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

Percentage Accurate: 91.2% → 96.3%

Time: 8.3s

Alternatives: 9

Speedup: 0.6×

• 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: 91.2% 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: 96.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{x}{a}}{2} - t \cdot \frac{z \cdot 4.5}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+282}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{y}}}{\frac{2}{\mathsf{fma}\left(-9, t \cdot \frac{z}{y}, x\right)}}\\ \end{array} \end{array} \]

FPCore

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 1e+282)
       (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
       (/ (/ 1.0 (/ a y)) (/ 2.0 (fma -9.0 (* t (/ z y)) x)))))))

C

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 <= 1e+282) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = (1.0 / (a / y)) / (2.0 / fma(-9.0, (t * (z / y)), x));
	}
	return tmp;
}

Julia

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(Float64(x / a) / 2.0)) - Float64(t * Float64(Float64(z * 4.5) / a)));
	elseif (t_1 <= 1e+282)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(1.0 / Float64(a / y)) / Float64(2.0 / fma(-9.0, Float64(t * Float64(z / y)), x)));
	end
	return tmp
end

Wolfram

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[(N[(x / a), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+282], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(a / y), $MachinePrecision]), $MachinePrecision] / N[(2.0 / N[(-9.0 * N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision] + x), $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 65.3%

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

      1. div-sub 60.6%

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

      2. sub-neg 60.6%

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

      3. *-commutative 60.6%

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

      4. associate-/l* 80.1%

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

      5. div-inv 80.1%

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

      6. *-commutative 80.1%

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

      7. associate-*l* 80.1%

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

      8. *-commutative 80.1%

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

      9. associate-/r* 80.1%

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

      10. metadata-eval 80.1%

          \[\leadsto y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   4. Applied egg-rr 80.1%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   5. Step-by-step derivation

      1. sub-neg 80.1%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-/r* 80.1%

         \[\leadsto y \cdot \color{blue}{\frac{\frac{x}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 80.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 80.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. *-commutative 80.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\left(\color{blue}{\left(t \cdot z\right)} \cdot 9\right) \cdot 0.5}{a} \]

      6. associate-*l* 80.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      7. metadata-eval 80.1%

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

      8. *-commutative 80.1%

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

      9. *-commutative 80.1%

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

      10. associate-*r* 80.1%

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

      11. associate-*l/ 95.2%

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

      12. associate-*r/ 95.1%

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

      13. *-commutative 95.1%

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

      14. *-commutative 95.1%

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

      15. associate-*l/ 95.2%

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

   6. Simplified 95.2%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 1.00000000000000003e282

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*r* 99.2%

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

      3. *-commutative 99.2%

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

   4. Applied egg-rr 99.2%

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

   if 1.00000000000000003e282 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 60.8%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. clear-num 68.3%

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

      2. times-frac 71.6%

         \[\leadsto \frac{1}{\color{blue}{\frac{a}{y} \cdot \frac{2}{x + -9 \cdot \frac{t \cdot z}{y}}}} \]

      3. +-commutative 71.6%

         \[\leadsto \frac{1}{\frac{a}{y} \cdot \frac{2}{\color{blue}{-9 \cdot \frac{t \cdot z}{y} + x}}} \]

      4. fma-define 71.6%

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

      5. associate-/l* 82.2%

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

   5. Applied egg-rr 82.2%

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

      1. associate-/r* 82.3%

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

   7. Simplified 82.3%

      \[\leadsto \color{blue}{\frac{\frac{1}{\frac{a}{y}}}{\frac{2}{\mathsf{fma}\left(-9, t \cdot \frac{z}{y}, x\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \frac{\frac{x}{a}}{2} - t \cdot \frac{z \cdot 4.5}{a}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+282}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{a}{y}}}{\frac{2}{\mathsf{fma}\left(-9, t \cdot \frac{z}{y}, x\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+48}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{a}}{2} - t \cdot \frac{z \cdot 4.5}{a}\\ \end{array} \end{array} \]

FPCore

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) 1e+48)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (- (* y (/ (/ x a) 2.0)) (* t (/ (* z 4.5) a)))))

C

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) <= 1e+48) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a));
	}
	return tmp;
}

Julia

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) <= 1e+48)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(Float64(x / a) / 2.0)) - Float64(t * Float64(Float64(z * 4.5) / a)));
	end
	return tmp
end

Wolfram

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], 1e+48], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x / a), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1.00000000000000004e48

   1. Initial program 93.0%

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

      1. div-sub 89.6%

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

      2. *-commutative 89.6%

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

      3. div-sub 93.0%

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

      4. cancel-sign-sub-inv 93.0%

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

      5. *-commutative 93.0%

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

      6. fma-define 94.4%

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

      7. distribute-rgt-neg-in 94.4%

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

      8. associate-*r* 94.4%

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

      9. distribute-lft-neg-in 94.4%

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

      10. *-commutative 94.4%

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

      11. distribute-rgt-neg-in 94.4%

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

      12. metadata-eval 94.4%

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

   3. Simplified 94.4%

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

   if 1.00000000000000004e48 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 74.1%

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

      1. div-sub 74.1%

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

      2. sub-neg 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-/l* 85.7%

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

      5. div-inv 85.6%

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

      6. *-commutative 85.6%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

      9. associate-/r* 85.6%

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

      10. metadata-eval 85.6%

          \[\leadsto y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   4. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   5. Step-by-step derivation

      1. sub-neg 85.6%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-/r* 85.6%

         \[\leadsto y \cdot \color{blue}{\frac{\frac{x}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. *-commutative 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\left(\color{blue}{\left(t \cdot z\right)} \cdot 9\right) \cdot 0.5}{a} \]

      6. associate-*l* 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      7. metadata-eval 85.7%

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

      8. *-commutative 85.7%

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

      9. *-commutative 85.7%

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

      10. associate-*r* 85.7%

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

      11. associate-*l/ 93.8%

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

      12. associate-*r/ 93.7%

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

      13. *-commutative 93.7%

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

      14. *-commutative 93.7%

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

      15. associate-*l/ 93.8%

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

   6. Simplified 93.8%

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

Alternative 3: 90.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-74}:\\ \;\;\;\;\frac{y \cdot \left(x + -9 \cdot \frac{z \cdot t}{y}\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{a}}{2} - t \cdot \frac{z \cdot 4.5}{a}\\ \end{array} \end{array} \]

FPCore

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) 4e-74)
   (/ (* y (+ x (* -9.0 (/ (* z t) y)))) (* a 2.0))
   (- (* y (/ (/ x a) 2.0)) (* t (/ (* z 4.5) a)))))

C

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) <= 4e-74) {
		tmp = (y * (x + (-9.0 * ((z * t) / y)))) / (a * 2.0);
	} else {
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a));
	}
	return tmp;
}

Fortran

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 ((a * 2.0d0) <= 4d-74) then
        tmp = (y * (x + ((-9.0d0) * ((z * t) / y)))) / (a * 2.0d0)
    else
        tmp = (y * ((x / a) / 2.0d0)) - (t * ((z * 4.5d0) / a))
    end if
    code = tmp
end function

Java

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 ((a * 2.0) <= 4e-74) {
		tmp = (y * (x + (-9.0 * ((z * t) / y)))) / (a * 2.0);
	} else {
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= 4e-74:
		tmp = (y * (x + (-9.0 * ((z * t) / y)))) / (a * 2.0)
	else:
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a))
	return tmp

Julia

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) <= 4e-74)
		tmp = Float64(Float64(y * Float64(x + Float64(-9.0 * Float64(Float64(z * t) / y)))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(Float64(x / a) / 2.0)) - Float64(t * Float64(Float64(z * 4.5) / a)));
	end
	return tmp
end

MATLAB

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 ((a * 2.0) <= 4e-74)
		tmp = (y * (x + (-9.0 * ((z * t) / y)))) / (a * 2.0);
	else
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 4e-74], N[(N[(y * N[(x + N[(-9.0 * N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x / a), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 3.99999999999999983e-74

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 90.1%

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

   if 3.99999999999999983e-74 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 84.4%

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

      1. div-sub 84.4%

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

      2. sub-neg 84.4%

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

      3. *-commutative 84.4%

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

      4. associate-/l* 90.0%

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

      5. div-inv 90.0%

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

      6. *-commutative 90.0%

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

      7. associate-*l* 90.0%

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

      8. *-commutative 90.0%

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

      9. associate-/r* 90.0%

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

      10. metadata-eval 90.0%

          \[\leadsto y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   4. Applied egg-rr 90.0%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   5. Step-by-step derivation

      1. sub-neg 90.0%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-/r* 90.0%

         \[\leadsto y \cdot \color{blue}{\frac{\frac{x}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 90.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 90.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. *-commutative 90.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\left(\color{blue}{\left(t \cdot z\right)} \cdot 9\right) \cdot 0.5}{a} \]

      6. associate-*l* 90.1%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      7. metadata-eval 90.1%

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

      8. *-commutative 90.1%

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

      9. *-commutative 90.1%

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

      10. associate-*r* 90.0%

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

      11. associate-*l/ 94.9%

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

      12. associate-*r/ 94.8%

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

      13. *-commutative 94.8%

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

      14. *-commutative 94.8%

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

      15. associate-*l/ 94.9%

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

   6. Simplified 94.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-74}:\\ \;\;\;\;\frac{y \cdot \left(x + -9 \cdot \frac{z \cdot t}{y}\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{a}}{2} - t \cdot \frac{z \cdot 4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+48}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{a}}{2} - t \cdot \frac{z \cdot 4.5}{a}\\ \end{array} \end{array} \]

FPCore

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) 1e+48)
   (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
   (- (* y (/ (/ x a) 2.0)) (* t (/ (* z 4.5) a)))))

C

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) <= 1e+48) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a));
	}
	return tmp;
}

Fortran

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 ((a * 2.0d0) <= 1d+48) then
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
    else
        tmp = (y * ((x / a) / 2.0d0)) - (t * ((z * 4.5d0) / a))
    end if
    code = tmp
end function

Java

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 ((a * 2.0) <= 1e+48) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= 1e+48:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	else:
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 4.5) / a))
	return tmp

Julia

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) <= 1e+48)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(Float64(x / a) / 2.0)) - Float64(t * Float64(Float64(z * 4.5) / a)));
	end
	return tmp
end

MATLAB

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 ((a * 2.0) <= 1e+48)
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	else
		tmp = (y * ((x / a) / 2.0)) - (t * ((z * 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 1e+48], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x / a), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1.00000000000000004e48

   1. Initial program 93.0%

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

   if 1.00000000000000004e48 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 74.1%

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

      1. div-sub 74.1%

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

      2. sub-neg 74.1%

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

      3. *-commutative 74.1%

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

      4. associate-/l* 85.7%

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

      5. div-inv 85.6%

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

      6. *-commutative 85.6%

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

      7. associate-*l* 85.6%

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

      8. *-commutative 85.6%

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

      9. associate-/r* 85.6%

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

      10. metadata-eval 85.6%

          \[\leadsto y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a}\right) \]

   4. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} + \left(-\left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\right)} \]
   5. Step-by-step derivation

      1. sub-neg 85.6%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

      2. associate-/r* 85.6%

         \[\leadsto y \cdot \color{blue}{\frac{\frac{x}{a}}{2}} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a} \]

      3. associate-*r/ 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \color{blue}{\frac{\left(9 \cdot \left(z \cdot t\right)\right) \cdot 0.5}{a}} \]

      4. *-commutative 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(\left(z \cdot t\right) \cdot 9\right)} \cdot 0.5}{a} \]

      5. *-commutative 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\left(\color{blue}{\left(t \cdot z\right)} \cdot 9\right) \cdot 0.5}{a} \]

      6. associate-*l* 85.7%

         \[\leadsto y \cdot \frac{\frac{x}{a}}{2} - \frac{\color{blue}{\left(t \cdot z\right) \cdot \left(9 \cdot 0.5\right)}}{a} \]

      7. metadata-eval 85.7%

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

      8. *-commutative 85.7%

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

      9. *-commutative 85.7%

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

      10. associate-*r* 85.7%

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

      11. associate-*l/ 93.8%

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

      12. associate-*r/ 93.7%

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

      13. *-commutative 93.7%

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

      14. *-commutative 93.7%

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

      15. associate-*l/ 93.8%

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

   6. Simplified 93.8%

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

Alternative 5: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -100000000000 \lor \neg \left(x \cdot y \leq 2000000000\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \end{array} \]

FPCore

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 (<= (* x y) -100000000000.0) (not (<= (* x y) 2000000000.0)))
   (* 0.5 (* x (/ y a)))
   (* (* t (/ z a)) -4.5)))

C

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) <= -100000000000.0) || !((x * y) <= 2000000000.0)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	return tmp;
}

Fortran

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) <= (-100000000000.0d0)) .or. (.not. ((x * y) <= 2000000000.0d0))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (t * (z / a)) * (-4.5d0)
    end if
    code = tmp
end function

Java

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) <= -100000000000.0) || !((x * y) <= 2000000000.0)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = (t * (z / a)) * -4.5;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -100000000000.0) or not ((x * y) <= 2000000000.0):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = (t * (z / a)) * -4.5
	return tmp

Julia

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) <= -100000000000.0) || !(Float64(x * y) <= 2000000000.0))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(Float64(t * Float64(z / a)) * -4.5);
	end
	return tmp
end

MATLAB

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) <= -100000000000.0) || ~(((x * y) <= 2000000000.0)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = (t * (z / a)) * -4.5;
	end
	tmp_2 = tmp;
end

Wolfram

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[N[(x * y), $MachinePrecision], -100000000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1e11 or 2e9 < (*.f64 x y)

   1. Initial program 84.5%

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

      1. fma-neg 87.0%

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

      2. distribute-lft-neg-in 87.0%

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

      3. distribute-rgt-neg-in 87.0%

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

      4. metadata-eval 87.0%

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

      5. associate-*r* 87.0%

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

      6. *-commutative 87.0%

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

      7. *-un-lft-identity 87.0%

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

      8. *-un-lft-identity 87.0%

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

      9. clear-num 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if -1e11 < (*.f64 x y) < 2e9

   1. Initial program 94.1%

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

   3. Taylor expanded in x around 0 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-/l* 80.1%

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

   5. Applied egg-rr 80.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -100000000000 \lor \neg \left(x \cdot y \leq 2000000000\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -100000000000 \lor \neg \left(x \cdot y \leq 2000000000\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -100000000000.0) (not (<= (* x y) 2000000000.0)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (* z (/ t a)))))

C

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) <= -100000000000.0) || !((x * y) <= 2000000000.0)) {
		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.
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) <= (-100000000000.0d0)) .or. (.not. ((x * y) <= 2000000000.0d0))) 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;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -100000000000.0) || !((x * y) <= 2000000000.0)) {
		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])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -100000000000.0) or not ((x * y) <= 2000000000.0):
		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])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -100000000000.0) || !(Float64(x * y) <= 2000000000.0))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	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])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -100000000000.0) || ~(((x * y) <= 2000000000.0)))
		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.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -100000000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2000000000.0]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1e11 or 2e9 < (*.f64 x y)

   1. Initial program 84.5%

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

      1. fma-neg 87.0%

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

      2. distribute-lft-neg-in 87.0%

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

      3. distribute-rgt-neg-in 87.0%

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

      4. metadata-eval 87.0%

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

      5. associate-*r* 87.0%

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

      6. *-commutative 87.0%

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

      7. *-un-lft-identity 87.0%

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

      8. *-un-lft-identity 87.0%

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

      9. clear-num 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. associate-/l* 76.8%

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

   7. Simplified 76.8%

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

   if -1e11 < (*.f64 x y) < 2e9

   1. Initial program 94.1%

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

      1. fma-neg 94.1%

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

      2. distribute-lft-neg-in 94.1%

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

      3. distribute-rgt-neg-in 94.1%

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

      4. metadata-eval 94.1%

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

      5. associate-*r* 94.0%

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

      6. *-commutative 94.0%

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

      7. *-un-lft-identity 94.0%

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

      8. *-un-lft-identity 94.0%

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

      9. clear-num 92.9%

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

   4. Applied egg-rr 92.9%

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

   5. Taylor expanded in x around 0 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-*r/ 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -100000000000 \lor \neg \left(x \cdot y \leq 2000000000\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 56.6%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 92.8%

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

      1. *-commutative 92.8%

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

      2. associate-*r* 92.8%

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

      3. *-commutative 92.8%

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

   4. Applied egg-rr 92.8%

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

4. Final simplification 93.5%

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

Alternative 8: 93.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 56.6%

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

   3. Taylor expanded in x around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 92.8%

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

      1. associate-*l* 92.8%

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

      2. *-commutative 92.8%

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

   4. Applied egg-rr 92.8%

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

4. Final simplification 93.5%

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

Alternative 9: 51.3% accurate, 1.9× speedup

Math

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

FPCore

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

MATLAB

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

Derivation

1. Initial program 89.4%

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

   1. fma-neg 90.6%

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

   2. distribute-lft-neg-in 90.6%

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

   3. distribute-rgt-neg-in 90.6%

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

   4. metadata-eval 90.6%

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

   5. associate-*r* 90.6%

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

   6. *-commutative 90.6%

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

   7. *-un-lft-identity 90.6%

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

   8. *-un-lft-identity 90.6%

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

   9. clear-num 90.0%

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

4. Applied egg-rr 90.0%

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

5. Taylor expanded in x around 0 51.9%

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

   1. *-commutative 51.9%

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

   2. associate-*r/ 53.9%

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

7. Simplified 53.9%

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

Developer target: 93.6% 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 2024096 
(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)))