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

Percentage Accurate: 91.3% → 97.0%

Time: 8.8s

Alternatives: 7

Speedup: 0.4×

• 27.6% 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: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 4.5}{a}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+269}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{t}, z \cdot -9\right)}{a} \cdot \frac{t}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (- (* y (/ x (* a 2.0))) (* t (/ (* z 4.5) a)))
     (if (<= t_1 4e+269)
       (/ (+ (* x y) (* z (* t -9.0))) (* a 2.0))
       (* (/ (fma x (/ y t) (* z -9.0)) a) (/ t 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 4.5) / a));
	} else if (t_1 <= 4e+269) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (fma(x, (y / t), (z * -9.0)) / a) * (t / 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z * 4.5) / a)));
	elseif (t_1 <= 4e+269)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(fma(x, Float64(y / t), Float64(z * -9.0)) / a) * Float64(t / 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+269], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[(y / t), $MachinePrecision] + N[(z * -9.0), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * N[(t / 2.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0

   1. Initial program 67.4%

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

      1. div-sub 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-/l* 79.7%

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

      4. *-commutative 79.7%

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

      5. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around 0 79.7%

      \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{\frac{t \cdot z}{a} \cdot 4.5} \]

      2. associate-/l* 99.8%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{\left(t \cdot \frac{z}{a}\right)} \cdot 4.5 \]

      3. associate-*r* 99.7%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{t \cdot \left(\frac{z}{a} \cdot 4.5\right)} \]

      4. *-commutative 99.7%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - t \cdot \color{blue}{\left(4.5 \cdot \frac{z}{a}\right)} \]

      5. associate-*r/ 99.8%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - t \cdot \color{blue}{\frac{4.5 \cdot z}{a}} \]

   7. Simplified 99.8%

      \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{t \cdot \frac{4.5 \cdot z}{a}} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.0000000000000002e269

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. +-commutative 99.5%

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

      3. distribute-lft-neg-in 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. metadata-eval 99.5%

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

      6. associate-*r* 99.6%

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

      7. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

   if 4.0000000000000002e269 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 68.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 70.7%

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

      1. *-commutative 70.7%

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

      2. times-frac 86.4%

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

      3. cancel-sign-sub-inv 86.4%

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

      4. associate-/l* 88.8%

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

      5. fma-define 88.8%

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

      6. metadata-eval 88.8%

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

   5. Applied egg-rr 88.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 4.5}{a}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+269}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{t}, z \cdot -9\right)}{a} \cdot \frac{t}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 4 \cdot 10^{+269}\right):\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 4e+269)))
     (- (* y (/ x (* a 2.0))) (* t (/ (* z 4.5) a)))
     (/ (+ (* x y) (* z (* t -9.0))) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 4e+269)) {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 4.5) / a));
	} else {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 4e+269)) {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 4.5) / a));
	} else {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 4e+269):
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 4.5) / a))
	else:
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 4e+269))
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z * 4.5) / a)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 4e+269)))
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 4.5) / a));
	else
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 4e+269]], $MachinePrecision]], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]), $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 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 4.0000000000000002e269 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 68.0%

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

      1. div-sub 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-/l* 79.5%

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

      4. *-commutative 79.5%

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

      5. associate-/l* 96.8%

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

   4. Applied egg-rr 96.8%

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

   5. Taylor expanded in t around 0 81.0%

      \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 81.0%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{\frac{t \cdot z}{a} \cdot 4.5} \]

      2. associate-/l* 96.8%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{\left(t \cdot \frac{z}{a}\right)} \cdot 4.5 \]

      3. associate-*r* 96.8%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{t \cdot \left(\frac{z}{a} \cdot 4.5\right)} \]

      4. *-commutative 96.8%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - t \cdot \color{blue}{\left(4.5 \cdot \frac{z}{a}\right)} \]

      5. associate-*r/ 96.8%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - t \cdot \color{blue}{\frac{4.5 \cdot z}{a}} \]

   7. Simplified 96.8%

      \[\leadsto y \cdot \frac{x}{a \cdot 2} - \color{blue}{t \cdot \frac{4.5 \cdot z}{a}} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.0000000000000002e269

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. +-commutative 99.5%

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

      3. distribute-lft-neg-in 99.5%

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

      4. distribute-rgt-neg-in 99.5%

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

      5. metadata-eval 99.5%

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

      6. associate-*r* 99.6%

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

      7. *-commutative 99.6%

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

   4. Applied egg-rr 99.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 4 \cdot 10^{+269}\right):\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+259}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* t (* -4.5 (/ z a)))
     (if (<= t_1 2e+259)
       (/ (+ (* x y) (* z (* t -9.0))) (* a 2.0))
       (* -4.5 (* z (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t * (-4.5 * (z / a));
	} else if (t_1 <= 2e+259) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t * (-4.5 * (z / a));
	} else if (t_1 <= 2e+259) {
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t * (-4.5 * (z / a))
	elif t_1 <= 2e+259:
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0)
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	elseif (t_1 <= 2e+259)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t * (-4.5 * (z / a));
	elseif (t_1 <= 2e+259)
		tmp = ((x * y) + (z * (t * -9.0))) / (a * 2.0);
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+259], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0

   1. Initial program 57.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.0%

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

      1. associate-/l* 94.4%

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

      2. associate-*r* 94.4%

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

      3. *-commutative 94.4%

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

      4. associate-*r* 94.4%

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

   5. Simplified 94.4%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 2e259

   1. Initial program 96.2%

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

      1. sub-neg 96.2%

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

      2. +-commutative 96.2%

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

      3. distribute-lft-neg-in 96.2%

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

      4. distribute-rgt-neg-in 96.2%

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

      5. metadata-eval 96.2%

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

      6. associate-*r* 96.3%

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

      7. *-commutative 96.3%

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

   4. Applied egg-rr 96.3%

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

   if 2e259 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 64.4%

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

      1. associate-/l/ 64.4%

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

      2. div-sub 64.4%

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

      3. associate-/l* 64.4%

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

      4. fmm-def 70.7%

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

      5. *-commutative 70.7%

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

      6. associate-/l* 70.7%

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

      7. distribute-rgt-neg-out 70.7%

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

      8. distribute-frac-neg 70.7%

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

      9. distribute-rgt-neg-in 70.7%

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

      10. associate-/l* 70.7%

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

      11. metadata-eval 70.7%

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

      12. metadata-eval 70.7%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 70.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 70.7%

      \[\leadsto \frac{\color{blue}{-4.5 \cdot \left(t \cdot z\right)}}{a} \]
   6. Step-by-step derivation

      1. associate-*r/ 70.8%

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

      2. *-commutative 70.8%

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

      3. *-commutative 70.8%

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

      4. associate-/l* 99.7%

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

   7. Applied egg-rr 99.7%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+259}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-70}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+34}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e-70)
   (* 0.5 (* y (/ x a)))
   (if (<= (* x y) 1e+34) (* -4.5 (/ (* z t) a)) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-70) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 1e+34) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d-70)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((x * y) <= 1d+34) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-70) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 1e+34) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e-70:
		tmp = 0.5 * (y * (x / a))
	elif (x * y) <= 1e+34:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e-70)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (Float64(x * y) <= 1e+34)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e-70)
		tmp = 0.5 * (y * (x / a));
	elseif ((x * y) <= 1e+34)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-70], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+34], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999996e-71

   1. Initial program 92.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-/l* 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in x around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-/l* 77.7%

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

   8. Simplified 77.7%

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

   if -9.99999999999999996e-71 < (*.f64 x y) < 9.99999999999999946e33

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.0%

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

   if 9.99999999999999946e33 < (*.f64 x y)

   1. Initial program 82.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.8%

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

      1. associate-/l* 80.9%

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

   5. Simplified 80.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]
   6. Step-by-step derivation

      1. clear-num 80.7%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) \]

      2. un-div-inv 82.4%

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

   7. Applied egg-rr 82.4%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-70}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+34}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-70}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+34}:\\ \;\;\;\;\frac{-4.5}{\frac{a}{z \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e-70)
   (* 0.5 (* y (/ x a)))
   (if (<= (* x y) 1e+34) (/ -4.5 (/ a (* z t))) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-70) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 1e+34) {
		tmp = -4.5 / (a / (z * t));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d-70)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((x * y) <= 1d+34) then
        tmp = (-4.5d0) / (a / (z * t))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e-70) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 1e+34) {
		tmp = -4.5 / (a / (z * t));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e-70:
		tmp = 0.5 * (y * (x / a))
	elif (x * y) <= 1e+34:
		tmp = -4.5 / (a / (z * t))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e-70)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (Float64(x * y) <= 1e+34)
		tmp = Float64(-4.5 / Float64(a / Float64(z * t)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e-70)
		tmp = 0.5 * (y * (x / a));
	elseif ((x * y) <= 1e+34)
		tmp = -4.5 / (a / (z * t));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e-70], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+34], N[(-4.5 / N[(a / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999996e-71

   1. Initial program 92.1%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-/l* 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in x around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-/l* 77.7%

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

   8. Simplified 77.7%

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

   if -9.99999999999999996e-71 < (*.f64 x y) < 9.99999999999999946e33

   1. Initial program 95.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.0%

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

      1. clear-num 81.0%

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

      2. un-div-inv 81.0%

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

      3. *-commutative 81.0%

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

   5. Applied egg-rr 81.0%

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

   if 9.99999999999999946e33 < (*.f64 x y)

   1. Initial program 82.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.8%

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

      1. associate-/l* 80.9%

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

   5. Simplified 80.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]
   6. Step-by-step derivation

      1. clear-num 80.7%

         \[\leadsto 0.5 \cdot \left(x \cdot \color{blue}{\frac{1}{\frac{a}{y}}}\right) \]

      2. un-div-inv 82.4%

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

   7. Applied egg-rr 82.4%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{-70}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{+34}:\\ \;\;\;\;\frac{-4.5}{\frac{a}{z \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-73} \lor \neg \left(y \leq 450000\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.5e-73) (not (<= y 450000.0)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.5e-73) || !(y <= 450000.0)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-3.5d-73)) .or. (.not. (y <= 450000.0d0))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.5e-73) || !(y <= 450000.0)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.5e-73) or not (y <= 450000.0):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.5e-73) || !(y <= 450000.0))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.5e-73) || ~((y <= 450000.0)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.5e-73], N[Not[LessEqual[y, 450000.0]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4999999999999998e-73 or 4.5e5 < y

   1. Initial program 89.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.5%

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

      1. associate-/l* 69.5%

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

   5. Simplified 69.5%

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

   if -3.4999999999999998e-73 < y < 4.5e5

   1. Initial program 94.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 69.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-73} \lor \neg \left(y \leq 450000\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \frac{z \cdot t}{a} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (/ (* z t) a)))

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * ((z * t) / a);
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.5%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 49.4%

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

4. Final simplification 49.4%

   \[\leadsto -4.5 \cdot \frac{z \cdot t}{a} \]
5. Add Preprocessing

Developer target: 94.0% accurate, 0.5× 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 2024130 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (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)))