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

Percentage Accurate: 92.1% → 96.5%

Time: 11.8s

Alternatives: 10

Speedup: 0.4×

• 28.6% 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: 92.1% 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: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \mathbf{elif}\;t\_1 \leq 10^{+286}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{fma}\left(-4.5, \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{z \cdot a}\right)\right)\\ \end{array} \end{array} \]

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 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (- (* y (/ x (* a 2.0))) (* t (/ (* z 9.0) (* a 2.0))))
     (if (<= t_1 1e+286)
       (/ (fma x (/ y 2.0) (* t (* z -4.5))) a)
       (* z (fma -4.5 (/ t a) (* 0.5 (* x (/ y (* z 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	} else if (t_1 <= 1e+286) {
		tmp = fma(x, (y / 2.0), (t * (z * -4.5))) / a;
	} else {
		tmp = z * fma(-4.5, (t / a), (0.5 * (x * (y / (z * 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(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 * 9.0) / Float64(a * 2.0))));
	elseif (t_1 <= 1e+286)
		tmp = Float64(fma(x, Float64(y / 2.0), Float64(t * Float64(z * -4.5))) / a);
	else
		tmp = Float64(z * fma(-4.5, Float64(t / a), Float64(0.5 * Float64(x * Float64(y / Float64(z * a))))));
	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 * 9.0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+286], N[(N[(x * N[(y / 2.0), $MachinePrecision] + N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision] + N[(0.5 * N[(x * N[(y / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 74.3%

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

      1. div-sub 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-/l* 90.0%

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

      4. *-commutative 90.0%

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

      5. associate-/l* 96.3%

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

   4. Applied egg-rr 96.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000003e286

   1. Initial program 99.2%

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

      1. associate-/l/ 99.6%

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

      2. div-sub 99.6%

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

      3. associate-/l* 99.6%

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

      4. fma-neg 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/l* 99.6%

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

      7. distribute-rgt-neg-out 99.6%

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

      8. distribute-frac-neg 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. associate-/l* 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   if 1.00000000000000003e286 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
   4. Step-by-step derivation

      1. fma-define 78.8%

         \[\leadsto z \cdot \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{a}, 0.5 \cdot \frac{x \cdot y}{a \cdot z}\right)} \]

      2. associate-/l* 82.5%

         \[\leadsto z \cdot \mathsf{fma}\left(-4.5, \frac{t}{a}, 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a \cdot z}\right)}\right) \]

      3. *-commutative 82.5%

         \[\leadsto z \cdot \mathsf{fma}\left(-4.5, \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{\color{blue}{z \cdot a}}\right)\right) \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{z \cdot \mathsf{fma}\left(-4.5, \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{z \cdot a}\right)\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 93.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{+37}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (if (<= (* a 2.0) 5e+37)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (- (* y (/ x (* a 2.0))) (* t (/ (* z 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 tmp;
	if ((a * 2.0) <= 5e+37) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 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)
	tmp = 0.0
	if (Float64(a * 2.0) <= 5e+37)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z * 9.0) / Float64(a * 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_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 5e+37], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 4.99999999999999989e37

   1. Initial program 93.5%

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

      1. div-sub 92.6%

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

      2. *-commutative 92.6%

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

      3. div-sub 93.5%

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

      4. cancel-sign-sub-inv 93.5%

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

      5. *-commutative 93.5%

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

      6. fma-define 94.5%

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

      7. distribute-rgt-neg-in 94.5%

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

      8. associate-*r* 94.0%

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

      9. distribute-lft-neg-in 94.0%

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

      10. *-commutative 94.0%

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

      11. distribute-rgt-neg-in 94.0%

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

      12. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   if 4.99999999999999989e37 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 87.1%

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

      1. div-sub 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-/l* 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-/l* 91.0%

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

   4. Applied egg-rr 91.0%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+264}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \mathbf{elif}\;t\_1 \leq 10^{+286}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{z \cdot a}\right)\\ \end{array} \end{array} \]

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 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+264)
     (- (* y (/ x (* a 2.0))) (* t (/ (* z 9.0) (* a 2.0))))
     (if (<= t_1 1e+286)
       (/ t_1 (* a 2.0))
       (* z (+ (* -4.5 (/ t a)) (* 0.5 (/ (* x y) (* z 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	} else if (t_1 <= 1e+286) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-5d+264)) then
        tmp = (y * (x / (a * 2.0d0))) - (t * ((z * 9.0d0) / (a * 2.0d0)))
    else if (t_1 <= 1d+286) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = z * (((-4.5d0) * (t / a)) + (0.5d0 * ((x * y) / (z * 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	} else if (t_1 <= 1e+286) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -5e+264:
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)))
	elif t_1 <= 1e+286:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+264)
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z * 9.0) / Float64(a * 2.0))));
	elseif (t_1 <= 1e+286)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(Float64(-4.5 * Float64(t / a)) + Float64(0.5 * Float64(Float64(x * y) / Float64(z * 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 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -5e+264)
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	elseif (t_1 <= 1e+286)
		tmp = t_1 / (a * 2.0);
	else
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+264], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+286], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5.00000000000000033e264

   1. Initial program 78.3%

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

      1. div-sub 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-/l* 90.1%

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

      4. *-commutative 90.1%

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

      5. associate-/l* 94.8%

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

   4. Applied egg-rr 94.8%

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

   if -5.00000000000000033e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000003e286

   1. Initial program 99.6%

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

   if 1.00000000000000003e286 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+264}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+286}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{z \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+264}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+286}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{z \cdot a}\right)\\ \end{array} \end{array} \]

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 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+264)
     (+ (* -4.5 (/ (* z t) a)) (* 0.5 (* y (/ x a))))
     (if (<= t_1 1e+286)
       (/ t_1 (* a 2.0))
       (* z (+ (* -4.5 (/ t a)) (* 0.5 (/ (* x y) (* z 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)));
	} else if (t_1 <= 1e+286) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-5d+264)) then
        tmp = ((-4.5d0) * ((z * t) / a)) + (0.5d0 * (y * (x / a)))
    else if (t_1 <= 1d+286) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = z * (((-4.5d0) * (t / a)) + (0.5d0 * ((x * y) / (z * 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)));
	} else if (t_1 <= 1e+286) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -5e+264:
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)))
	elif t_1 <= 1e+286:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+264)
		tmp = Float64(Float64(-4.5 * Float64(Float64(z * t) / a)) + Float64(0.5 * Float64(y * Float64(x / a))));
	elseif (t_1 <= 1e+286)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(Float64(-4.5 * Float64(t / a)) + Float64(0.5 * Float64(Float64(x * y) / Float64(z * 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 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -5e+264)
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)));
	elseif (t_1 <= 1e+286)
		tmp = t_1 / (a * 2.0);
	else
		tmp = z * ((-4.5 * (t / a)) + (0.5 * ((x * y) / (z * 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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+264], N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+286], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5.00000000000000033e264

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0 80.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. div-inv 80.8%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)} \]

      2. *-commutative 80.8%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{1}{a}\right) \]

      3. associate-*l* 92.6%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \left(x \cdot \frac{1}{a}\right)\right)} \]

      4. div-inv 92.6%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(y \cdot \color{blue}{\frac{x}{a}}\right) \]

   5. Applied egg-rr 92.6%

      \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)} \]

   if -5.00000000000000033e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000003e286

   1. Initial program 99.6%

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

   if 1.00000000000000003e286 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 63.1%

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

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{a \cdot z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+264}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+286}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a} + 0.5 \cdot \frac{x \cdot y}{z \cdot a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+264}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+246}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right) + 0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+264)
     (+ (* -4.5 (/ (* z t) a)) (* 0.5 (* y (/ x a))))
     (if (<= t_1 1e+246)
       (/ t_1 (* a 2.0))
       (+ (* -4.5 (* z (/ t a))) (* 0.5 (/ (* x y) 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 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)));
	} else if (t_1 <= 1e+246) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (-4.5 * (z * (t / a))) + (0.5 * ((x * y) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if (t_1 <= (-5d+264)) then
        tmp = ((-4.5d0) * ((z * t) / a)) + (0.5d0 * (y * (x / a)))
    else if (t_1 <= 1d+246) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = ((-4.5d0) * (z * (t / a))) + (0.5d0 * ((x * y) / 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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+264) {
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)));
	} else if (t_1 <= 1e+246) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (-4.5 * (z * (t / a))) + (0.5 * ((x * y) / 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 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -5e+264:
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)))
	elif t_1 <= 1e+246:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (-4.5 * (z * (t / a))) + (0.5 * ((x * y) / 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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+264)
		tmp = Float64(Float64(-4.5 * Float64(Float64(z * t) / a)) + Float64(0.5 * Float64(y * Float64(x / a))));
	elseif (t_1 <= 1e+246)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(-4.5 * Float64(z * Float64(t / a))) + Float64(0.5 * Float64(Float64(x * y) / 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 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -5e+264)
		tmp = (-4.5 * ((z * t) / a)) + (0.5 * (y * (x / a)));
	elseif (t_1 <= 1e+246)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (-4.5 * (z * (t / a))) + (0.5 * ((x * y) / 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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+264], N[(N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+246], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -5.00000000000000033e264

   1. Initial program 78.3%

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

   3. Taylor expanded in x around 0 80.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. div-inv 80.8%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)} \]

      2. *-commutative 80.8%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{1}{a}\right) \]

      3. associate-*l* 92.6%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \left(x \cdot \frac{1}{a}\right)\right)} \]

      4. div-inv 92.6%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(y \cdot \color{blue}{\frac{x}{a}}\right) \]

   5. Applied egg-rr 92.6%

      \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)} \]

   if -5.00000000000000033e264 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000007e246

   1. Initial program 99.7%

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

   if 1.00000000000000007e246 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 66.6%

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

   3. Taylor expanded in x around 0 66.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 66.6%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} + 0.5 \cdot \frac{x \cdot y}{a} \]

      2. associate-*l/ 66.6%

         \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]

      3. associate-*r* 66.6%

         \[\leadsto \frac{\color{blue}{t \cdot \left(z \cdot -4.5\right)}}{a} + 0.5 \cdot \frac{x \cdot y}{a} \]

   5. Applied egg-rr 66.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(z \cdot -4.5\right)}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]

   6. Taylor expanded in t around 0 66.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]
   7. Step-by-step derivation

      1. associate-*l/ 81.0%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} + 0.5 \cdot \frac{x \cdot y}{a} \]

   8. Simplified 81.0%

      \[\leadsto \color{blue}{-4.5 \cdot \left(\frac{t}{a} \cdot z\right)} + 0.5 \cdot \frac{x \cdot y}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+264}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+246}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right) + 0.5 \cdot \frac{x \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \end{array} \]

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 (/ (* z -4.5) a))
     (if (<= t_1 5e+292)
       (/ (- (* x y) t_1) (* a 2.0))
       (* z (* t (/ -4.5 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 * ((z * -4.5) / a);
	} else if (t_1 <= 5e+292) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / 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 * ((z * -4.5) / a);
	} else if (t_1 <= 5e+292) {
		tmp = ((x * y) - t_1) / (a * 2.0);
	} else {
		tmp = z * (t * (-4.5 / 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 * ((z * -4.5) / a)
	elif t_1 <= 5e+292:
		tmp = ((x * y) - t_1) / (a * 2.0)
	else:
		tmp = z * (t * (-4.5 / 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(Float64(z * -4.5) / a));
	elseif (t_1 <= 5e+292)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(t * Float64(-4.5 / 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 * ((z * -4.5) / a);
	elseif (t_1 <= 5e+292)
		tmp = ((x * y) - t_1) / (a * 2.0);
	else
		tmp = z * (t * (-4.5 / 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[(N[(z * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+292], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(t * N[(-4.5 / 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 57.6%

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

   3. Taylor expanded in x around 0 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r/ 99.6%

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

   5. Simplified 99.6%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999996e292

   1. Initial program 96.0%

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

   if 4.9999999999999996e292 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 69.7%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. *-commutative 82.2%

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

      3. associate-*r* 82.2%

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

      4. *-commutative 82.2%

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

   5. Simplified 82.2%

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

      1. associate-*r/ 99.8%

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

      2. associate-*r/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*l* 99.9%

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

   7. Applied egg-rr 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. div-inv 99.8%

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

      4. div-inv 99.8%

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

      5. associate-/r* 99.8%

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

      6. *-commutative 99.8%

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

   9. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{\frac{t \cdot -4.5}{a}}{\frac{1}{z}}} \]
   10. Step-by-step derivation

       1. associate-/r/ 99.8%

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

       2. /-rgt-identity 99.8%

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

       3. associate-/l* 99.9%

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

   11. Applied egg-rr 99.9%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(t \cdot \frac{-4.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* x y) -2e+106)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) 1e+32) (/ (* t (* z -4.5)) a) (* 0.5 (* y (/ x 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 ((x * y) <= -2e+106) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 1e+32) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (y * (x / 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 ((x * y) <= (-2d+106)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= 1d+32) then
        tmp = (t * (z * (-4.5d0))) / a
    else
        tmp = 0.5d0 * (y * (x / 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 ((x * y) <= -2e+106) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 1e+32) {
		tmp = (t * (z * -4.5)) / a;
	} else {
		tmp = 0.5 * (y * (x / 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 (x * y) <= -2e+106:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= 1e+32:
		tmp = (t * (z * -4.5)) / a
	else:
		tmp = 0.5 * (y * (x / 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 (Float64(x * y) <= -2e+106)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= 1e+32)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / 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 ((x * y) <= -2e+106)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= 1e+32)
		tmp = (t * (z * -4.5)) / a;
	else
		tmp = 0.5 * (y * (x / 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[LessEqual[N[(x * y), $MachinePrecision], -2e+106], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000018e106

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 79.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} + 0.5 \cdot \frac{x \cdot y}{a} \]

      2. associate-*l/ 79.6%

         \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]

      3. associate-*r* 79.6%

         \[\leadsto \frac{\color{blue}{t \cdot \left(z \cdot -4.5\right)}}{a} + 0.5 \cdot \frac{x \cdot y}{a} \]

   5. Applied egg-rr 79.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(z \cdot -4.5\right)}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]

   6. Taylor expanded in t around 0 74.4%

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

      1. associate-*r/ 81.7%

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

      2. *-rgt-identity 81.7%

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

      3. associate-*r/ 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-/r/ 81.7%

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

      6. associate-/l* 81.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x \cdot 1}{\frac{a}{y}}} \]

      7. *-rgt-identity 81.7%

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

   8. Simplified 81.7%

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

   if -2.00000000000000018e106 < (*.f64 x y) < 1.00000000000000005e32

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 74.9%

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

      1. associate-*r/ 74.9%

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

      2. *-commutative 74.9%

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

      3. associate-*r* 74.9%

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

      4. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   if 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 88.0%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. div-inv 86.1%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)} \]

      2. *-commutative 86.1%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{1}{a}\right) \]

      3. associate-*l* 83.0%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \left(x \cdot \frac{1}{a}\right)\right)} \]

      4. div-inv 83.1%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(y \cdot \color{blue}{\frac{x}{a}}\right) \]

   5. Applied egg-rr 75.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

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
 (if (<= (* x y) -2e+106)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) 1e+32) (* -4.5 (/ (* z t) a)) (* 0.5 (* y (/ x 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 ((x * y) <= -2e+106) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 1e+32) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / 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 ((x * y) <= (-2d+106)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= 1d+32) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (y * (x / 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 ((x * y) <= -2e+106) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 1e+32) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / 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 (x * y) <= -2e+106:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= 1e+32:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (y * (x / 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 (Float64(x * y) <= -2e+106)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= 1e+32)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / 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 ((x * y) <= -2e+106)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= 1e+32)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (y * (x / 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[LessEqual[N[(x * y), $MachinePrecision], -2e+106], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+32], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.00000000000000018e106

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 79.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. *-commutative 79.7%

         \[\leadsto \color{blue}{\frac{t \cdot z}{a} \cdot -4.5} + 0.5 \cdot \frac{x \cdot y}{a} \]

      2. associate-*l/ 79.6%

         \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -4.5}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]

      3. associate-*r* 79.6%

         \[\leadsto \frac{\color{blue}{t \cdot \left(z \cdot -4.5\right)}}{a} + 0.5 \cdot \frac{x \cdot y}{a} \]

   5. Applied egg-rr 79.6%

      \[\leadsto \color{blue}{\frac{t \cdot \left(z \cdot -4.5\right)}{a}} + 0.5 \cdot \frac{x \cdot y}{a} \]

   6. Taylor expanded in t around 0 74.4%

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

      1. associate-*r/ 81.7%

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

      2. *-rgt-identity 81.7%

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

      3. associate-*r/ 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-/r/ 81.7%

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

      6. associate-/l* 81.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x \cdot 1}{\frac{a}{y}}} \]

      7. *-rgt-identity 81.7%

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

   8. Simplified 81.7%

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

   if -2.00000000000000018e106 < (*.f64 x y) < 1.00000000000000005e32

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 74.9%

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

   if 1.00000000000000005e32 < (*.f64 x y)

   1. Initial program 88.0%

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

   3. Taylor expanded in x around inf 79.0%

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

      1. div-inv 86.1%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)} \]

      2. *-commutative 86.1%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{1}{a}\right) \]

      3. associate-*l* 83.0%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \left(x \cdot \frac{1}{a}\right)\right)} \]

      4. div-inv 83.1%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(y \cdot \color{blue}{\frac{x}{a}}\right) \]

   5. Applied egg-rr 75.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+32}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 0.006:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

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 (<= t -2.4e-156)
   (* -4.5 (/ (* z t) a))
   (if (<= t 0.006) (* 0.5 (* y (/ x a))) (* -4.5 (/ t (/ a z))))))

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 (t <= -2.4e-156) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 0.006) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	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 (t <= (-2.4d-156)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 0.006d0) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = (-4.5d0) * (t / (a / z))
    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 (t <= -2.4e-156) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 0.006) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	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 t <= -2.4e-156:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 0.006:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = -4.5 * (t / (a / z))
	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 (t <= -2.4e-156)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 0.006)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	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 (t <= -2.4e-156)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 0.006)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = -4.5 * (t / (a / z));
	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[t, -2.4e-156], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.006], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e-156

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 59.7%

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

   if -2.4e-156 < t < 0.0060000000000000001

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 70.2%

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

      1. div-inv 96.8%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{a}\right)} \]

      2. *-commutative 96.8%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(\color{blue}{\left(y \cdot x\right)} \cdot \frac{1}{a}\right) \]

      3. associate-*l* 92.0%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \color{blue}{\left(y \cdot \left(x \cdot \frac{1}{a}\right)\right)} \]

      4. div-inv 92.0%

         \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \left(y \cdot \color{blue}{\frac{x}{a}}\right) \]

   5. Applied egg-rr 67.4%

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

   if 0.0060000000000000001 < t

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0 65.6%

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

      1. associate-*r/ 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 65.7%

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

      4. *-commutative 65.7%

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

   5. Simplified 65.7%

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

      1. associate-*r/ 68.7%

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

      2. associate-*r/ 68.7%

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

      3. *-commutative 68.7%

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

      4. *-commutative 68.7%

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

      5. associate-*l* 68.8%

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

   7. Applied egg-rr 68.8%

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

      1. *-commutative 68.8%

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

      2. clear-num 68.7%

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

      3. div-inv 68.7%

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

      4. div-inv 68.7%

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

      5. associate-/r* 67.2%

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

      6. *-commutative 67.2%

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

   9. Applied egg-rr 67.2%

      \[\leadsto \color{blue}{\frac{\frac{t \cdot -4.5}{a}}{\frac{1}{z}}} \]
   10. Step-by-step derivation

       1. associate-/l/ 68.7%

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

       2. *-commutative 68.7%

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

       3. associate-/l* 68.6%

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

       4. associate-*l/ 68.7%

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

       5. *-un-lft-identity 68.7%

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

   11. Applied egg-rr 68.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-156}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 0.006:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.9% accurate, 1.9× speedup

Math

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

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 (/ t (/ a z))))

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 * (t / (a / z));
}

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) * (t / (a / z))
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 * (t / (a / z));
}

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 * (t / (a / z))

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(t / Float64(a / z)))
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 * (t / (a / z));
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[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.4%

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

3. Taylor expanded in x around 0 53.2%

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

   1. associate-*r/ 53.2%

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

   2. *-commutative 53.2%

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

   3. associate-*r* 53.2%

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

   4. *-commutative 53.2%

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

5. Simplified 53.2%

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

   1. associate-*r/ 54.6%

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

   2. associate-*r/ 54.6%

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

   3. *-commutative 54.6%

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

   4. *-commutative 54.6%

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

   5. associate-*l* 54.6%

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

7. Applied egg-rr 54.6%

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

   1. *-commutative 54.6%

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

   2. clear-num 54.6%

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

   3. div-inv 54.9%

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

   4. div-inv 54.9%

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

   5. associate-/r* 53.0%

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

   6. *-commutative 53.0%

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

9. Applied egg-rr 53.0%

   \[\leadsto \color{blue}{\frac{\frac{t \cdot -4.5}{a}}{\frac{1}{z}}} \]
10. Step-by-step derivation

    1. associate-/l/ 54.9%

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

    2. *-commutative 54.9%

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

    3. associate-/l* 54.9%

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

    4. associate-*l/ 55.0%

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

    5. *-un-lft-identity 55.0%

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

11. Applied egg-rr 55.0%

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

Developer Target 1: 93.7% 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 2024112 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

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