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

Percentage Accurate: 93.5% → 99.6%

Time: 11.5s

Alternatives: 15

Speedup: 1.0×

• 24.4% 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: 93.5% 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: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+292} \lor \neg \left(t_1 \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -2e+292) (not (<= t_1 2e+246)))
     (+ 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 <= -2e+292) || !(t_1 <= 2e+246)) {
		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 <= (-2d+292)) .or. (.not. (t_1 <= 2d+246))) 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 <= -2e+292) || !(t_1 <= 2e+246)) {
		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 <= -2e+292) or not (t_1 <= 2e+246):
		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 <= -2e+292) || !(t_1 <= 2e+246))
		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 <= -2e+292) || ~((t_1 <= 2e+246)))
		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, -2e+292], N[Not[LessEqual[t$95$1, 2e+246]], $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)) < -2e292 or 2.00000000000000014e246 < (*.f64 y (-.f64 z t))

   1. Initial program 71.0%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

   if -2e292 < (*.f64 y (-.f64 z t)) < 2.00000000000000014e246

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+292} \lor \neg \left(y \cdot \left(z - t\right) \leq 2 \cdot 10^{+246}\right):\\ \;\;\;\;x + \frac{t - z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]

Alternative 2: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+174}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+260}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -2e+174)
     (- x (* (- z t) (/ y a)))
     (if (<= t_1 4e+260)
       (+ x (/ (* y (- t z)) a))
       (- x (/ y (/ a (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -2e+174) {
		tmp = x - ((z - t) * (y / a));
	} else if (t_1 <= 4e+260) {
		tmp = x + ((y * (t - z)) / a);
	} 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)
    if (t_1 <= (-2d+174)) then
        tmp = x - ((z - t) * (y / a))
    else if (t_1 <= 4d+260) then
        tmp = x + ((y * (t - z)) / a)
    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);
	double tmp;
	if (t_1 <= -2e+174) {
		tmp = x - ((z - t) * (y / a));
	} else if (t_1 <= 4e+260) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -2e+174:
		tmp = x - ((z - t) * (y / a))
	elif t_1 <= 4e+260:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+174)
		tmp = Float64(x - Float64(Float64(z - t) * Float64(y / a)));
	elseif (t_1 <= 4e+260)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	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);
	tmp = 0.0;
	if (t_1 <= -2e+174)
		tmp = x - ((z - t) * (y / a));
	elseif (t_1 <= 4e+260)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+174], N[(x - N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+260], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -2.00000000000000014e174

   1. Initial program 83.4%

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

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

   if -2.00000000000000014e174 < (*.f64 y (-.f64 z t)) < 4.00000000000000026e260

   1. Initial program 99.2%

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

   if 4.00000000000000026e260 < (*.f64 y (-.f64 z t))

   1. Initial program 71.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+174}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 4 \cdot 10^{+260}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 3: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a} \cdot \left(-y\right)\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ z a) (- y))))
   (if (<= t -1.26e+60)
     (/ t (/ a y))
     (if (<= t -2.5e-110)
       x
       (if (<= t 1.4e-174)
         t_1
         (if (<= t 5.2e-62)
           x
           (if (<= t 5.4e-46) t_1 (if (<= t 1.15e-12) x (* t (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / a) * -y;
	double tmp;
	if (t <= -1.26e+60) {
		tmp = t / (a / y);
	} else if (t <= -2.5e-110) {
		tmp = x;
	} else if (t <= 1.4e-174) {
		tmp = t_1;
	} else if (t <= 5.2e-62) {
		tmp = x;
	} else if (t <= 5.4e-46) {
		tmp = t_1;
	} else if (t <= 1.15e-12) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z / a) * -y
    if (t <= (-1.26d+60)) then
        tmp = t / (a / y)
    else if (t <= (-2.5d-110)) then
        tmp = x
    else if (t <= 1.4d-174) then
        tmp = t_1
    else if (t <= 5.2d-62) then
        tmp = x
    else if (t <= 5.4d-46) then
        tmp = t_1
    else if (t <= 1.15d-12) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / a) * -y;
	double tmp;
	if (t <= -1.26e+60) {
		tmp = t / (a / y);
	} else if (t <= -2.5e-110) {
		tmp = x;
	} else if (t <= 1.4e-174) {
		tmp = t_1;
	} else if (t <= 5.2e-62) {
		tmp = x;
	} else if (t <= 5.4e-46) {
		tmp = t_1;
	} else if (t <= 1.15e-12) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z / a) * -y
	tmp = 0
	if t <= -1.26e+60:
		tmp = t / (a / y)
	elif t <= -2.5e-110:
		tmp = x
	elif t <= 1.4e-174:
		tmp = t_1
	elif t <= 5.2e-62:
		tmp = x
	elif t <= 5.4e-46:
		tmp = t_1
	elif t <= 1.15e-12:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / a) * Float64(-y))
	tmp = 0.0
	if (t <= -1.26e+60)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= -2.5e-110)
		tmp = x;
	elseif (t <= 1.4e-174)
		tmp = t_1;
	elseif (t <= 5.2e-62)
		tmp = x;
	elseif (t <= 5.4e-46)
		tmp = t_1;
	elseif (t <= 1.15e-12)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / a) * -y;
	tmp = 0.0;
	if (t <= -1.26e+60)
		tmp = t / (a / y);
	elseif (t <= -2.5e-110)
		tmp = x;
	elseif (t <= 1.4e-174)
		tmp = t_1;
	elseif (t <= 5.2e-62)
		tmp = x;
	elseif (t <= 5.4e-46)
		tmp = t_1;
	elseif (t <= 1.15e-12)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[t, -1.26e+60], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e-110], x, If[LessEqual[t, 1.4e-174], t$95$1, If[LessEqual[t, 5.2e-62], x, If[LessEqual[t, 5.4e-46], t$95$1, If[LessEqual[t, 1.15e-12], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.26e60

   1. Initial program 89.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 70.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -1.26e60 < t < -2.5e-110 or 1.39999999999999999e-174 < t < 5.1999999999999999e-62 or 5.4e-46 < t < 1.14999999999999995e-12

   1. Initial program 92.5%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 62.9%

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

   if -2.5e-110 < t < 1.39999999999999999e-174 or 5.1999999999999999e-62 < t < 5.4e-46

   1. Initial program 89.1%

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

      1. associate-*l/ 90.7%

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

   3. Simplified 90.7%

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

      1. associate-/r/ 95.1%

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

      2. div-inv 95.2%

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

      3. associate-/r* 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in z around inf 55.8%

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

      1. mul-1-neg 55.8%

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

      2. associate-*r/ 63.9%

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

      3. distribute-rgt-neg-in 63.9%

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

      4. distribute-neg-frac 63.9%

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

   8. Simplified 63.9%

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

   if 1.14999999999999995e-12 < t

   1. Initial program 91.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 52.5%

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

      1. associate-*r/ 57.9%

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

   6. Simplified 57.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+59}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-175}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e+59)
   (/ t (/ a y))
   (if (<= t -3.3e-110)
     x
     (if (<= t 4.7e-175)
       (* (/ z a) (- y))
       (if (<= t 2.3e-61)
         x
         (if (<= t 5.2e-42)
           (* z (/ y (- a)))
           (if (<= t 1.12e-11) x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+59) {
		tmp = t / (a / y);
	} else if (t <= -3.3e-110) {
		tmp = x;
	} else if (t <= 4.7e-175) {
		tmp = (z / a) * -y;
	} else if (t <= 2.3e-61) {
		tmp = x;
	} else if (t <= 5.2e-42) {
		tmp = z * (y / -a);
	} else if (t <= 1.12e-11) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6d+59)) then
        tmp = t / (a / y)
    else if (t <= (-3.3d-110)) then
        tmp = x
    else if (t <= 4.7d-175) then
        tmp = (z / a) * -y
    else if (t <= 2.3d-61) then
        tmp = x
    else if (t <= 5.2d-42) then
        tmp = z * (y / -a)
    else if (t <= 1.12d-11) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e+59) {
		tmp = t / (a / y);
	} else if (t <= -3.3e-110) {
		tmp = x;
	} else if (t <= 4.7e-175) {
		tmp = (z / a) * -y;
	} else if (t <= 2.3e-61) {
		tmp = x;
	} else if (t <= 5.2e-42) {
		tmp = z * (y / -a);
	} else if (t <= 1.12e-11) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e+59:
		tmp = t / (a / y)
	elif t <= -3.3e-110:
		tmp = x
	elif t <= 4.7e-175:
		tmp = (z / a) * -y
	elif t <= 2.3e-61:
		tmp = x
	elif t <= 5.2e-42:
		tmp = z * (y / -a)
	elif t <= 1.12e-11:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e+59)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= -3.3e-110)
		tmp = x;
	elseif (t <= 4.7e-175)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (t <= 2.3e-61)
		tmp = x;
	elseif (t <= 5.2e-42)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (t <= 1.12e-11)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e+59)
		tmp = t / (a / y);
	elseif (t <= -3.3e-110)
		tmp = x;
	elseif (t <= 4.7e-175)
		tmp = (z / a) * -y;
	elseif (t <= 2.3e-61)
		tmp = x;
	elseif (t <= 5.2e-42)
		tmp = z * (y / -a);
	elseif (t <= 1.12e-11)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e+59], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e-110], x, If[LessEqual[t, 4.7e-175], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 2.3e-61], x, If[LessEqual[t, 5.2e-42], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e-11], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.0000000000000001e59

   1. Initial program 89.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 70.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -6.0000000000000001e59 < t < -3.2999999999999999e-110 or 4.69999999999999998e-175 < t < 2.29999999999999992e-61 or 5.2e-42 < t < 1.1200000000000001e-11

   1. Initial program 92.5%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 62.9%

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

   if -3.2999999999999999e-110 < t < 4.69999999999999998e-175

   1. Initial program 89.8%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

      1. associate-/r/ 94.7%

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

      2. div-inv 94.8%

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

      3. associate-/r* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in z around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-*r/ 61.2%

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

      3. distribute-rgt-neg-in 61.2%

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

      4. distribute-neg-frac 61.2%

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

   8. Simplified 61.2%

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

   if 2.29999999999999992e-61 < t < 5.2e-42

   1. Initial program 80.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. associate-*l/ 98.9%

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

      3. *-commutative 98.9%

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

      4. distribute-rgt-neg-in 98.9%

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

      5. *-lft-identity 98.9%

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

      6. associate-*l/ 98.9%

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

      7. remove-double-neg 98.9%

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

      8. neg-mul-1 98.9%

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

      9. associate-*r* 98.9%

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

      10. *-commutative 98.9%

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

      11. associate-*r/ 98.9%

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

      12. metadata-eval 98.9%

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

      13. metadata-eval 98.9%

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

      14. associate-/r* 98.9%

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

      15. neg-mul-1 98.9%

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

      16. *-commutative 98.9%

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

      17. associate-*r/ 98.9%

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

      18. *-rgt-identity 98.9%

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

      19. distribute-frac-neg 98.9%

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

      20. remove-double-neg 98.9%

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

   6. Simplified 98.9%

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

   if 1.1200000000000001e-11 < t

   1. Initial program 91.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 52.5%

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

      1. associate-*r/ 57.9%

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

   6. Simplified 57.9%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+59}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-110}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-175}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 49.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+59}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e+59)
   (/ t (/ a y))
   (if (<= t -8.4e-109)
     x
     (if (<= t 1.2e-174)
       (/ y (/ (- a) z))
       (if (<= t 6.6e-62)
         x
         (if (<= t 4e-39)
           (* z (/ y (- a)))
           (if (<= t 1.32e-11) x (* t (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+59) {
		tmp = t / (a / y);
	} else if (t <= -8.4e-109) {
		tmp = x;
	} else if (t <= 1.2e-174) {
		tmp = y / (-a / z);
	} else if (t <= 6.6e-62) {
		tmp = x;
	} else if (t <= 4e-39) {
		tmp = z * (y / -a);
	} else if (t <= 1.32e-11) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-3d+59)) then
        tmp = t / (a / y)
    else if (t <= (-8.4d-109)) then
        tmp = x
    else if (t <= 1.2d-174) then
        tmp = y / (-a / z)
    else if (t <= 6.6d-62) then
        tmp = x
    else if (t <= 4d-39) then
        tmp = z * (y / -a)
    else if (t <= 1.32d-11) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e+59) {
		tmp = t / (a / y);
	} else if (t <= -8.4e-109) {
		tmp = x;
	} else if (t <= 1.2e-174) {
		tmp = y / (-a / z);
	} else if (t <= 6.6e-62) {
		tmp = x;
	} else if (t <= 4e-39) {
		tmp = z * (y / -a);
	} else if (t <= 1.32e-11) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e+59:
		tmp = t / (a / y)
	elif t <= -8.4e-109:
		tmp = x
	elif t <= 1.2e-174:
		tmp = y / (-a / z)
	elif t <= 6.6e-62:
		tmp = x
	elif t <= 4e-39:
		tmp = z * (y / -a)
	elif t <= 1.32e-11:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e+59)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= -8.4e-109)
		tmp = x;
	elseif (t <= 1.2e-174)
		tmp = Float64(y / Float64(Float64(-a) / z));
	elseif (t <= 6.6e-62)
		tmp = x;
	elseif (t <= 4e-39)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (t <= 1.32e-11)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e+59)
		tmp = t / (a / y);
	elseif (t <= -8.4e-109)
		tmp = x;
	elseif (t <= 1.2e-174)
		tmp = y / (-a / z);
	elseif (t <= 6.6e-62)
		tmp = x;
	elseif (t <= 4e-39)
		tmp = z * (y / -a);
	elseif (t <= 1.32e-11)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e+59], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.4e-109], x, If[LessEqual[t, 1.2e-174], N[(y / N[((-a) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-62], x, If[LessEqual[t, 4e-39], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e-11], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3e59

   1. Initial program 89.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 70.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -3e59 < t < -8.39999999999999984e-109 or 1.2e-174 < t < 6.60000000000000009e-62 or 3.99999999999999972e-39 < t < 1.32e-11

   1. Initial program 92.5%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 62.9%

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

   if -8.39999999999999984e-109 < t < 1.2e-174

   1. Initial program 89.8%

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

      1. associate-*l/ 90.0%

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

   3. Simplified 90.0%

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

      1. associate-/r/ 94.7%

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

      2. div-inv 94.8%

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

      3. associate-/r* 90.0%

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

   5. Applied egg-rr 90.0%

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

   6. Taylor expanded in z around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-*r/ 61.2%

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

      3. distribute-rgt-neg-in 61.2%

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

      4. distribute-neg-frac 61.2%

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

   8. Simplified 61.2%

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

      1. frac-2neg 61.2%

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

      2. remove-double-neg 61.2%

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

      3. associate-*r/ 53.9%

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

   10. Applied egg-rr 53.9%

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

       1. associate-/l* 61.9%

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

   12. Simplified 61.9%

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

   if 6.60000000000000009e-62 < t < 3.99999999999999972e-39

   1. Initial program 80.5%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 80.5%

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

      1. mul-1-neg 80.5%

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

      2. associate-*l/ 98.9%

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

      3. *-commutative 98.9%

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

      4. distribute-rgt-neg-in 98.9%

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

      5. *-lft-identity 98.9%

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

      6. associate-*l/ 98.9%

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

      7. remove-double-neg 98.9%

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

      8. neg-mul-1 98.9%

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

      9. associate-*r* 98.9%

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

      10. *-commutative 98.9%

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

      11. associate-*r/ 98.9%

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

      12. metadata-eval 98.9%

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

      13. metadata-eval 98.9%

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

      14. associate-/r* 98.9%

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

      15. neg-mul-1 98.9%

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

      16. *-commutative 98.9%

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

      17. associate-*r/ 98.9%

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

      18. *-rgt-identity 98.9%

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

      19. distribute-frac-neg 98.9%

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

      20. remove-double-neg 98.9%

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

   6. Simplified 98.9%

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

   if 1.32e-11 < t

   1. Initial program 91.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 52.5%

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

      1. associate-*r/ 57.9%

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

   6. Simplified 57.9%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+59}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-109}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{y}{\frac{-a}{z}}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 78:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -1.02e+60)
     t_1
     (if (<= t 78.0)
       (- x (* y (/ z a)))
       (if (<= t 2.3e+119) (* (/ y a) (- t z)) 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 <= -1.02e+60) {
		tmp = t_1;
	} else if (t <= 78.0) {
		tmp = x - (y * (z / a));
	} else if (t <= 2.3e+119) {
		tmp = (y / a) * (t - z);
	} 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 <= (-1.02d+60)) then
        tmp = t_1
    else if (t <= 78.0d0) then
        tmp = x - (y * (z / a))
    else if (t <= 2.3d+119) then
        tmp = (y / a) * (t - z)
    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 <= -1.02e+60) {
		tmp = t_1;
	} else if (t <= 78.0) {
		tmp = x - (y * (z / a));
	} else if (t <= 2.3e+119) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -1.02e+60:
		tmp = t_1
	elif t <= 78.0:
		tmp = x - (y * (z / a))
	elif t <= 2.3e+119:
		tmp = (y / a) * (t - z)
	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 <= -1.02e+60)
		tmp = t_1;
	elseif (t <= 78.0)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (t <= 2.3e+119)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	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 <= -1.02e+60)
		tmp = t_1;
	elseif (t <= 78.0)
		tmp = x - (y * (z / a));
	elseif (t <= 2.3e+119)
		tmp = (y / a) * (t - z);
	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, -1.02e+60], t$95$1, If[LessEqual[t, 78.0], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+119], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.0200000000000001e60 or 2.3000000000000001e119 < t

   1. Initial program 89.9%

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

      1. associate-*l/ 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. mul-1-neg 84.3%

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

      3. remove-double-neg 84.3%

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

      4. +-commutative 84.3%

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

      5. associate-*r/ 91.6%

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

   6. Simplified 91.6%

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

   if -1.0200000000000001e60 < t < 78

   1. Initial program 90.9%

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

      1. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

      1. associate-/r/ 97.4%

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

      2. div-inv 97.4%

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

      3. associate-/r* 93.7%

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

   5. Applied egg-rr 93.7%

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

   6. Taylor expanded in z around inf 83.9%

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

      1. associate-*r/ 89.2%

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

   8. Simplified 89.2%

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

   if 78 < t < 2.3000000000000001e119

   1. Initial program 95.1%

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

      1. associate-/r/ 94.2%

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

      2. div-inv 94.2%

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

      3. associate-/r* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around 0 80.0%

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

      1. associate-*l/ 84.9%

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

      2. neg-mul-1 84.9%

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

      3. sub-neg 84.9%

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

      4. distribute-lft-out 48.0%

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

      5. +-commutative 48.0%

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

      6. distribute-neg-in 48.0%

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

      7. distribute-rgt-neg-out 48.0%

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

      8. *-commutative 48.0%

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

      9. associate-*r/ 47.9%

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

      10. associate-*l/ 43.0%

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

      11. remove-double-neg 43.0%

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

      12. sub-neg 43.0%

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

      13. associate-*l/ 47.9%

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

      14. associate-*r/ 48.0%

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

      15. *-commutative 48.0%

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

      16. distribute-lft-out-- 84.9%

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

   8. Simplified 84.9%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+60}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 78:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+119}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-70} \lor \neg \left(y \leq 1.18 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.42e-70) (not (<= y 1.18e+109)))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.42e-70) || !(y <= 1.18e+109)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.42d-70)) .or. (.not. (y <= 1.18d+109))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.42e-70) || !(y <= 1.18e+109)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.42e-70) or not (y <= 1.18e+109):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.42e-70) || !(y <= 1.18e+109))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.42e-70) || ~((y <= 1.18e+109)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.42e-70], N[Not[LessEqual[y, 1.18e+109]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.42000000000000002e-70 or 1.17999999999999998e109 < y

   1. Initial program 82.5%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.7%

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

      3. associate-/r* 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in x around 0 74.3%

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

      1. associate-*l/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. sub-neg 83.5%

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

      4. distribute-lft-out 67.7%

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

      5. +-commutative 67.7%

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

      6. distribute-neg-in 67.7%

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

      7. distribute-rgt-neg-out 67.7%

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

      8. *-commutative 67.7%

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

      9. associate-*r/ 63.6%

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

      10. associate-*l/ 69.5%

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

      11. remove-double-neg 69.5%

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

      12. sub-neg 69.5%

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

      13. associate-*l/ 63.6%

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

      14. associate-*r/ 67.7%

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

      15. *-commutative 67.7%

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

      16. distribute-lft-out-- 83.5%

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

   8. Simplified 83.5%

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

   if -1.42000000000000002e-70 < y < 1.17999999999999998e109

   1. Initial program 99.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 87.6%

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

      1. sub-neg 87.6%

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

      2. mul-1-neg 87.6%

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

      3. remove-double-neg 87.6%

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

      4. +-commutative 87.6%

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

      5. associate-*r/ 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-70} \lor \neg \left(y \leq 1.18 \cdot 10^{+109}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-70} \lor \neg \left(y \leq 1.65 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.05e-70) (not (<= y 1.65e+107)))
   (* (/ y a) (- t z))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.05e-70) || !(y <= 1.65e+107)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.05d-70)) .or. (.not. (y <= 1.65d+107))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.05e-70) || !(y <= 1.65e+107)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.05e-70) or not (y <= 1.65e+107):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.05e-70) || !(y <= 1.65e+107))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.05e-70) || ~((y <= 1.65e+107)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.05e-70], N[Not[LessEqual[y, 1.65e+107]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.04999999999999989e-70 or 1.65000000000000016e107 < y

   1. Initial program 82.5%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.7%

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

      3. associate-/r* 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in x around 0 74.3%

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

      1. associate-*l/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. sub-neg 83.5%

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

      4. distribute-lft-out 67.7%

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

      5. +-commutative 67.7%

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

      6. distribute-neg-in 67.7%

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

      7. distribute-rgt-neg-out 67.7%

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

      8. *-commutative 67.7%

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

      9. associate-*r/ 63.6%

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

      10. associate-*l/ 69.5%

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

      11. remove-double-neg 69.5%

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

      12. sub-neg 69.5%

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

      13. associate-*l/ 63.6%

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

      14. associate-*r/ 67.7%

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

      15. *-commutative 67.7%

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

      16. distribute-lft-out-- 83.5%

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

   8. Simplified 83.5%

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

   if -2.04999999999999989e-70 < y < 1.65000000000000016e107

   1. Initial program 99.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 87.6%

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

      1. sub-neg 87.6%

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

      2. mul-1-neg 87.6%

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

      3. remove-double-neg 87.6%

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

      4. +-commutative 87.6%

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

      5. associate-*r/ 86.9%

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

   6. Simplified 86.9%

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

      1. associate-*r/ 87.6%

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

      2. *-commutative 87.6%

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

   8. Applied egg-rr 87.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-70} \lor \neg \left(y \leq 1.65 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 9: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-70} \lor \neg \left(y \leq 3.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.7e-70) (not (<= y 3.9e+107)))
   (/ y (/ a (- t z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e-70) || !(y <= 3.9e+107)) {
		tmp = y / (a / (t - z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.7d-70)) .or. (.not. (y <= 3.9d+107))) then
        tmp = y / (a / (t - z))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e-70) || !(y <= 3.9e+107)) {
		tmp = y / (a / (t - z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.7e-70) or not (y <= 3.9e+107):
		tmp = y / (a / (t - z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.7e-70) || !(y <= 3.9e+107))
		tmp = Float64(y / Float64(a / Float64(t - z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.7e-70) || ~((y <= 3.9e+107)))
		tmp = y / (a / (t - z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.7e-70], N[Not[LessEqual[y, 3.9e+107]], $MachinePrecision]], N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e-70 or 3.8999999999999998e107 < y

   1. Initial program 82.5%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

      1. associate-/r/ 99.8%

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

      2. div-inv 99.7%

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

      3. associate-/r* 93.9%

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

   5. Applied egg-rr 93.9%

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

   6. Taylor expanded in x around 0 74.3%

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

      1. associate-*l/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. sub-neg 83.5%

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

      4. distribute-lft-out 67.7%

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

      5. +-commutative 67.7%

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

      6. distribute-neg-in 67.7%

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

      7. distribute-rgt-neg-out 67.7%

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

      8. *-commutative 67.7%

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

      9. associate-*r/ 63.6%

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

      10. associate-*l/ 69.5%

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

      11. remove-double-neg 69.5%

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

      12. sub-neg 69.5%

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

      13. associate-*l/ 63.6%

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

      14. associate-*r/ 67.7%

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

      15. *-commutative 67.7%

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

      16. distribute-lft-out-- 83.5%

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

   8. Simplified 83.5%

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

   9. Taylor expanded in y around 0 74.3%

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

       1. associate-/l* 89.4%

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

   11. Simplified 89.4%

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

   if -2.7000000000000001e-70 < y < 3.8999999999999998e107

   1. Initial program 99.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 87.6%

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

      1. sub-neg 87.6%

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

      2. mul-1-neg 87.6%

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

      3. remove-double-neg 87.6%

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

      4. +-commutative 87.6%

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

      5. associate-*r/ 86.9%

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

   6. Simplified 86.9%

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

      1. associate-*r/ 87.6%

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

      2. *-commutative 87.6%

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

   8. Applied egg-rr 87.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-70} \lor \neg \left(y \leq 3.9 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 10: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-70} \lor \neg \left(y \leq 5.6 \cdot 10^{+108}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.7e-70) (not (<= y 5.6e+108)))
   (* y (/ (- t z) a))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e-70) || !(y <= 5.6e+108)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.7d-70)) .or. (.not. (y <= 5.6d+108))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e-70) || !(y <= 5.6e+108)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.7e-70) or not (y <= 5.6e+108):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.7e-70) || !(y <= 5.6e+108))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.7e-70) || ~((y <= 5.6e+108)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.7e-70], N[Not[LessEqual[y, 5.6e+108]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e-70 or 5.5999999999999996e108 < y

   1. Initial program 82.5%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r/ 89.5%

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

      3. distribute-rgt-neg-out 89.5%

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

      4. distribute-neg-frac 89.5%

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

   6. Simplified 89.5%

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

   if -2.7000000000000001e-70 < y < 5.5999999999999996e108

   1. Initial program 99.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 87.6%

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

      1. sub-neg 87.6%

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

      2. mul-1-neg 87.6%

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

      3. remove-double-neg 87.6%

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

      4. +-commutative 87.6%

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

      5. associate-*r/ 86.9%

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

   6. Simplified 86.9%

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

      1. associate-*r/ 87.6%

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

      2. *-commutative 87.6%

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

   8. Applied egg-rr 87.6%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-70} \lor \neg \left(y \leq 5.6 \cdot 10^{+108}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 11: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.7e+223) x (if (<= x 1.52e+122) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.7e+223) {
		tmp = x;
	} else if (x <= 1.52e+122) {
		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 (x <= (-3.7d+223)) then
        tmp = x
    else if (x <= 1.52d+122) 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 (x <= -3.7e+223) {
		tmp = x;
	} else if (x <= 1.52e+122) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.7e+223:
		tmp = x
	elif x <= 1.52e+122:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.7e+223)
		tmp = x;
	elseif (x <= 1.52e+122)
		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 (x <= -3.7e+223)
		tmp = x;
	elseif (x <= 1.52e+122)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.7e+223], x, If[LessEqual[x, 1.52e+122], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000002e223 or 1.52e122 < x

   1. Initial program 91.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 69.4%

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

   if -3.7000000000000002e223 < x < 1.52e122

   1. Initial program 90.5%

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

      1. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

      1. associate-/r/ 93.4%

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

      2. div-inv 93.3%

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

      3. associate-/r* 95.0%

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

   5. Applied egg-rr 95.0%

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

   6. Taylor expanded in x around 0 68.2%

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

      1. associate-*l/ 73.0%

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

      2. neg-mul-1 73.0%

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

      3. sub-neg 73.0%

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

      4. distribute-lft-out 62.9%

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

      5. +-commutative 62.9%

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

      6. distribute-neg-in 62.9%

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

      7. distribute-rgt-neg-out 62.9%

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

      8. *-commutative 62.9%

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

      9. associate-*r/ 60.8%

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

      10. associate-*l/ 58.1%

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

      11. remove-double-neg 58.1%

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

      12. sub-neg 58.1%

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

      13. associate-*l/ 60.8%

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

      14. associate-*r/ 62.9%

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

      15. *-commutative 62.9%

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

      16. distribute-lft-out-- 73.0%

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

   8. Simplified 73.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.52 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 51.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59} \lor \neg \left(t \leq 1.02 \cdot 10^{-11}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.2e+59) (not (<= t 1.02e-11))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.2e+59) || !(t <= 1.02e-11)) {
		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 ((t <= (-6.2d+59)) .or. (.not. (t <= 1.02d-11))) 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 ((t <= -6.2e+59) || !(t <= 1.02e-11)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.2e+59) or not (t <= 1.02e-11):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.2e+59) || !(t <= 1.02e-11))
		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 ((t <= -6.2e+59) || ~((t <= 1.02e-11)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.2e+59], N[Not[LessEqual[t, 1.02e-11]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000029e59 or 1.01999999999999994e-11 < t

   1. Initial program 90.9%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around inf 60.5%

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

      1. associate-*r/ 65.2%

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

   6. Simplified 65.2%

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

   if -6.20000000000000029e59 < t < 1.01999999999999994e-11

   1. Initial program 90.7%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in x around inf 47.2%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+59} \lor \neg \left(t \leq 1.02 \cdot 10^{-11}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.7e+60) (/ t (/ a y)) (if (<= t 4.1e-13) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+60) {
		tmp = t / (a / y);
	} else if (t <= 4.1e-13) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.7d+60)) then
        tmp = t / (a / y)
    else if (t <= 4.1d-13) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.7e+60) {
		tmp = t / (a / y);
	} else if (t <= 4.1e-13) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.7e+60:
		tmp = t / (a / y)
	elif t <= 4.1e-13:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.7e+60)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= 4.1e-13)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.7e+60)
		tmp = t / (a / y);
	elseif (t <= 4.1e-13)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.7e+60], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e-13], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7e60

   1. Initial program 89.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around inf 70.4%

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

      1. associate-/l* 74.3%

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

   6. Simplified 74.3%

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

   if -1.7e60 < t < 4.1000000000000002e-13

   1. Initial program 90.7%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in x around inf 47.2%

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

   if 4.1000000000000002e-13 < t

   1. Initial program 91.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 52.5%

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

      1. associate-*r/ 57.9%

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

   6. Simplified 57.9%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+60}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 14: 97.3% 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 90.8%

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

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

Alternative 15: 40.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Taylor expanded in x around inf 34.9%

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

5. Final simplification 34.9%

   \[\leadsto x \]

Developer target: 99.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023310 
(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)))