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

Percentage Accurate: 93.6% → 99.6%

Time: 10.0s

Alternatives: 13

Speedup: 0.4×

• 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: 93.6% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+246}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -2e+174)
     (fma (/ y a) (- z t) x)
     (if (<= t_1 2e+246) (+ x (/ t_1 a)) (+ x (/ (- z t) (/ a y)))))))

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 = fma((y / a), (z - t), x);
	} else if (t_1 <= 2e+246) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	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 = fma(Float64(y / a), Float64(z - t), x);
	elseif (t_1 <= 2e+246)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return 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[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2e+246], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $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. +-commutative 83.4%

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

      2. associate-*l/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

   if -2.00000000000000014e174 < (*.f64 y (-.f64 z t)) < 2.00000000000000014e246

   1. Initial program 99.2%

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

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

   1. Initial program 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+174}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+246}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 2: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+292} \lor \neg \left(t_1 \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -2e+292) (not (<= t_1 5e+288)))
     (* y (/ (- z t) a))
     (+ 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 <= 5e+288)) {
		tmp = y * ((z - t) / a);
	} 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 <= 5d+288))) then
        tmp = y * ((z - t) / a)
    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 <= 5e+288)) {
		tmp = y * ((z - t) / a);
	} 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 <= 5e+288):
		tmp = y * ((z - t) / a)
	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 <= 5e+288))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	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 <= 5e+288)))
		tmp = y * ((z - t) / a);
	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, 5e+288]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $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 5.0000000000000003e288 < (*.f64 y (-.f64 z t))

   1. Initial program 66.4%

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

   2. Taylor expanded in x around 0 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-*l/ 95.4%

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

   4. Applied egg-rr 95.4%

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

   if -2e292 < (*.f64 y (-.f64 z t)) < 5.0000000000000003e288

   1. Initial program 99.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+292} \lor \neg \left(y \cdot \left(z - t\right) \leq 5 \cdot 10^{+288}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]

Alternative 3: 99.6% accurate, 0.4× speedup

Math

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

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 (/ (- z t) (/ 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 + ((z - t) / (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 + ((z - t) / (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 + ((z - t) / (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 + ((z - t) / (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(z - t) / 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 + ((z - t) / (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[(z - t), $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 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   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%

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

Alternative 4: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+246}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY))
     (+ x (/ (/ y a) (/ 1.0 (- z t))))
     (if (<= t_1 2e+246) (+ x (/ t_1 a)) (+ x (/ (- z t) (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y / a) / (1.0 / (z - t)));
	} else if (t_1 <= 2e+246) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y / a) / (1.0 / (z - t)));
	} else if (t_1 <= 2e+246) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y / a) / (1.0 / (z - t)))
	elif t_1 <= 2e+246:
		tmp = x + (t_1 / a)
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y / a) / Float64(1.0 / Float64(z - t))));
	elseif (t_1 <= 2e+246)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	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 <= -Inf)
		tmp = x + ((y / a) / (1.0 / (z - t)));
	elseif (t_1 <= 2e+246)
		tmp = x + (t_1 / a);
	else
		tmp = x + ((z - t) / (a / y));
	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, (-Infinity)], N[(x + N[(N[(y / a), $MachinePrecision] / N[(1.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+246], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0

   1. Initial program 64.4%

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

      1. clear-num 64.4%

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

      2. inv-pow 64.4%

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

   3. Applied egg-rr 64.4%

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

      1. associate-/r* 99.7%

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

      2. div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

      2. associate-/r* 99.8%

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

      3. clear-num 99.9%

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

   7. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 2.00000000000000014e246

   1. Initial program 99.3%

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

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

   1. Initial program 72.3%

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

      1. *-commutative 72.3%

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

      2. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;x + \frac{\frac{y}{a}}{\frac{1}{z - t}}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+246}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 49.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{-42}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.285:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= t -3.6e+59)
     t_1
     (if (<= t -5.8e-173)
       x
       (if (<= t 2.35e-175)
         (/ y (/ a z))
         (if (<= t 1.02e-62)
           x
           (if (<= t 1e-42) (* y (/ z a)) (if (<= t 0.285) x t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -3.6e+59) {
		tmp = t_1;
	} else if (t <= -5.8e-173) {
		tmp = x;
	} else if (t <= 2.35e-175) {
		tmp = y / (a / z);
	} else if (t <= 1.02e-62) {
		tmp = x;
	} else if (t <= 1e-42) {
		tmp = y * (z / a);
	} else if (t <= 0.285) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (t <= (-3.6d+59)) then
        tmp = t_1
    else if (t <= (-5.8d-173)) then
        tmp = x
    else if (t <= 2.35d-175) then
        tmp = y / (a / z)
    else if (t <= 1.02d-62) then
        tmp = x
    else if (t <= 1d-42) then
        tmp = y * (z / a)
    else if (t <= 0.285d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -3.6e+59) {
		tmp = t_1;
	} else if (t <= -5.8e-173) {
		tmp = x;
	} else if (t <= 2.35e-175) {
		tmp = y / (a / z);
	} else if (t <= 1.02e-62) {
		tmp = x;
	} else if (t <= 1e-42) {
		tmp = y * (z / a);
	} else if (t <= 0.285) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if t <= -3.6e+59:
		tmp = t_1
	elif t <= -5.8e-173:
		tmp = x
	elif t <= 2.35e-175:
		tmp = y / (a / z)
	elif t <= 1.02e-62:
		tmp = x
	elif t <= 1e-42:
		tmp = y * (z / a)
	elif t <= 0.285:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -3.6e+59)
		tmp = t_1;
	elseif (t <= -5.8e-173)
		tmp = x;
	elseif (t <= 2.35e-175)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 1.02e-62)
		tmp = x;
	elseif (t <= 1e-42)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 0.285)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (t <= -3.6e+59)
		tmp = t_1;
	elseif (t <= -5.8e-173)
		tmp = x;
	elseif (t <= 2.35e-175)
		tmp = y / (a / z);
	elseif (t <= 1.02e-62)
		tmp = x;
	elseif (t <= 1e-42)
		tmp = y * (z / a);
	elseif (t <= 0.285)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+59], t$95$1, If[LessEqual[t, -5.8e-173], x, If[LessEqual[t, 2.35e-175], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-62], x, If[LessEqual[t, 1e-42], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.285], x, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.5999999999999999e59 or 0.284999999999999976 < t

   1. Initial program 90.6%

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

   2. Taylor expanded in x around 0 70.9%

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

   3. Taylor expanded in z around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-*r/ 66.1%

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

      3. distribute-rgt-neg-in 66.1%

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

   5. Simplified 66.1%

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

   if -3.5999999999999999e59 < t < -5.7999999999999997e-173 or 2.34999999999999999e-175 < t < 1.02000000000000005e-62 or 1.00000000000000004e-42 < t < 0.284999999999999976

   1. Initial program 91.3%

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

   2. Taylor expanded in x around inf 59.8%

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

   if -5.7999999999999997e-173 < t < 2.34999999999999999e-175

   1. Initial program 91.0%

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

   2. Taylor expanded in x around 0 60.5%

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

   3. Taylor expanded in z around inf 58.4%

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

      1. associate-/l* 65.0%

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

   5. Simplified 65.0%

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

   if 1.02000000000000005e-62 < t < 1.00000000000000004e-42

   1. Initial program 80.5%

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

   2. Taylor expanded in x around 0 80.5%

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

   3. Taylor expanded in z around inf 80.5%

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

      1. associate-/l* 98.6%

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

   5. Simplified 98.6%

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

      1. clear-num 98.6%

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

      2. associate-/r/ 98.6%

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

      3. clear-num 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-173}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-175}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-62}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 10^{-42}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 0.285:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 6: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-78} \lor \neg \left(y \leq -4 \cdot 10^{-166} \lor \neg \left(y \leq -2.9 \cdot 10^{-216}\right) \land y \leq 1.7 \cdot 10^{+49}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.4e-78)
         (not (or (<= y -4e-166) (and (not (<= y -2.9e-216)) (<= y 1.7e+49)))))
   (* y (/ (- z t) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.4e-78) || !((y <= -4e-166) || (!(y <= -2.9e-216) && (y <= 1.7e+49)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.4d-78)) .or. (.not. (y <= (-4d-166)) .or. (.not. (y <= (-2.9d-216))) .and. (y <= 1.7d+49))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.4e-78) || !((y <= -4e-166) || (!(y <= -2.9e-216) && (y <= 1.7e+49)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.4e-78) or not ((y <= -4e-166) or (not (y <= -2.9e-216) and (y <= 1.7e+49))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.4e-78) || !((y <= -4e-166) || (!(y <= -2.9e-216) && (y <= 1.7e+49))))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.4e-78) || ~(((y <= -4e-166) || (~((y <= -2.9e-216)) && (y <= 1.7e+49)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.4e-78], N[Not[Or[LessEqual[y, -4e-166], And[N[Not[LessEqual[y, -2.9e-216]], $MachinePrecision], LessEqual[y, 1.7e+49]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.39999999999999987e-78 or -4.00000000000000016e-166 < y < -2.9000000000000001e-216 or 1.7e49 < y

   1. Initial program 85.0%

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

   2. Taylor expanded in x around 0 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*l/ 85.2%

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

   4. Applied egg-rr 85.2%

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

   if -5.39999999999999987e-78 < y < -4.00000000000000016e-166 or -2.9000000000000001e-216 < y < 1.7e49

   1. Initial program 98.9%

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

   2. Taylor expanded in x around inf 62.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-78} \lor \neg \left(y \leq -4 \cdot 10^{-166} \lor \neg \left(y \leq -2.9 \cdot 10^{-216}\right) \land y \leq 1.7 \cdot 10^{+49}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 76.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 104 \lor \neg \left(t \leq 8 \cdot 10^{+75}\right) \land t \leq 1.1 \cdot 10^{+163}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.4e+75)
   (* t (/ (- y) a))
   (if (or (<= t 104.0) (and (not (<= t 8e+75)) (<= t 1.1e+163)))
     (+ x (* z (/ y a)))
     (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.4e+75) {
		tmp = t * (-y / a);
	} else if ((t <= 104.0) || (!(t <= 8e+75) && (t <= 1.1e+163))) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * ((z - 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 (t <= (-1.4d+75)) then
        tmp = t * (-y / a)
    else if ((t <= 104.0d0) .or. (.not. (t <= 8d+75)) .and. (t <= 1.1d+163)) then
        tmp = x + (z * (y / a))
    else
        tmp = y * ((z - 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 (t <= -1.4e+75) {
		tmp = t * (-y / a);
	} else if ((t <= 104.0) || (!(t <= 8e+75) && (t <= 1.1e+163))) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.4e+75:
		tmp = t * (-y / a)
	elif (t <= 104.0) or (not (t <= 8e+75) and (t <= 1.1e+163)):
		tmp = x + (z * (y / a))
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.4e+75)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif ((t <= 104.0) || (!(t <= 8e+75) && (t <= 1.1e+163)))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.4e+75)
		tmp = t * (-y / a);
	elseif ((t <= 104.0) || (~((t <= 8e+75)) && (t <= 1.1e+163)))
		tmp = x + (z * (y / a));
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.4e+75], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 104.0], And[N[Not[LessEqual[t, 8e+75]], $MachinePrecision], LessEqual[t, 1.1e+163]]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.40000000000000006e75

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 72.2%

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

   3. Taylor expanded in z around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

   5. Simplified 74.5%

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

   if -1.40000000000000006e75 < t < 104 or 7.99999999999999941e75 < t < 1.09999999999999993e163

   1. Initial program 91.1%

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

   2. Taylor expanded in z around inf 82.0%

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

      1. associate-*l/ 43.9%

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

      2. *-commutative 43.9%

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

   4. Simplified 87.1%

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

   if 104 < t < 7.99999999999999941e75 or 1.09999999999999993e163 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*l/ 73.7%

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

   4. Applied egg-rr 73.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 104 \lor \neg \left(t \leq 8 \cdot 10^{+75}\right) \land t \leq 1.1 \cdot 10^{+163}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 8: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 104:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+76} \lor \neg \left(t \leq 4.3 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+75)
   (* t (/ (- y) a))
   (if (<= t 104.0)
     (+ x (/ y (/ a z)))
     (if (or (<= t 4.5e+76) (not (<= t 4.3e+164)))
       (* y (/ (- z t) a))
       (+ x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+75) {
		tmp = t * (-y / a);
	} else if (t <= 104.0) {
		tmp = x + (y / (a / z));
	} else if ((t <= 4.5e+76) || !(t <= 4.3e+164)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.05d+75)) then
        tmp = t * (-y / a)
    else if (t <= 104.0d0) then
        tmp = x + (y / (a / z))
    else if ((t <= 4.5d+76) .or. (.not. (t <= 4.3d+164))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+75) {
		tmp = t * (-y / a);
	} else if (t <= 104.0) {
		tmp = x + (y / (a / z));
	} else if ((t <= 4.5e+76) || !(t <= 4.3e+164)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+75:
		tmp = t * (-y / a)
	elif t <= 104.0:
		tmp = x + (y / (a / z))
	elif (t <= 4.5e+76) or not (t <= 4.3e+164):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+75)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (t <= 104.0)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif ((t <= 4.5e+76) || !(t <= 4.3e+164))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+75)
		tmp = t * (-y / a);
	elseif (t <= 104.0)
		tmp = x + (y / (a / z));
	elseif ((t <= 4.5e+76) || ~((t <= 4.3e+164)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+75], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 104.0], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 4.5e+76], N[Not[LessEqual[t, 4.3e+164]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.04999999999999999e75

   1. Initial program 90.8%

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

   2. Taylor expanded in x around 0 72.2%

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

   3. Taylor expanded in z around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 74.5%

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

      3. distribute-rgt-neg-in 74.5%

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

   5. Simplified 74.5%

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

   if -1.04999999999999999e75 < t < 104

   1. Initial program 90.3%

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

   2. Taylor expanded in z around inf 82.6%

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

      1. associate-/l* 47.4%

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

   4. Simplified 89.6%

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

   if 104 < t < 4.4999999999999997e76 or 4.3e164 < t

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 72.1%

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

      1. *-commutative 72.1%

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

      2. associate-*l/ 73.7%

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

   4. Applied egg-rr 73.7%

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

   if 4.4999999999999997e76 < t < 4.3e164

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 75.3%

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

      1. associate-*l/ 35.1%

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

      2. *-commutative 35.1%

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

   4. Simplified 75.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 104:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+76} \lor \neg \left(t \leq 4.3 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+74} \lor \neg \left(t \leq 58000000000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e+74) (not (<= t 58000000000000.0)))
   (- x (* t (/ y a)))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e+74) || !(t <= 58000000000000.0)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.35d+74)) .or. (.not. (t <= 58000000000000.0d0))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e+74) || !(t <= 58000000000000.0)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35e+74) or not (t <= 58000000000000.0):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e+74) || !(t <= 58000000000000.0))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35e+74) || ~((t <= 58000000000000.0)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.35e+74], N[Not[LessEqual[t, 58000000000000.0]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3499999999999999e74 or 5.8e13 < t

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 81.7%

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

      1. mul-1-neg 81.7%

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

      2. associate-*l/ 79.4%

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

      3. unsub-neg 79.4%

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

      4. associate-*l/ 81.7%

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

      5. associate-*r/ 88.2%

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

   4. Simplified 88.2%

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

   if -1.3499999999999999e74 < t < 5.8e13

   1. Initial program 89.8%

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

   2. Taylor expanded in z around inf 81.5%

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

      1. associate-/l* 47.5%

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

   4. Simplified 89.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+74} \lor \neg \left(t \leq 58000000000000\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-28} \lor \neg \left(y \leq 2.15 \cdot 10^{+83}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.6e-28) (not (<= y 2.15e+83))) (* z (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e-28) || !(y <= 2.15e+83)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.6d-28)) .or. (.not. (y <= 2.15d+83))) then
        tmp = z * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e-28) || !(y <= 2.15e+83)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.6e-28) or not (y <= 2.15e+83):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.6e-28) || !(y <= 2.15e+83))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.6e-28) || ~((y <= 2.15e+83)))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.6e-28], N[Not[LessEqual[y, 2.15e+83]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-28 or 2.15e83 < y

   1. Initial program 81.1%

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

   2. Taylor expanded in x around 0 74.2%

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

   3. Taylor expanded in z around inf 48.4%

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

      1. associate-*l/ 56.1%

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

      2. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   if -2.6e-28 < y < 2.15e83

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 55.0%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-28} \lor \neg \left(y \leq 2.15 \cdot 10^{+83}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.7e-27) (* y (/ z a)) (if (<= y 2.15e+91) x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e-27) {
		tmp = y * (z / a);
	} else if (y <= 2.15e+91) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.7d-27)) then
        tmp = y * (z / a)
    else if (y <= 2.15d+91) then
        tmp = x
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e-27) {
		tmp = y * (z / a);
	} else if (y <= 2.15e+91) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.7e-27:
		tmp = y * (z / a)
	elif y <= 2.15e+91:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.7e-27)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 2.15e+91)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.7e-27)
		tmp = y * (z / a);
	elseif (y <= 2.15e+91)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.7e-27], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e+91], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999989e-27

   1. Initial program 78.4%

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

   2. Taylor expanded in x around 0 67.9%

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

   3. Taylor expanded in z around inf 46.6%

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

      1. associate-/l* 61.0%

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

   5. Simplified 61.0%

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

      1. clear-num 61.0%

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

      2. associate-/r/ 61.0%

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

      3. clear-num 61.1%

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

   7. Applied egg-rr 61.1%

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

   if -2.69999999999999989e-27 < y < 2.15e91

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 55.0%

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

   if 2.15e91 < y

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 83.0%

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

   3. Taylor expanded in z around inf 50.9%

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

      1. associate-*l/ 54.8%

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

      2. *-commutative 54.8%

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

   5. Simplified 54.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 12: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e-27) (* y (/ z a)) (if (<= y 3.4e+82) x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e-27) {
		tmp = y * (z / a);
	} else if (y <= 3.4e+82) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1d-27)) then
        tmp = y * (z / a)
    else if (y <= 3.4d+82) then
        tmp = x
    else
        tmp = z / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1e-27) {
		tmp = y * (z / a);
	} else if (y <= 3.4e+82) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1e-27:
		tmp = y * (z / a)
	elif y <= 3.4e+82:
		tmp = x
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1e-27)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 3.4e+82)
		tmp = x;
	else
		tmp = Float64(z / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1e-27)
		tmp = y * (z / a);
	elseif (y <= 3.4e+82)
		tmp = x;
	else
		tmp = z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1e-27], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+82], x, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e-27

   1. Initial program 78.4%

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

   2. Taylor expanded in x around 0 67.9%

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

   3. Taylor expanded in z around inf 46.6%

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

      1. associate-/l* 61.0%

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

   5. Simplified 61.0%

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

      1. clear-num 61.0%

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

      2. associate-/r/ 61.0%

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

      3. clear-num 61.1%

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

   7. Applied egg-rr 61.1%

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

   if -1e-27 < y < 3.39999999999999994e82

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 55.0%

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

   if 3.39999999999999994e82 < y

   1. Initial program 84.9%

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

   2. Taylor expanded in x around 0 83.0%

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

   3. Taylor expanded in z around inf 50.9%

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

      1. associate-*l/ 54.8%

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

      2. *-commutative 54.8%

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

   5. Simplified 54.8%

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

      1. clear-num 54.8%

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

      2. un-div-inv 54.8%

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

   7. Applied egg-rr 54.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+82}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 13: 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 90.7%

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

2. Taylor expanded in x around inf 34.7%

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

3. Final simplification 34.7%

   \[\leadsto x \]

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, E"
  :precision binary64

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

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