Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 91.3% → 93.5%

Time: 10.7s

Alternatives: 10

Speedup: 0.8×

• 27.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

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 * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* x (/ (* y 0.5) a))
   (/ (fma x y (* -9.0 (* z t))) (* a 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = fma(x, y, (-9.0 * (z * t))) / (a * 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(fma(x, y, Float64(-9.0 * Float64(z * t))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 64.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 64.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a} \cdot 0.5} \]

      2. *-commutative 64.7%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \cdot 0.5 \]

      3. associate-*l/ 64.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      4. associate-*r/ 64.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      5. associate-*l* 96.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      6. associate-*r/ 96.3%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   6. Simplified 96.3%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]

   if -inf.0 < (*.f64 x y)

   1. Initial program 96.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. fma-neg 96.4%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      2. *-commutative 96.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, -\color{blue}{\left(9 \cdot z\right)} \cdot t\right)}{a \cdot 2} \]

      3. associate-*l* 96.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, -\color{blue}{9 \cdot \left(z \cdot t\right)}\right)}{a \cdot 2} \]

      4. distribute-lft-neg-in 96.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}{a \cdot 2} \]

      5. metadata-eval 96.4%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}{a \cdot 2} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -9 \cdot \left(z \cdot t\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* x (/ (* y 0.5) a))
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y * 0.5) / a);
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = x * ((y * 0.5) / a)
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = x * ((y * 0.5) / a);
	else
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 64.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 64.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a} \cdot 0.5} \]

      2. *-commutative 64.7%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \cdot 0.5 \]

      3. associate-*l/ 64.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      4. associate-*r/ 64.7%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      5. associate-*l* 96.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      6. associate-*r/ 96.3%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   6. Simplified 96.3%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]

   if -inf.0 < (*.f64 x y)

   1. Initial program 96.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 3: 65.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-5}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82} \lor \neg \left(y \leq 2.2 \cdot 10^{+96}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ y (/ a x)))))
   (if (<= y -3.1e-90)
     t_1
     (if (<= y 6.2e-5)
       (* -4.5 (/ (* z t) a))
       (if (or (<= y 1.7e+82) (not (<= y 2.2e+96)))
         t_1
         (* -4.5 (/ t (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y / (a / x));
	double tmp;
	if (y <= -3.1e-90) {
		tmp = t_1;
	} else if (y <= 6.2e-5) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((y <= 1.7e+82) || !(y <= 2.2e+96)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t / (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (y / (a / x))
    if (y <= (-3.1d-90)) then
        tmp = t_1
    else if (y <= 6.2d-5) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((y <= 1.7d+82) .or. (.not. (y <= 2.2d+96))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y / (a / x));
	double tmp;
	if (y <= -3.1e-90) {
		tmp = t_1;
	} else if (y <= 6.2e-5) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((y <= 1.7e+82) || !(y <= 2.2e+96)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 0.5 * (y / (a / x))
	tmp = 0
	if y <= -3.1e-90:
		tmp = t_1
	elif y <= 6.2e-5:
		tmp = -4.5 * ((z * t) / a)
	elif (y <= 1.7e+82) or not (y <= 2.2e+96):
		tmp = t_1
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(y / Float64(a / x)))
	tmp = 0.0
	if (y <= -3.1e-90)
		tmp = t_1;
	elseif (y <= 6.2e-5)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif ((y <= 1.7e+82) || !(y <= 2.2e+96))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y / (a / x));
	tmp = 0.0;
	if (y <= -3.1e-90)
		tmp = t_1;
	elseif (y <= 6.2e-5)
		tmp = -4.5 * ((z * t) / a);
	elseif ((y <= 1.7e+82) || ~((y <= 2.2e+96)))
		tmp = t_1;
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-90], t$95$1, If[LessEqual[y, 6.2e-5], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.7e+82], N[Not[LessEqual[y, 2.2e+96]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000001e-90 or 6.20000000000000027e-5 < y < 1.69999999999999997e82 or 2.1999999999999999e96 < y

   1. Initial program 90.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 90.6%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 63.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 67.8%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Simplified 67.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]

   if -3.1000000000000001e-90 < y < 6.20000000000000027e-5

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 1.69999999999999997e82 < y < 2.1999999999999999e96

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 66.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 36.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 22.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-5}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82} \lor \neg \left(y \leq 2.2 \cdot 10^{+96}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 4: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-5}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ y (/ a x)))))
   (if (<= y -3.1e-93)
     t_1
     (if (<= y 4e-5)
       (* -4.5 (/ (* z t) a))
       (if (<= y 1.7e+82)
         (* x (/ (* y 0.5) a))
         (if (<= y 4.4e+96) (* -4.5 (/ t (/ a z))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y / (a / x));
	double tmp;
	if (y <= -3.1e-93) {
		tmp = t_1;
	} else if (y <= 4e-5) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.7e+82) {
		tmp = x * ((y * 0.5) / a);
	} else if (y <= 4.4e+96) {
		tmp = -4.5 * (t / (a / 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 = 0.5d0 * (y / (a / x))
    if (y <= (-3.1d-93)) then
        tmp = t_1
    else if (y <= 4d-5) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (y <= 1.7d+82) then
        tmp = x * ((y * 0.5d0) / a)
    else if (y <= 4.4d+96) then
        tmp = (-4.5d0) * (t / (a / 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 = 0.5 * (y / (a / x));
	double tmp;
	if (y <= -3.1e-93) {
		tmp = t_1;
	} else if (y <= 4e-5) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.7e+82) {
		tmp = x * ((y * 0.5) / a);
	} else if (y <= 4.4e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 0.5 * (y / (a / x))
	tmp = 0
	if y <= -3.1e-93:
		tmp = t_1
	elif y <= 4e-5:
		tmp = -4.5 * ((z * t) / a)
	elif y <= 1.7e+82:
		tmp = x * ((y * 0.5) / a)
	elif y <= 4.4e+96:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(y / Float64(a / x)))
	tmp = 0.0
	if (y <= -3.1e-93)
		tmp = t_1;
	elseif (y <= 4e-5)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (y <= 1.7e+82)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (y <= 4.4e+96)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y / (a / x));
	tmp = 0.0;
	if (y <= -3.1e-93)
		tmp = t_1;
	elseif (y <= 4e-5)
		tmp = -4.5 * ((z * t) / a);
	elseif (y <= 1.7e+82)
		tmp = x * ((y * 0.5) / a);
	elseif (y <= 4.4e+96)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-93], t$95$1, If[LessEqual[y, 4e-5], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+82], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+96], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.1e-93 or 4.3999999999999998e96 < y

   1. Initial program 89.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 89.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 65.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Simplified 65.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]

   if -3.1e-93 < y < 4.00000000000000033e-5

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 4.00000000000000033e-5 < y < 1.69999999999999997e82

   1. Initial program 99.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 99.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 80.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a} \cdot 0.5} \]

      2. *-commutative 80.1%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \cdot 0.5 \]

      3. associate-*l/ 80.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      4. associate-*r/ 79.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      5. associate-*l* 80.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      6. associate-*r/ 80.2%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]

   if 1.69999999999999997e82 < y < 4.3999999999999998e96

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 66.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 36.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 22.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-93}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-5}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 5: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-91}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -8e-91)
   (* 0.5 (/ y (/ a x)))
   (if (<= y 0.054)
     (* -4.5 (/ (* z t) a))
     (if (<= y 1.7e+82)
       (* x (/ (* y 0.5) a))
       (if (<= y 2.2e+96) (* -4.5 (/ t (/ a z))) (* (/ y 2.0) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -8e-91) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 0.054) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.7e+82) {
		tmp = x * ((y * 0.5) / a);
	} else if (y <= 2.2e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (y / 2.0) * (x / 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 <= (-8d-91)) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 0.054d0) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (y <= 1.7d+82) then
        tmp = x * ((y * 0.5d0) / a)
    else if (y <= 2.2d+96) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (y / 2.0d0) * (x / 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 <= -8e-91) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 0.054) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.7e+82) {
		tmp = x * ((y * 0.5) / a);
	} else if (y <= 2.2e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -8e-91:
		tmp = 0.5 * (y / (a / x))
	elif y <= 0.054:
		tmp = -4.5 * ((z * t) / a)
	elif y <= 1.7e+82:
		tmp = x * ((y * 0.5) / a)
	elif y <= 2.2e+96:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = (y / 2.0) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -8e-91)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 0.054)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (y <= 1.7e+82)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a));
	elseif (y <= 2.2e+96)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -8e-91)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 0.054)
		tmp = -4.5 * ((z * t) / a);
	elseif (y <= 1.7e+82)
		tmp = x * ((y * 0.5) / a);
	elseif (y <= 2.2e+96)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = (y / 2.0) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -8e-91], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.054], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+82], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+96], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -8.00000000000000018e-91

   1. Initial program 91.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Simplified 58.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]

   if -8.00000000000000018e-91 < y < 0.0539999999999999994

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 0.0539999999999999994 < y < 1.69999999999999997e82

   1. Initial program 99.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 99.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 80.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. *-commutative 80.1%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a} \cdot 0.5} \]

      2. *-commutative 80.1%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \cdot 0.5 \]

      3. associate-*l/ 80.1%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} \]

      4. associate-*r/ 79.9%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a}} \]

      5. associate-*l* 80.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} \]

      6. associate-*r/ 80.2%

         \[\leadsto x \cdot \color{blue}{\frac{y \cdot 0.5}{a}} \]

   6. Simplified 80.2%

      \[\leadsto \color{blue}{x \cdot \frac{y \cdot 0.5}{a}} \]

   if 1.69999999999999997e82 < y < 2.1999999999999999e96

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 66.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 36.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 22.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]

   if 2.1999999999999999e96 < y

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 86.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 69.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. *-commutative 69.4%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      2. times-frac 78.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-91}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 0.054:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 6: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-5}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.1e-90)
   (* 0.5 (/ y (/ a x)))
   (if (<= y 8e-5)
     (* -4.5 (/ (* z t) a))
     (if (<= y 1.7e+82)
       (* (/ y a) (* x 0.5))
       (if (<= y 2.3e+96) (* -4.5 (/ t (/ a z))) (* (/ y 2.0) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.1e-90) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 8e-5) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.7e+82) {
		tmp = (y / a) * (x * 0.5);
	} else if (y <= 2.3e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (y / 2.0) * (x / 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 <= (-3.1d-90)) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 8d-5) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (y <= 1.7d+82) then
        tmp = (y / a) * (x * 0.5d0)
    else if (y <= 2.3d+96) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (y / 2.0d0) * (x / 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 <= -3.1e-90) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 8e-5) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.7e+82) {
		tmp = (y / a) * (x * 0.5);
	} else if (y <= 2.3e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.1e-90:
		tmp = 0.5 * (y / (a / x))
	elif y <= 8e-5:
		tmp = -4.5 * ((z * t) / a)
	elif y <= 1.7e+82:
		tmp = (y / a) * (x * 0.5)
	elif y <= 2.3e+96:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = (y / 2.0) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.1e-90)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 8e-5)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (y <= 1.7e+82)
		tmp = Float64(Float64(y / a) * Float64(x * 0.5));
	elseif (y <= 2.3e+96)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.1e-90)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 8e-5)
		tmp = -4.5 * ((z * t) / a);
	elseif (y <= 1.7e+82)
		tmp = (y / a) * (x * 0.5);
	elseif (y <= 2.3e+96)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = (y / 2.0) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.1e-90], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-5], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+82], N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+96], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.1000000000000001e-90

   1. Initial program 91.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Simplified 58.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]

   if -3.1000000000000001e-90 < y < 8.00000000000000065e-5

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 8.00000000000000065e-5 < y < 1.69999999999999997e82

   1. Initial program 99.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 99.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 80.1%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 80.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

      2. div-inv 80.2%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 80.2%

         \[\leadsto \frac{y}{a} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(x \cdot 0.5\right)} \]

   if 1.69999999999999997e82 < y < 2.30000000000000015e96

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 66.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 36.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 22.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]

   if 2.30000000000000015e96 < y

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 86.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 69.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. *-commutative 69.4%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      2. times-frac 78.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-5}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 7: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 0.018:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.6e-90)
   (* 0.5 (/ y (/ a x)))
   (if (<= y 0.018)
     (* -4.5 (/ (* z t) a))
     (if (<= y 1.3e+82)
       (* (/ y a) (* x 0.5))
       (if (<= y 4.1e+96) (/ (* t -4.5) (/ a z)) (* (/ y 2.0) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.6e-90) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 0.018) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.3e+82) {
		tmp = (y / a) * (x * 0.5);
	} else if (y <= 4.1e+96) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = (y / 2.0) * (x / 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 <= (-1.6d-90)) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 0.018d0) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (y <= 1.3d+82) then
        tmp = (y / a) * (x * 0.5d0)
    else if (y <= 4.1d+96) then
        tmp = (t * (-4.5d0)) / (a / z)
    else
        tmp = (y / 2.0d0) * (x / 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 <= -1.6e-90) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 0.018) {
		tmp = -4.5 * ((z * t) / a);
	} else if (y <= 1.3e+82) {
		tmp = (y / a) * (x * 0.5);
	} else if (y <= 4.1e+96) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.6e-90:
		tmp = 0.5 * (y / (a / x))
	elif y <= 0.018:
		tmp = -4.5 * ((z * t) / a)
	elif y <= 1.3e+82:
		tmp = (y / a) * (x * 0.5)
	elif y <= 4.1e+96:
		tmp = (t * -4.5) / (a / z)
	else:
		tmp = (y / 2.0) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.6e-90)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 0.018)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (y <= 1.3e+82)
		tmp = Float64(Float64(y / a) * Float64(x * 0.5));
	elseif (y <= 4.1e+96)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	else
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.6e-90)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 0.018)
		tmp = -4.5 * ((z * t) / a);
	elseif (y <= 1.3e+82)
		tmp = (y / a) * (x * 0.5);
	elseif (y <= 4.1e+96)
		tmp = (t * -4.5) / (a / z);
	else
		tmp = (y / 2.0) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.6e-90], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.018], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+82], N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+96], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.60000000000000004e-90

   1. Initial program 91.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Simplified 58.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]

   if -1.60000000000000004e-90 < y < 0.0179999999999999986

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 0.0179999999999999986 < y < 1.2999999999999999e82

   1. Initial program 99.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 99.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 80.1%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 80.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

      2. div-inv 80.2%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 80.2%

         \[\leadsto \frac{y}{a} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(x \cdot 0.5\right)} \]

   if 1.2999999999999999e82 < y < 4.09999999999999998e96

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 66.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 36.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 22.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 22.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

   8. Applied egg-rr 22.5%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

   if 4.09999999999999998e96 < y

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 86.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 69.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. *-commutative 69.4%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      2. times-frac 78.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 0.018:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 8: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.2e-90)
   (* 0.5 (/ y (/ a x)))
   (if (<= y 0.06)
     (/ (* -4.5 (* z t)) a)
     (if (<= y 1.6e+82)
       (* (/ y a) (* x 0.5))
       (if (<= y 2.2e+96) (/ (* t -4.5) (/ a z)) (* (/ y 2.0) (/ x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.2e-90) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 0.06) {
		tmp = (-4.5 * (z * t)) / a;
	} else if (y <= 1.6e+82) {
		tmp = (y / a) * (x * 0.5);
	} else if (y <= 2.2e+96) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = (y / 2.0) * (x / 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 <= (-2.2d-90)) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 0.06d0) then
        tmp = ((-4.5d0) * (z * t)) / a
    else if (y <= 1.6d+82) then
        tmp = (y / a) * (x * 0.5d0)
    else if (y <= 2.2d+96) then
        tmp = (t * (-4.5d0)) / (a / z)
    else
        tmp = (y / 2.0d0) * (x / 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 <= -2.2e-90) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 0.06) {
		tmp = (-4.5 * (z * t)) / a;
	} else if (y <= 1.6e+82) {
		tmp = (y / a) * (x * 0.5);
	} else if (y <= 2.2e+96) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = (y / 2.0) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.2e-90:
		tmp = 0.5 * (y / (a / x))
	elif y <= 0.06:
		tmp = (-4.5 * (z * t)) / a
	elif y <= 1.6e+82:
		tmp = (y / a) * (x * 0.5)
	elif y <= 2.2e+96:
		tmp = (t * -4.5) / (a / z)
	else:
		tmp = (y / 2.0) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.2e-90)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 0.06)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	elseif (y <= 1.6e+82)
		tmp = Float64(Float64(y / a) * Float64(x * 0.5));
	elseif (y <= 2.2e+96)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	else
		tmp = Float64(Float64(y / 2.0) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.2e-90)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 0.06)
		tmp = (-4.5 * (z * t)) / a;
	elseif (y <= 1.6e+82)
		tmp = (y / a) * (x * 0.5);
	elseif (y <= 2.2e+96)
		tmp = (t * -4.5) / (a / z);
	else
		tmp = (y / 2.0) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.2e-90], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.06], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.6e+82], N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+96], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.19999999999999986e-90

   1. Initial program 91.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 91.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Simplified 58.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]

   if -2.19999999999999986e-90 < y < 0.059999999999999998

   1. Initial program 96.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 96.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 72.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 72.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

   8. Applied egg-rr 72.1%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]
   9. Step-by-step derivation

      1. div-inv 71.4%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{1}{\frac{a}{z}}} \]

      2. clear-num 71.9%

         \[\leadsto \left(-4.5 \cdot t\right) \cdot \color{blue}{\frac{z}{a}} \]

      3. associate-*r* 71.9%

         \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

      4. *-commutative 71.9%

         \[\leadsto \color{blue}{\left(t \cdot \frac{z}{a}\right) \cdot -4.5} \]

      5. associate-*l* 71.9%

         \[\leadsto \color{blue}{t \cdot \left(\frac{z}{a} \cdot -4.5\right)} \]

   10. Applied egg-rr 71.9%

       \[\leadsto \color{blue}{t \cdot \left(\frac{z}{a} \cdot -4.5\right)} \]

   11. Taylor expanded in t around 0 74.7%

       \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   12. Step-by-step derivation

       1. associate-*r/ 74.8%

          \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

   13. Simplified 74.8%

       \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

   if 0.059999999999999998 < y < 1.59999999999999987e82

   1. Initial program 99.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 99.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 80.1%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 80.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot \frac{x}{2}} \]

      2. div-inv 80.2%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 80.2%

         \[\leadsto \frac{y}{a} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 80.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot \left(x \cdot 0.5\right)} \]

   if 1.59999999999999987e82 < y < 2.1999999999999999e96

   1. Initial program 66.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 66.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around 0 36.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 22.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   6. Simplified 22.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 22.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

   8. Applied egg-rr 22.5%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot t}{\frac{a}{z}}} \]

   if 2.1999999999999999e96 < y

   1. Initial program 86.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. associate-*l* 86.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 86.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

   4. Taylor expanded in x around inf 69.4%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]
   5. Step-by-step derivation

      1. *-commutative 69.4%

         \[\leadsto \frac{y \cdot x}{\color{blue}{2 \cdot a}} \]

      2. times-frac 78.7%

         \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]

   6. Applied egg-rr 78.7%

      \[\leadsto \color{blue}{\frac{y}{2} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-90}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 0.06:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 9: 52.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (* t (/ z a))))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (t * (z / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (t * (z / a));
}

Python

def code(x, y, z, t, a):
	return -4.5 * (t * (z / a))

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(t * Float64(z / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (t * (z / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.1%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Step-by-step derivation

   1. associate-*l* 93.1%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

3. Simplified 93.1%

   \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
4. Step-by-step derivation

   1. div-inv 93.0%

      \[\leadsto \color{blue}{\left(x \cdot y - z \cdot \left(9 \cdot t\right)\right) \cdot \frac{1}{a \cdot 2}} \]

   2. fma-neg 93.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -z \cdot \left(9 \cdot t\right)\right)} \cdot \frac{1}{a \cdot 2} \]

   3. distribute-rgt-neg-in 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right) \cdot \frac{1}{a \cdot 2} \]

   4. *-commutative 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right) \cdot \frac{1}{a \cdot 2} \]

   5. distribute-rgt-neg-in 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right) \cdot \frac{1}{a \cdot 2} \]

   6. metadata-eval 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right) \cdot \frac{1}{a \cdot 2} \]

   7. *-commutative 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} \]

   8. associate-/r* 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

   9. metadata-eval 93.0%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{\color{blue}{0.5}}{a} \]

5. Applied egg-rr 93.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]

6. Taylor expanded in x around 0 52.8%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
7. Step-by-step derivation

   1. associate-*r/ 49.9%

      \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]

8. Simplified 49.9%

   \[\leadsto \color{blue}{-4.5 \cdot \left(t \cdot \frac{z}{a}\right)} \]

9. Final simplification 49.9%

   \[\leadsto -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \]

Alternative 10: 50.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ -4.5 \cdot \frac{z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* -4.5 (/ (* z t) a)))

C

double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((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 = (-4.5d0) * ((z * t) / a)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * ((z * t) / a);
}

Python

def code(x, y, z, t, a):
	return -4.5 * ((z * t) / a)

Julia

function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(Float64(z * t) / a))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -4.5 * ((z * t) / a);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.1%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Step-by-step derivation

   1. associate-*l* 93.1%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

3. Simplified 93.1%

   \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

4. Taylor expanded in x around 0 52.8%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

5. Final simplification 52.8%

   \[\leadsto -4.5 \cdot \frac{z \cdot t}{a} \]

Developer target: 93.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))