%

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

      4. associate-*r/ 88.0%

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

      5. *-commutative 88.0%

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

      6. associate-/l* 85.8%

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

   9. Applied egg-rr 85.8%

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

   if 1.75000000000000003e50 < z < 1.14999999999999994e167

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/l* 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in x around 0 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*r/ 94.4%

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

      3. associate-*r* 94.4%

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

      4. neg-mul-1 94.4%

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

      5. *-commutative 94.4%

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

      6. neg-sub0 94.4%

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

      7. associate--r- 94.4%

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

      8. neg-sub0 94.4%

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

      9. +-commutative 94.4%

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

      10. sub-neg 94.4%

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

   7. Simplified 94.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+18}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+245}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+245}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (- x (/ y (/ a z)))))
   (if (<= z -4.1e+71)
     t_2
     (if (<= z 1.26e+51)
       t_1
       (if (<= z 1.15e+167)
         (* (/ y a) (- t z))
         (if (<= z 6.5e+245) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = x - (y / (a / z));
	double tmp;
	if (z <= -4.1e+71) {
		tmp = t_2;
	} else if (z <= 1.26e+51) {
		tmp = t_1;
	} else if (z <= 1.15e+167) {
		tmp = (y / a) * (t - z);
	} else if (z <= 6.5e+245) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (t / a))
    t_2 = x - (y / (a / z))
    if (z <= (-4.1d+71)) then
        tmp = t_2
    else if (z <= 1.26d+51) then
        tmp = t_1
    else if (z <= 1.15d+167) then
        tmp = (y / a) * (t - z)
    else if (z <= 6.5d+245) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = x - (y / (a / z));
	double tmp;
	if (z <= -4.1e+71) {
		tmp = t_2;
	} else if (z <= 1.26e+51) {
		tmp = t_1;
	} else if (z <= 1.15e+167) {
		tmp = (y / a) * (t - z);
	} else if (z <= 6.5e+245) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = x - (y / (a / z))
	tmp = 0
	if z <= -4.1e+71:
		tmp = t_2
	elif z <= 1.26e+51:
		tmp = t_1
	elif z <= 1.15e+167:
		tmp = (y / a) * (t - z)
	elif z <= 6.5e+245:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -4.1e+71)
		tmp = t_2;
	elseif (z <= 1.26e+51)
		tmp = t_1;
	elseif (z <= 1.15e+167)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= 6.5e+245)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	t_2 = x - (y / (a / z));
	tmp = 0.0;
	if (z <= -4.1e+71)
		tmp = t_2;
	elseif (z <= 1.26e+51)
		tmp = t_1;
	elseif (z <= 1.15e+167)
		tmp = (y / a) * (t - z);
	elseif (z <= 6.5e+245)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.1e+71], t$95$2, If[LessEqual[z, 1.26e+51], t$95$1, If[LessEqual[z, 1.15e+167], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+245], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1000000000000002e71 or 6.50000000000000035e245 < z

   1. Initial program 89.1%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. clear-num 91.6%

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

      2. un-div-inv 92.3%

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

   6. Applied egg-rr 92.3%

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

   7. Taylor expanded in z around inf 86.4%

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

   if -4.1000000000000002e71 < z < 1.25999999999999997e51 or 1.14999999999999994e167 < z < 6.50000000000000035e245

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. associate-/l* 97.1%

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

   4. Applied egg-rr 97.1%

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

   5. Taylor expanded in z around 0 86.5%

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

      1. mul-1-neg 86.5%

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

      2. associate-/l* 88.8%

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

      3. distribute-lft-neg-out 88.8%

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

      4. *-commutative 88.8%

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

   7. Simplified 88.8%

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

      1. *-commutative 88.8%

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

      2. cancel-sign-sub 88.8%

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

      3. +-commutative 88.8%

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

      4. associate-*r/ 86.5%

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

      5. *-commutative 86.5%

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

      6. associate-/l* 85.0%

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

   9. Applied egg-rr 85.0%

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

   if 1.25999999999999997e51 < z < 1.14999999999999994e167

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

      2. associate-/l* 98.0%

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

   4. Applied egg-rr 98.0%

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

   5. Taylor expanded in x around 0 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*r/ 94.4%

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

      3. associate-*r* 94.4%

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

      4. neg-mul-1 94.4%

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

      5. *-commutative 94.4%

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

      6. neg-sub0 94.4%

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

      7. associate--r- 94.4%

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

      8. neg-sub0 94.4%

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

      9. +-commutative 94.4%

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

      10. sub-neg 94.4%

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

   7. Simplified 94.4%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+167}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+245}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{+104}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -2.35e+104)
     t_1
     (if (<= t -2.8e+40)
       (/ (- t z) (/ a y))
       (if (<= t 4.8e-79) (- x (/ (* z y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -2.35e+104) {
		tmp = t_1;
	} else if (t <= -2.8e+40) {
		tmp = (t - z) / (a / y);
	} else if (t <= 4.8e-79) {
		tmp = x - ((z * y) / a);
	} 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 = x + (t * (y / a))
    if (t <= (-2.35d+104)) then
        tmp = t_1
    else if (t <= (-2.8d+40)) then
        tmp = (t - z) / (a / y)
    else if (t <= 4.8d-79) then
        tmp = x - ((z * y) / a)
    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 = x + (t * (y / a));
	double tmp;
	if (t <= -2.35e+104) {
		tmp = t_1;
	} else if (t <= -2.8e+40) {
		tmp = (t - z) / (a / y);
	} else if (t <= 4.8e-79) {
		tmp = x - ((z * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -2.35e+104:
		tmp = t_1
	elif t <= -2.8e+40:
		tmp = (t - z) / (a / y)
	elif t <= 4.8e-79:
		tmp = x - ((z * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -2.35e+104)
		tmp = t_1;
	elseif (t <= -2.8e+40)
		tmp = Float64(Float64(t - z) / Float64(a / y));
	elseif (t <= 4.8e-79)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -2.35e+104)
		tmp = t_1;
	elseif (t <= -2.8e+40)
		tmp = (t - z) / (a / y);
	elseif (t <= 4.8e-79)
		tmp = x - ((z * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e+104], t$95$1, If[LessEqual[t, -2.8e+40], N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-79], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.35000000000000008e104 or 4.80000000000000011e-79 < t

   1. Initial program 92.6%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. associate-/l* 86.8%

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

      3. distribute-rgt-neg-in 86.8%

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

      4. distribute-neg-frac2 86.8%

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

   7. Simplified 86.8%

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

   if -2.35000000000000008e104 < t < -2.8000000000000001e40

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-/l* 99.2%

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

   4. Applied egg-rr 99.2%

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

   5. Taylor expanded in x around 0 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r/ 99.2%

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

      3. associate-*r* 99.2%

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

      4. neg-mul-1 99.2%

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

      5. *-commutative 99.2%

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

      6. neg-sub0 99.2%

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

      7. associate--r- 99.2%

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

      8. neg-sub0 99.2%

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

      9. +-commutative 99.2%

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

      10. sub-neg 99.2%

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

   7. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.5%

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

      3. un-div-inv 99.6%

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

   9. Applied egg-rr 99.6%

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

   if -2.8000000000000001e40 < t < 4.80000000000000011e-79

   1. Initial program 96.0%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 90.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+104}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+40}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-79}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 47.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 6400000:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.45e+110)
   (/ (* x y) y)
   (if (<= x 2.3e-176)
     (/ t (/ a y))
     (if (<= x 6400000.0) (* y (/ z (- a))) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.45e+110) {
		tmp = (x * y) / y;
	} else if (x <= 2.3e-176) {
		tmp = t / (a / y);
	} else if (x <= 6400000.0) {
		tmp = y * (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 (x <= (-1.45d+110)) then
        tmp = (x * y) / y
    else if (x <= 2.3d-176) then
        tmp = t / (a / y)
    else if (x <= 6400000.0d0) then
        tmp = y * (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 (x <= -1.45e+110) {
		tmp = (x * y) / y;
	} else if (x <= 2.3e-176) {
		tmp = t / (a / y);
	} else if (x <= 6400000.0) {
		tmp = y * (z / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.45e+110:
		tmp = (x * y) / y
	elif x <= 2.3e-176:
		tmp = t / (a / y)
	elif x <= 6400000.0:
		tmp = y * (z / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.45e+110)
		tmp = Float64(Float64(x * y) / y);
	elseif (x <= 2.3e-176)
		tmp = Float64(t / Float64(a / y));
	elseif (x <= 6400000.0)
		tmp = Float64(y * Float64(z / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.45e+110)
		tmp = (x * y) / y;
	elseif (x <= 2.3e-176)
		tmp = t / (a / y);
	elseif (x <= 6400000.0)
		tmp = y * (z / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.45e+110], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 2.3e-176], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6400000.0], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.45e110

   1. Initial program 94.9%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. +-commutative 71.2%

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

      3. associate--r- 71.2%

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

      4. div-sub 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in x around inf 33.6%

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

      1. associate-*r/ 59.9%

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

   10. Applied egg-rr 59.9%

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

   if -1.45e110 < x < 2.3000000000000001e-176

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. associate-/l* 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in t around inf 58.2%

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

      1. associate-/l* 60.4%

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

   7. Simplified 60.4%

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

      1. clear-num 60.5%

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

      2. div-inv 60.5%

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

   9. Applied egg-rr 60.5%

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

   if 2.3000000000000001e-176 < x < 6.4e6

   1. Initial program 92.4%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 54.4%

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

      1. mul-1-neg 54.4%

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

      2. associate-/l* 51.6%

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

      3. distribute-rgt-neg-in 51.6%

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

      4. distribute-frac-neg2 51.6%

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

   7. Simplified 51.6%

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

   if 6.4e6 < x

   1. Initial program 95.3%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf 62.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-176}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;x \leq 6400000:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-107} \lor \neg \left(y \leq 6.1 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.2e-107) (not (<= y 6.1e-139))) (* (/ y a) (- t z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.2e-107) || !(y <= 6.1e-139)) {
		tmp = (y / a) * (t - z);
	} 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 <= (-5.2d-107)) .or. (.not. (y <= 6.1d-139))) then
        tmp = (y / a) * (t - z)
    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 <= -5.2e-107) || !(y <= 6.1e-139)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.2e-107) or not (y <= 6.1e-139):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.2e-107) || !(y <= 6.1e-139))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.2e-107) || ~((y <= 6.1e-139)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.2e-107], N[Not[LessEqual[y, 6.1e-139]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e-107 or 6.0999999999999998e-139 < y

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-/l* 97.7%

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

   4. Applied egg-rr 97.7%

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

   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. *-commutative 70.3%

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

      2. associate-*r/ 76.2%

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

      3. associate-*r* 76.2%

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

      4. neg-mul-1 76.2%

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

      5. *-commutative 76.2%

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

      6. neg-sub0 76.2%

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

      7. associate--r- 76.2%

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

      8. neg-sub0 76.2%

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

      9. +-commutative 76.2%

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

      10. sub-neg 76.2%

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

   7. Simplified 76.2%

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

   if -5.2000000000000001e-107 < y < 6.0999999999999998e-139

   1. Initial program 99.5%

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

      1. associate-/l* 80.0%

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

   3. Simplified 80.0%

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

   5. Taylor expanded in x around inf 64.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-107} \lor \neg \left(y \leq 6.1 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-112} \lor \neg \left(x \leq 3700000000\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.8e-112) (not (<= x 3700000000.0)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e-112) || !(x <= 3700000000.0)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.8d-112)) .or. (.not. (x <= 3700000000.0d0))) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e-112) || !(x <= 3700000000.0)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.8e-112) or not (x <= 3700000000.0):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.8e-112) || !(x <= 3700000000.0))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.8e-112) || ~((x <= 3700000000.0)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.8e-112], N[Not[LessEqual[x, 3700000000.0]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.80000000000000023e-112 or 3.7e9 < x

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-/l* 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in z around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 79.4%

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

      3. distribute-lft-neg-out 79.4%

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

      4. *-commutative 79.4%

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

   7. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. cancel-sign-sub 79.4%

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

      3. +-commutative 79.4%

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

      4. associate-*r/ 78.9%

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

      5. *-commutative 78.9%

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

      6. associate-/l* 78.8%

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

   9. Applied egg-rr 78.8%

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

   if -2.80000000000000023e-112 < x < 3.7e9

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-/l* 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in x around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-*r/ 85.0%

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

      3. associate-*r* 85.0%

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

      4. neg-mul-1 85.0%

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

      5. *-commutative 85.0%

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

      6. neg-sub0 85.0%

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

      7. associate--r- 85.0%

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

      8. neg-sub0 85.0%

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

      9. +-commutative 85.0%

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

      10. sub-neg 85.0%

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

   7. Simplified 85.0%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-112} \lor \neg \left(x \leq 3700000000\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+71)
   (- x (/ y (/ a z)))
   (if (<= z 1.55e+53) (+ x (* y (/ t a))) (- x (/ (* z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+71) {
		tmp = x - (y / (a / z));
	} else if (z <= 1.55e+53) {
		tmp = x + (y * (t / 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 (z <= (-3d+71)) then
        tmp = x - (y / (a / z))
    else if (z <= 1.55d+53) then
        tmp = x + (y * (t / 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 (z <= -3e+71) {
		tmp = x - (y / (a / z));
	} else if (z <= 1.55e+53) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+71:
		tmp = x - (y / (a / z))
	elif z <= 1.55e+53:
		tmp = x + (y * (t / a))
	else:
		tmp = x - ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+71)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	elseif (z <= 1.55e+53)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+71)
		tmp = x - (y / (a / z));
	elseif (z <= 1.55e+53)
		tmp = x + (y * (t / a));
	else
		tmp = x - ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+71], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+53], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.00000000000000013e71

   1. Initial program 90.0%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

      1. clear-num 91.5%

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

      2. un-div-inv 92.4%

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

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in z around inf 85.1%

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

   if -3.00000000000000013e71 < z < 1.5500000000000001e53

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      2. associate-/l* 97.3%

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

   4. Applied egg-rr 97.3%

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

   5. Taylor expanded in z around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. associate-/l* 88.3%

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

      3. distribute-lft-neg-out 88.3%

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

      4. *-commutative 88.3%

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

   7. Simplified 88.3%

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

      1. *-commutative 88.3%

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

      2. cancel-sign-sub 88.3%

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

      3. +-commutative 88.3%

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

      4. associate-*r/ 85.9%

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

      5. *-commutative 85.9%

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

      6. associate-/l* 84.2%

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

   9. Applied egg-rr 84.2%

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

   if 1.5500000000000001e53 < z

   1. Initial program 91.6%

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

      1. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in z around inf 83.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+71}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+53}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.05e+110) x (if (<= x 9e-139) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.05e+110) {
		tmp = x;
	} else if (x <= 9e-139) {
		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 (x <= (-1.05d+110)) then
        tmp = x
    else if (x <= 9d-139) 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 (x <= -1.05e+110) {
		tmp = x;
	} else if (x <= 9e-139) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.05e+110:
		tmp = x
	elif x <= 9e-139:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.05e+110)
		tmp = x;
	elseif (x <= 9e-139)
		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 (x <= -1.05e+110)
		tmp = x;
	elseif (x <= 9e-139)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.05e+110], x, If[LessEqual[x, 9e-139], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000007e110 or 9.00000000000000046e-139 < x

   1. Initial program 94.7%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 52.7%

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

   if -1.05000000000000007e110 < x < 9.00000000000000046e-139

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/l* 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in t around inf 56.6%

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

      1. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.8e+109) x (if (<= x 9e-139) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.8e+109) {
		tmp = x;
	} else if (x <= 9e-139) {
		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 (x <= (-9.8d+109)) then
        tmp = x
    else if (x <= 9d-139) 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 (x <= -9.8e+109) {
		tmp = x;
	} else if (x <= 9e-139) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9.8e+109:
		tmp = x
	elif x <= 9e-139:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9.8e+109)
		tmp = x;
	elseif (x <= 9e-139)
		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 (x <= -9.8e+109)
		tmp = x;
	elseif (x <= 9e-139)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9.8e+109], x, If[LessEqual[x, 9e-139], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -9.8000000000000007e109 or 9.00000000000000046e-139 < x

   1. Initial program 94.7%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in x around inf 52.7%

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

   if -9.8000000000000007e109 < x < 9.00000000000000046e-139

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/l* 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in t around inf 56.6%

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

      1. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

      1. clear-num 59.5%

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

      2. div-inv 59.5%

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

   9. Applied egg-rr 59.5%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.22e+110) (/ (* x y) y) (if (<= x 9e-139) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.22e+110) {
		tmp = (x * y) / y;
	} else if (x <= 9e-139) {
		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 (x <= (-1.22d+110)) then
        tmp = (x * y) / y
    else if (x <= 9d-139) 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 (x <= -1.22e+110) {
		tmp = (x * y) / y;
	} else if (x <= 9e-139) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.22e+110:
		tmp = (x * y) / y
	elif x <= 9e-139:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.22e+110)
		tmp = Float64(Float64(x * y) / y);
	elseif (x <= 9e-139)
		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 (x <= -1.22e+110)
		tmp = (x * y) / y;
	elseif (x <= 9e-139)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.22e+110], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 9e-139], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -1.22000000000000002e110

   1. Initial program 94.9%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in y around inf 71.2%

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

      1. associate--l+ 71.2%

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

      2. +-commutative 71.2%

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

      3. associate--r- 71.2%

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

      4. div-sub 74.0%

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

   7. Simplified 74.0%

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

   8. Taylor expanded in x around inf 33.6%

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

      1. associate-*r/ 59.9%

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

   10. Applied egg-rr 59.9%

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

   if -1.22000000000000002e110 < x < 9.00000000000000046e-139

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-/l* 96.9%

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

   4. Applied egg-rr 96.9%

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

   5. Taylor expanded in t around inf 56.6%

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

      1. associate-/l* 59.4%

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

   7. Simplified 59.4%

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

      1. clear-num 59.5%

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

      2. div-inv 59.5%

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

   9. Applied egg-rr 59.5%

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

   if 9.00000000000000046e-139 < x

   1. Initial program 94.7%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around inf 51.0%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-/l* 92.0%

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

3. Simplified 92.0%

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

5. Final simplification 92.0%

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

Alternative 14: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. *-commutative 93.9%

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

   2. associate-/l* 97.6%

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

4. Applied egg-rr 97.6%

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

5. Final simplification 97.6%

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

Alternative 15: 39.3% 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 93.9%

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

   1. associate-/l* 92.0%

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

3. Simplified 92.0%

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

5. Taylor expanded in x around inf 34.8%

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

6. Final simplification 34.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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