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

Percentage Accurate: 92.9% → 99.3%

Time: 14.0s

Alternatives: 16

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+201} \lor \neg \left(t\_1 \leq 10^{+161}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -5e+201) (not (<= t_1 1e+161)))
     (+ x (/ (- t z) (/ a y)))
     (- x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -5e+201) || !(t_1 <= 1e+161)) {
		tmp = x + ((t - z) / (a / y));
	} else {
		tmp = x - (t_1 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if ((t_1 <= (-5d+201)) .or. (.not. (t_1 <= 1d+161))) then
        tmp = x + ((t - z) / (a / y))
    else
        tmp = x - (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -5e+201) || !(t_1 <= 1e+161)) {
		tmp = x + ((t - z) / (a / y));
	} else {
		tmp = x - (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -5e+201) or not (t_1 <= 1e+161):
		tmp = x + ((t - z) / (a / y))
	else:
		tmp = x - (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -5e+201) || !(t_1 <= 1e+161))
		tmp = Float64(x + Float64(Float64(t - z) / Float64(a / y)));
	else
		tmp = Float64(x - Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e+201) || ~((t_1 <= 1e+161)))
		tmp = x + ((t - z) / (a / y));
	else
		tmp = x - (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+201], N[Not[LessEqual[t$95$1, 1e+161]], $MachinePrecision]], N[(x + N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -4.9999999999999995e201 or 1e161 < (*.f64 y (-.f64 z t))

   1. Initial program 85.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-/l* 99.9%

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

   7. Simplified 99.9%

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

   if -4.9999999999999995e201 < (*.f64 y (-.f64 z t)) < 1e161

   1. Initial program 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -5 \cdot 10^{+201} \lor \neg \left(y \cdot \left(z - t\right) \leq 10^{+161}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+301}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x - t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -2e+301)
     (+ x (* (/ y a) (- t z)))
     (if (<= t_1 5e+274) (- x t_1) (- x (/ y (/ a (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -2e+301) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 5e+274) {
		tmp = x - t_1;
	} else {
		tmp = x - (y / (a / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= (-2d+301)) then
        tmp = x + ((y / a) * (t - z))
    else if (t_1 <= 5d+274) then
        tmp = x - t_1
    else
        tmp = x - (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -2e+301) {
		tmp = x + ((y / a) * (t - z));
	} else if (t_1 <= 5e+274) {
		tmp = x - t_1;
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -2e+301:
		tmp = x + ((y / a) * (t - z))
	elif t_1 <= 5e+274:
		tmp = x - t_1
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -2e+301)
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	elseif (t_1 <= 5e+274)
		tmp = Float64(x - t_1);
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -2e+301)
		tmp = x + ((y / a) * (t - z));
	elseif (t_1 <= 5e+274)
		tmp = x - t_1;
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+301], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(x - t$95$1), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.00000000000000011e301

   1. Initial program 88.4%

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

   if -2.00000000000000011e301 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.9999999999999998e274

   1. Initial program 99.8%

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

   if 4.9999999999999998e274 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 78.3%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{+301}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ t_2 := x - \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-217}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 1300:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))) (t_2 (- x (/ z (/ a y)))))
   (if (<= z -1.18e+81)
     t_2
     (if (<= z -4.3e-42)
       t_1
       (if (<= z 4e-217)
         (- x (/ y (/ (- a) t)))
         (if (<= z 1300.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double t_2 = x - (z / (a / y));
	double tmp;
	if (z <= -1.18e+81) {
		tmp = t_2;
	} else if (z <= -4.3e-42) {
		tmp = t_1;
	} else if (z <= 4e-217) {
		tmp = x - (y / (-a / t));
	} else if (z <= 1300.0) {
		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 + (t * (y / a))
    t_2 = x - (z / (a / y))
    if (z <= (-1.18d+81)) then
        tmp = t_2
    else if (z <= (-4.3d-42)) then
        tmp = t_1
    else if (z <= 4d-217) then
        tmp = x - (y / (-a / t))
    else if (z <= 1300.0d0) 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 + (t * (y / a));
	double t_2 = x - (z / (a / y));
	double tmp;
	if (z <= -1.18e+81) {
		tmp = t_2;
	} else if (z <= -4.3e-42) {
		tmp = t_1;
	} else if (z <= 4e-217) {
		tmp = x - (y / (-a / t));
	} else if (z <= 1300.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	t_2 = x - (z / (a / y))
	tmp = 0
	if z <= -1.18e+81:
		tmp = t_2
	elif z <= -4.3e-42:
		tmp = t_1
	elif z <= 4e-217:
		tmp = x - (y / (-a / t))
	elif z <= 1300.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	t_2 = Float64(x - Float64(z / Float64(a / y)))
	tmp = 0.0
	if (z <= -1.18e+81)
		tmp = t_2;
	elseif (z <= -4.3e-42)
		tmp = t_1;
	elseif (z <= 4e-217)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif (z <= 1300.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	t_2 = x - (z / (a / y));
	tmp = 0.0;
	if (z <= -1.18e+81)
		tmp = t_2;
	elseif (z <= -4.3e-42)
		tmp = t_1;
	elseif (z <= 4e-217)
		tmp = x - (y / (-a / t));
	elseif (z <= 1300.0)
		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[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.18e+81], t$95$2, If[LessEqual[z, -4.3e-42], t$95$1, If[LessEqual[z, 4e-217], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1300.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.17999999999999995e81 or 1300 < z

   1. Initial program 87.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around inf 83.3%

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

   6. Taylor expanded in y around 0 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 91.0%

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

   8. Simplified 91.0%

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

   if -1.17999999999999995e81 < z < -4.3000000000000001e-42 or 4.00000000000000033e-217 < z < 1300

   1. Initial program 98.6%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around 0 88.4%

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

      1. cancel-sign-sub-inv 88.4%

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

      2. metadata-eval 88.4%

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

      3. *-lft-identity 88.4%

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

      4. +-commutative 88.4%

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

      5. associate-*r/ 92.0%

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

   7. Simplified 92.0%

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

   if -4.3000000000000001e-42 < z < 4.00000000000000033e-217

   1. Initial program 99.9%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 93.1%

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

      1. associate-*r/ 93.1%

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

      2. neg-mul-1 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+81}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-42}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-217}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 1300:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -8.4e+36)
   x
   (if (<= x -1.6e-131)
     (/ (* y t) a)
     (if (<= x 6.5e-286)
       (* z (/ y (- a)))
       (if (<= x 1.2e+96) (/ t (/ a y)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -8.4e+36) {
		tmp = x;
	} else if (x <= -1.6e-131) {
		tmp = (y * t) / a;
	} else if (x <= 6.5e-286) {
		tmp = z * (y / -a);
	} else if (x <= 1.2e+96) {
		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 <= (-8.4d+36)) then
        tmp = x
    else if (x <= (-1.6d-131)) then
        tmp = (y * t) / a
    else if (x <= 6.5d-286) then
        tmp = z * (y / -a)
    else if (x <= 1.2d+96) 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 <= -8.4e+36) {
		tmp = x;
	} else if (x <= -1.6e-131) {
		tmp = (y * t) / a;
	} else if (x <= 6.5e-286) {
		tmp = z * (y / -a);
	} else if (x <= 1.2e+96) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -8.4e+36:
		tmp = x
	elif x <= -1.6e-131:
		tmp = (y * t) / a
	elif x <= 6.5e-286:
		tmp = z * (y / -a)
	elif x <= 1.2e+96:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -8.4e+36)
		tmp = x;
	elseif (x <= -1.6e-131)
		tmp = Float64(Float64(y * t) / a);
	elseif (x <= 6.5e-286)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (x <= 1.2e+96)
		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 <= -8.4e+36)
		tmp = x;
	elseif (x <= -1.6e-131)
		tmp = (y * t) / a;
	elseif (x <= 6.5e-286)
		tmp = z * (y / -a);
	elseif (x <= 1.2e+96)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -8.4e+36], x, If[LessEqual[x, -1.6e-131], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 6.5e-286], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e+96], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.40000000000000018e36 or 1.19999999999999996e96 < x

   1. Initial program 94.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 68.9%

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

   if -8.40000000000000018e36 < x < -1.6e-131

   1. Initial program 90.9%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around inf 53.4%

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

      1. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if -1.6e-131 < x < 6.5000000000000004e-286

   1. Initial program 95.0%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. associate-*l/ 52.4%

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

      3. *-commutative 52.4%

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

      4. distribute-rgt-neg-in 52.4%

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

      5. *-lft-identity 52.4%

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

      6. associate-*l/ 52.3%

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

      7. remove-double-neg 52.3%

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

      8. neg-mul-1 52.3%

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

      9. associate-*r* 52.3%

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

      10. *-commutative 52.3%

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

      11. neg-mul-1 52.3%

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

      12. *-commutative 52.3%

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

      13. distribute-neg-frac 52.3%

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

      14. metadata-eval 52.3%

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

      15. metadata-eval 52.3%

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

      16. associate-/r* 52.3%

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

      17. neg-mul-1 52.3%

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

      18. associate-*r/ 52.4%

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

      19. *-rgt-identity 52.4%

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

      20. distribute-frac-neg 52.4%

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

      21. remove-double-neg 52.4%

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

   7. Simplified 52.4%

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

   if 6.5000000000000004e-286 < x < 1.19999999999999996e96

   1. Initial program 95.0%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 48.9%

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

      1. associate-*r/ 50.1%

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

   7. Simplified 50.1%

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

      1. clear-num 50.1%

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

      2. div-inv 50.2%

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

   9. Applied egg-rr 50.2%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.4 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-124}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-260}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+93}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4e+38)
   x
   (if (<= x -1.9e-124)
     (/ (* y t) a)
     (if (<= x 1.52e-260)
       (/ (- y) (/ a z))
       (if (<= x 5.4e+93) (/ t (/ a y)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+38) {
		tmp = x;
	} else if (x <= -1.9e-124) {
		tmp = (y * t) / a;
	} else if (x <= 1.52e-260) {
		tmp = -y / (a / z);
	} else if (x <= 5.4e+93) {
		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 <= (-4d+38)) then
        tmp = x
    else if (x <= (-1.9d-124)) then
        tmp = (y * t) / a
    else if (x <= 1.52d-260) then
        tmp = -y / (a / z)
    else if (x <= 5.4d+93) 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 <= -4e+38) {
		tmp = x;
	} else if (x <= -1.9e-124) {
		tmp = (y * t) / a;
	} else if (x <= 1.52e-260) {
		tmp = -y / (a / z);
	} else if (x <= 5.4e+93) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4e+38:
		tmp = x
	elif x <= -1.9e-124:
		tmp = (y * t) / a
	elif x <= 1.52e-260:
		tmp = -y / (a / z)
	elif x <= 5.4e+93:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4e+38)
		tmp = x;
	elseif (x <= -1.9e-124)
		tmp = Float64(Float64(y * t) / a);
	elseif (x <= 1.52e-260)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (x <= 5.4e+93)
		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 <= -4e+38)
		tmp = x;
	elseif (x <= -1.9e-124)
		tmp = (y * t) / a;
	elseif (x <= 1.52e-260)
		tmp = -y / (a / z);
	elseif (x <= 5.4e+93)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4e+38], x, If[LessEqual[x, -1.9e-124], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 1.52e-260], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.4e+93], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.99999999999999991e38 or 5.3999999999999999e93 < x

   1. Initial program 94.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 68.9%

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

   if -3.99999999999999991e38 < x < -1.90000000000000006e-124

   1. Initial program 90.9%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around inf 53.4%

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

      1. *-commutative 53.4%

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

   7. Simplified 53.4%

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

   if -1.90000000000000006e-124 < x < 1.52e-260

   1. Initial program 93.5%

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

      1. associate-*l/ 85.2%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in z around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. associate-*l/ 49.9%

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

      3. *-commutative 49.9%

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

      4. distribute-rgt-neg-in 49.9%

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

      5. *-lft-identity 49.9%

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

      6. associate-*l/ 49.9%

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

      7. remove-double-neg 49.9%

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

      8. neg-mul-1 49.9%

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

      9. associate-*r* 49.9%

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

      10. *-commutative 49.9%

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

      11. neg-mul-1 49.9%

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

      12. *-commutative 49.9%

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

      13. distribute-neg-frac 49.9%

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

      14. metadata-eval 49.9%

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

      15. metadata-eval 49.9%

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

      16. associate-/r* 49.9%

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

      17. neg-mul-1 49.9%

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

      18. associate-*r/ 49.9%

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

      19. *-rgt-identity 49.9%

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

      20. distribute-frac-neg 49.9%

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

      21. remove-double-neg 49.9%

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

   7. Simplified 49.9%

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

      1. *-commutative 49.9%

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

      2. frac-2neg 49.9%

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

      3. remove-double-neg 49.9%

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

      4. distribute-frac-neg 49.9%

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

      5. distribute-lft-neg-in 49.9%

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

      6. associate-/r/ 50.3%

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

      7. distribute-neg-frac 50.3%

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

   9. Applied egg-rr 50.3%

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

   if 1.52e-260 < x < 5.3999999999999999e93

   1. Initial program 95.9%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 48.8%

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

      1. associate-*r/ 51.3%

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

   7. Simplified 51.3%

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

      1. clear-num 51.3%

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

      2. div-inv 51.4%

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

   9. Applied egg-rr 51.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-124}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{-260}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+93}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-28} \lor \neg \left(x \leq 1.3 \cdot 10^{-208}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.8e-28) (not (<= x 1.3e-208)))
   (+ 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 <= -5.8e-28) || !(x <= 1.3e-208)) {
		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 <= (-5.8d-28)) .or. (.not. (x <= 1.3d-208))) 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 <= -5.8e-28) || !(x <= 1.3e-208)) {
		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 <= -5.8e-28) or not (x <= 1.3e-208):
		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 <= -5.8e-28) || !(x <= 1.3e-208))
		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 <= -5.8e-28) || ~((x <= 1.3e-208)))
		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, -5.8e-28], N[Not[LessEqual[x, 1.3e-208]], $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 < -5.80000000000000026e-28 or 1.30000000000000008e-208 < x

   1. Initial program 95.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 80.6%

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

      1. cancel-sign-sub-inv 80.6%

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

      2. metadata-eval 80.6%

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

      3. *-lft-identity 80.6%

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

      4. +-commutative 80.6%

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

      5. associate-*r/ 83.6%

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

   7. Simplified 83.6%

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

   if -5.80000000000000026e-28 < x < 1.30000000000000008e-208

   1. Initial program 92.2%

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

      1. associate-*l/ 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-*r/ 77.8%

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

      3. distribute-rgt-neg-out 77.8%

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

      4. *-rgt-identity 77.8%

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

      5. *-rgt-identity 77.8%

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

      6. distribute-neg-frac 77.8%

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

      7. neg-sub0 77.8%

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

      8. associate--r- 77.8%

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

      9. neg-sub0 77.8%

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

      10. +-commutative 77.8%

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

      11. sub-neg 77.8%

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

   7. Simplified 77.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-28} \lor \neg \left(x \leq 1.3 \cdot 10^{-208}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+81} \lor \neg \left(z \leq 1.8\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.55e+81) (not (<= z 1.8)))
   (- x (* y (/ z a)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.55e+81) || !(z <= 1.8)) {
		tmp = x - (y * (z / a));
	} 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 <= (-1.55d+81)) .or. (.not. (z <= 1.8d0))) then
        tmp = x - (y * (z / a))
    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 <= -1.55e+81) || !(z <= 1.8)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.55e+81) or not (z <= 1.8):
		tmp = x - (y * (z / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.55e+81) || !(z <= 1.8))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	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 <= -1.55e+81) || ~((z <= 1.8)))
		tmp = x - (y * (z / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.55e+81], N[Not[LessEqual[z, 1.8]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e81 or 1.80000000000000004 < z

   1. Initial program 87.0%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. *-commutative 87.0%

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

      2. associate-/l* 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in z around inf 83.1%

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

      1. associate-*r/ 83.3%

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

   10. Simplified 83.3%

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

   if -1.55e81 < z < 1.80000000000000004

   1. Initial program 99.3%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around 0 91.3%

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

      1. cancel-sign-sub-inv 91.3%

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

      2. metadata-eval 91.3%

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

      3. *-lft-identity 91.3%

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

      4. +-commutative 91.3%

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

      5. associate-*r/ 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+81} \lor \neg \left(z \leq 1.8\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+80} \lor \neg \left(z \leq 3000000\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+80) (not (<= z 3000000.0)))
   (- x (/ z (/ a y)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+80) || !(z <= 3000000.0)) {
		tmp = x - (z / (a / y));
	} 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 <= (-2.8d+80)) .or. (.not. (z <= 3000000.0d0))) then
        tmp = x - (z / (a / y))
    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 <= -2.8e+80) || !(z <= 3000000.0)) {
		tmp = x - (z / (a / y));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+80) or not (z <= 3000000.0):
		tmp = x - (z / (a / y))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+80) || !(z <= 3000000.0))
		tmp = Float64(x - Float64(z / Float64(a / y)));
	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 <= -2.8e+80) || ~((z <= 3000000.0)))
		tmp = x - (z / (a / y));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+80], N[Not[LessEqual[z, 3000000.0]], $MachinePrecision]], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999984e80 or 3e6 < z

   1. Initial program 87.0%

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

      1. associate-/l* 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around inf 83.3%

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

   6. Taylor expanded in y around 0 83.1%

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

      1. *-commutative 83.1%

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

      2. associate-/l* 91.0%

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

   8. Simplified 91.0%

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

   if -2.79999999999999984e80 < z < 3e6

   1. Initial program 99.3%

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

      1. associate-*l/ 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in z around 0 91.3%

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

      1. cancel-sign-sub-inv 91.3%

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

      2. metadata-eval 91.3%

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

      3. *-lft-identity 91.3%

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

      4. +-commutative 91.3%

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

      5. associate-*r/ 89.4%

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

   7. Simplified 89.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+80} \lor \neg \left(z \leq 3000000\right):\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.9e+96) x (if (<= x 4e+117) (* y (/ (- t z) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.9e+96) {
		tmp = x;
	} else if (x <= 4e+117) {
		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 (x <= (-4.9d+96)) then
        tmp = x
    else if (x <= 4d+117) 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 (x <= -4.9e+96) {
		tmp = x;
	} else if (x <= 4e+117) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.9e+96:
		tmp = x
	elif x <= 4e+117:
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.9e+96)
		tmp = x;
	elseif (x <= 4e+117)
		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 (x <= -4.9e+96)
		tmp = x;
	elseif (x <= 4e+117)
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.9e+96], x, If[LessEqual[x, 4e+117], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8999999999999996e96 or 4.0000000000000002e117 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 75.0%

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

   if -4.8999999999999996e96 < x < 4.0000000000000002e117

   1. Initial program 94.9%

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

      1. associate-*l/ 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in x around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-*r/ 69.0%

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

      3. distribute-rgt-neg-out 69.0%

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

      4. *-rgt-identity 69.0%

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

      5. *-rgt-identity 69.0%

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

      6. distribute-neg-frac 69.0%

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

      7. neg-sub0 69.0%

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

      8. associate--r- 69.0%

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

      9. neg-sub0 69.0%

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

      10. +-commutative 69.0%

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

      11. sub-neg 69.0%

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

   7. Simplified 69.0%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3700000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+38) x (if (<= a 3700000000.0) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+38) {
		tmp = x;
	} else if (a <= 3700000000.0) {
		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 (a <= (-1.9d+38)) then
        tmp = x
    else if (a <= 3700000000.0d0) 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 (a <= -1.9e+38) {
		tmp = x;
	} else if (a <= 3700000000.0) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+38:
		tmp = x
	elif a <= 3700000000.0:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+38)
		tmp = x;
	elseif (a <= 3700000000.0)
		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 (a <= -1.9e+38)
		tmp = x;
	elseif (a <= 3700000000.0)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+38], x, If[LessEqual[a, 3700000000.0], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8999999999999999e38 or 3.7e9 < a

   1. Initial program 88.2%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 64.4%

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

   if -1.8999999999999999e38 < a < 3.7e9

   1. Initial program 99.2%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. associate-*r/ 49.5%

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

   7. Simplified 49.5%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3700000000:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5000000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+37) x (if (<= a 5000000000.0) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.4e+37) {
		tmp = x;
	} else if (a <= 5000000000.0) {
		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 (a <= (-3.4d+37)) then
        tmp = x
    else if (a <= 5000000000.0d0) 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 (a <= -3.4e+37) {
		tmp = x;
	} else if (a <= 5000000000.0) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.4e+37:
		tmp = x
	elif a <= 5000000000.0:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.4e+37)
		tmp = x;
	elseif (a <= 5000000000.0)
		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 (a <= -3.4e+37)
		tmp = x;
	elseif (a <= 5000000000.0)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.4e+37], x, If[LessEqual[a, 5000000000.0], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.40000000000000006e37 or 5e9 < a

   1. Initial program 88.2%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around inf 64.4%

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

   if -3.40000000000000006e37 < a < 5e9

   1. Initial program 99.2%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in t around inf 49.5%

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

      1. associate-*r/ 49.5%

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

   7. Simplified 49.5%

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

      1. clear-num 49.5%

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

      2. div-inv 49.5%

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

   9. Applied egg-rr 49.5%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5000000000:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+93}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.22e+37) x (if (<= x 7e+93) (/ (* y t) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.22e+37) {
		tmp = x;
	} else if (x <= 7e+93) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.22d+37)) then
        tmp = x
    else if (x <= 7d+93) then
        tmp = (y * t) / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.22e+37) {
		tmp = x;
	} else if (x <= 7e+93) {
		tmp = (y * t) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.22e+37:
		tmp = x
	elif x <= 7e+93:
		tmp = (y * t) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.22e+37)
		tmp = x;
	elseif (x <= 7e+93)
		tmp = Float64(Float64(y * t) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.22e+37)
		tmp = x;
	elseif (x <= 7e+93)
		tmp = (y * t) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.22e+37], x, If[LessEqual[x, 7e+93], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.22e37 or 6.99999999999999996e93 < x

   1. Initial program 94.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 68.9%

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

   if -1.22e37 < x < 6.99999999999999996e93

   1. Initial program 94.2%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 45.8%

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

      1. *-commutative 45.8%

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

   7. Simplified 45.8%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+93}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 96.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-201}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.7e-201) (+ x (* y (/ (- t z) a))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e-201) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.7d-201)) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e-201) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.7e-201:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.7e-201)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + 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 (y <= -1.7e-201)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.7e-201], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.69999999999999993e-201

   1. Initial program 91.1%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

      1. clear-num 97.1%

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

      2. associate-/r/ 97.1%

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

      3. clear-num 97.1%

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

   6. Applied egg-rr 97.1%

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

   if -1.69999999999999993e-201 < y

   1. Initial program 96.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-201}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-194}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5e-194) (- x (/ y (/ a (- z t)))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e-194) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5d-194)) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e-194) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5e-194:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5e-194)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + 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 (y <= -5e-194)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5e-194], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e-194

   1. Initial program 91.0%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   if -5.0000000000000002e-194 < y

   1. Initial program 96.7%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-194}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 94.3%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 96.3%

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

Alternative 16: 39.4% 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 94.3%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 inf 41.7%

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

6. Final simplification 41.7%

   \[\leadsto x \]
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 2024040 
(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)))