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

Percentage Accurate: 90.9% → 94.7%

Time: 11.2s

Alternatives: 14

Speedup: 0.6×

• 28.0% 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: 90.9% 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: 94.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+48}:\\ \;\;\;\;{\left(2 \cdot \frac{a\_m}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2}{y} \cdot \frac{a\_m}{x}} - \left(z \cdot 9\right) \cdot \frac{t}{a\_m \cdot 2}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* a_m 2.0) 1e+48)
    (pow (* 2.0 (/ a_m (fma x y (* t (* z -9.0))))) -1.0)
    (- (/ 1.0 (* (/ 2.0 y) (/ a_m x))) (* (* z 9.0) (/ t (* a_m 2.0)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 1e+48) {
		tmp = pow((2.0 * (a_m / fma(x, y, (t * (z * -9.0))))), -1.0);
	} else {
		tmp = (1.0 / ((2.0 / y) * (a_m / x))) - ((z * 9.0) * (t / (a_m * 2.0)));
	}
	return a_s * tmp;
}

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+48)
		tmp = Float64(2.0 * Float64(a_m / fma(x, y, Float64(t * Float64(z * -9.0))))) ^ -1.0;
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 / y) * Float64(a_m / x))) - Float64(Float64(z * 9.0) * Float64(t / Float64(a_m * 2.0))));
	end
	return Float64(a_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 1e+48], N[Power[N[(2.0 * N[(a$95$m / N[(x * y + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(N[(1.0 / N[(N[(2.0 / y), $MachinePrecision] * N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 1.00000000000000004e48

   1. Initial program 92.4%

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

      1. clear-num 92.3%

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

      2. inv-pow 92.3%

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

      3. *-commutative 92.3%

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

      4. associate-/l* 92.3%

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

      5. fma-neg 92.8%

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

      6. *-commutative 92.8%

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

      7. distribute-rgt-neg-in 92.8%

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

      8. distribute-rgt-neg-in 92.8%

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

      9. metadata-eval 92.8%

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

   4. Applied egg-rr 92.8%

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

   if 1.00000000000000004e48 < (*.f64 a 2)

   1. Initial program 72.6%

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

      1. div-sub 72.6%

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

      2. associate-/l* 77.3%

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

      3. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

      1. associate-*r/ 85.3%

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

      2. clear-num 85.1%

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

      3. *-commutative 85.1%

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

      4. *-commutative 85.1%

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

      5. times-frac 91.3%

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

   6. Applied egg-rr 91.3%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+48}:\\ \;\;\;\;{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2}{y} \cdot \frac{a}{x}} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 4 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2}{y} \cdot \frac{a\_m}{x}} - \left(z \cdot 9\right) \cdot \frac{t}{a\_m \cdot 2}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* a_m 2.0) 4e-59)
    (* (fma x y (* t (* z -9.0))) (/ 0.5 a_m))
    (- (/ 1.0 (* (/ 2.0 y) (/ a_m x))) (* (* z 9.0) (/ t (* a_m 2.0)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 4e-59) {
		tmp = fma(x, y, (t * (z * -9.0))) * (0.5 / a_m);
	} else {
		tmp = (1.0 / ((2.0 / y) * (a_m / x))) - ((z * 9.0) * (t / (a_m * 2.0)));
	}
	return a_s * tmp;
}

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 4e-59)
		tmp = Float64(fma(x, y, Float64(t * Float64(z * -9.0))) * Float64(0.5 / a_m));
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 / y) * Float64(a_m / x))) - Float64(Float64(z * 9.0) * Float64(t / Float64(a_m * 2.0))));
	end
	return Float64(a_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 4e-59], N[(N[(x * y + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[(2.0 / y), $MachinePrecision] * N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 4.0000000000000001e-59

   1. Initial program 91.7%

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

      1. div-inv 91.7%

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

      2. fma-neg 92.2%

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

      3. *-commutative 92.2%

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

      4. distribute-rgt-neg-in 92.2%

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

      5. distribute-rgt-neg-in 92.2%

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

      6. metadata-eval 92.2%

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

      7. *-commutative 92.2%

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

      8. associate-/r* 92.2%

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

      9. metadata-eval 92.2%

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

   4. Applied egg-rr 92.2%

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

   if 4.0000000000000001e-59 < (*.f64 a 2)

   1. Initial program 78.9%

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

      1. div-sub 78.9%

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

      2. associate-/l* 82.5%

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

      3. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

      1. associate-*r/ 88.6%

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

      2. clear-num 88.4%

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

      3. *-commutative 88.4%

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

      4. *-commutative 88.4%

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

      5. times-frac 93.2%

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

   6. Applied egg-rr 93.2%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2}{y} \cdot \frac{a}{x}} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 0.5\right) \cdot \frac{y}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+51}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \mathbf{elif}\;x \cdot y \leq -0.05:\\ \;\;\;\;\frac{x \cdot y}{a\_m \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+77}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (* x 0.5) (/ y a_m))))
   (*
    a_s
    (if (<= (* x y) -5e+140)
      t_1
      (if (<= (* x y) -5e+51)
        (* (* t (/ z a_m)) -4.5)
        (if (<= (* x y) -0.05)
          (/ (* x y) (* a_m 2.0))
          (if (<= (* x y) 1e+77) (* z (/ (* t -4.5) a_m)) t_1)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * 0.5) * (y / a_m);
	double tmp;
	if ((x * y) <= -5e+140) {
		tmp = t_1;
	} else if ((x * y) <= -5e+51) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x * y) <= -0.05) {
		tmp = (x * y) / (a_m * 2.0);
	} else if ((x * y) <= 1e+77) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 0.5d0) * (y / a_m)
    if ((x * y) <= (-5d+140)) then
        tmp = t_1
    else if ((x * y) <= (-5d+51)) then
        tmp = (t * (z / a_m)) * (-4.5d0)
    else if ((x * y) <= (-0.05d0)) then
        tmp = (x * y) / (a_m * 2.0d0)
    else if ((x * y) <= 1d+77) then
        tmp = z * ((t * (-4.5d0)) / a_m)
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * 0.5) * (y / a_m);
	double tmp;
	if ((x * y) <= -5e+140) {
		tmp = t_1;
	} else if ((x * y) <= -5e+51) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x * y) <= -0.05) {
		tmp = (x * y) / (a_m * 2.0);
	} else if ((x * y) <= 1e+77) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x * 0.5) * (y / a_m)
	tmp = 0
	if (x * y) <= -5e+140:
		tmp = t_1
	elif (x * y) <= -5e+51:
		tmp = (t * (z / a_m)) * -4.5
	elif (x * y) <= -0.05:
		tmp = (x * y) / (a_m * 2.0)
	elif (x * y) <= 1e+77:
		tmp = z * ((t * -4.5) / a_m)
	else:
		tmp = t_1
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x * 0.5) * Float64(y / a_m))
	tmp = 0.0
	if (Float64(x * y) <= -5e+140)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+51)
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	elseif (Float64(x * y) <= -0.05)
		tmp = Float64(Float64(x * y) / Float64(a_m * 2.0));
	elseif (Float64(x * y) <= 1e+77)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a_m));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x * 0.5) * (y / a_m);
	tmp = 0.0;
	if ((x * y) <= -5e+140)
		tmp = t_1;
	elseif ((x * y) <= -5e+51)
		tmp = (t * (z / a_m)) * -4.5;
	elseif ((x * y) <= -0.05)
		tmp = (x * y) / (a_m * 2.0);
	elseif ((x * y) <= 1e+77)
		tmp = z * ((t * -4.5) / a_m);
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+140], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+51], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -0.05], N[(N[(x * y), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+77], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.00000000000000008e140 or 9.99999999999999983e76 < (*.f64 x y)

   1. Initial program 78.9%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. associate-/l* 88.9%

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

      2. associate-*r* 88.9%

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

   5. Simplified 88.9%

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

   if -5.00000000000000008e140 < (*.f64 x y) < -5e51

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 54.9%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

   if -5e51 < (*.f64 x y) < -0.050000000000000003

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 70.9%

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

   if -0.050000000000000003 < (*.f64 x y) < 9.99999999999999983e76

   1. Initial program 92.1%

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

      1. div-sub 92.1%

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

      2. associate-/l* 89.2%

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

      3. associate-/l* 90.5%

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

   4. Applied egg-rr 90.5%

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

      1. associate-*r/ 93.5%

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

      2. clear-num 93.3%

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

      3. *-commutative 93.3%

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

      4. *-commutative 93.3%

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

      5. times-frac 87.2%

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

   6. Applied egg-rr 87.2%

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

   7. Taylor expanded in y around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*r/ 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-*l* 75.6%

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

      5. associate-*l/ 75.7%

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

      6. *-commutative 75.7%

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

   9. Simplified 75.7%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+140}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+51}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{elif}\;x \cdot y \leq -0.05:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+77}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 0.5\right) \cdot \frac{y}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+51}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \mathbf{elif}\;x \cdot y \leq -0.05:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a\_m}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+77}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (* x 0.5) (/ y a_m))))
   (*
    a_s
    (if (<= (* x y) -5e+140)
      t_1
      (if (<= (* x y) -5e+51)
        (* (* t (/ z a_m)) -4.5)
        (if (<= (* x y) -0.05)
          (/ (* y 0.5) (/ a_m x))
          (if (<= (* x y) 1e+77) (* z (/ (* t -4.5) a_m)) t_1)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * 0.5) * (y / a_m);
	double tmp;
	if ((x * y) <= -5e+140) {
		tmp = t_1;
	} else if ((x * y) <= -5e+51) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x * y) <= -0.05) {
		tmp = (y * 0.5) / (a_m / x);
	} else if ((x * y) <= 1e+77) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * 0.5d0) * (y / a_m)
    if ((x * y) <= (-5d+140)) then
        tmp = t_1
    else if ((x * y) <= (-5d+51)) then
        tmp = (t * (z / a_m)) * (-4.5d0)
    else if ((x * y) <= (-0.05d0)) then
        tmp = (y * 0.5d0) / (a_m / x)
    else if ((x * y) <= 1d+77) then
        tmp = z * ((t * (-4.5d0)) / a_m)
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x * 0.5) * (y / a_m);
	double tmp;
	if ((x * y) <= -5e+140) {
		tmp = t_1;
	} else if ((x * y) <= -5e+51) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x * y) <= -0.05) {
		tmp = (y * 0.5) / (a_m / x);
	} else if ((x * y) <= 1e+77) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x * 0.5) * (y / a_m)
	tmp = 0
	if (x * y) <= -5e+140:
		tmp = t_1
	elif (x * y) <= -5e+51:
		tmp = (t * (z / a_m)) * -4.5
	elif (x * y) <= -0.05:
		tmp = (y * 0.5) / (a_m / x)
	elif (x * y) <= 1e+77:
		tmp = z * ((t * -4.5) / a_m)
	else:
		tmp = t_1
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x * 0.5) * Float64(y / a_m))
	tmp = 0.0
	if (Float64(x * y) <= -5e+140)
		tmp = t_1;
	elseif (Float64(x * y) <= -5e+51)
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	elseif (Float64(x * y) <= -0.05)
		tmp = Float64(Float64(y * 0.5) / Float64(a_m / x));
	elseif (Float64(x * y) <= 1e+77)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a_m));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x * 0.5) * (y / a_m);
	tmp = 0.0;
	if ((x * y) <= -5e+140)
		tmp = t_1;
	elseif ((x * y) <= -5e+51)
		tmp = (t * (z / a_m)) * -4.5;
	elseif ((x * y) <= -0.05)
		tmp = (y * 0.5) / (a_m / x);
	elseif ((x * y) <= 1e+77)
		tmp = z * ((t * -4.5) / a_m);
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x * 0.5), $MachinePrecision] * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -5e+140], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -5e+51], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -0.05], N[(N[(y * 0.5), $MachinePrecision] / N[(a$95$m / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+77], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.00000000000000008e140 or 9.99999999999999983e76 < (*.f64 x y)

   1. Initial program 78.9%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. associate-/l* 88.9%

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

      2. associate-*r* 88.9%

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

   5. Simplified 88.9%

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

   if -5.00000000000000008e140 < (*.f64 x y) < -5e51

   1. Initial program 88.6%

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

   3. Taylor expanded in x around 0 54.9%

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

      1. associate-/l* 71.4%

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

   5. Simplified 71.4%

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

   if -5e51 < (*.f64 x y) < -0.050000000000000003

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. times-frac 49.2%

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

   5. Applied egg-rr 49.2%

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

      1. frac-times 70.9%

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

      2. *-commutative 70.9%

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

      3. times-frac 63.5%

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

      4. clear-num 63.3%

         \[\leadsto \frac{y}{2} \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      5. div-inv 65.8%

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

      6. div-inv 65.8%

         \[\leadsto \frac{\color{blue}{y \cdot \frac{1}{2}}}{\frac{a}{x}} \]

      7. metadata-eval 65.8%

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

   7. Applied egg-rr 65.8%

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

   if -0.050000000000000003 < (*.f64 x y) < 9.99999999999999983e76

   1. Initial program 92.1%

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

      1. div-sub 92.1%

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

      2. associate-/l* 89.2%

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

      3. associate-/l* 90.5%

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

   4. Applied egg-rr 90.5%

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

      1. associate-*r/ 93.5%

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

      2. clear-num 93.3%

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

      3. *-commutative 93.3%

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

      4. *-commutative 93.3%

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

      5. times-frac 87.2%

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

   6. Applied egg-rr 87.2%

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

   7. Taylor expanded in y around 0 73.9%

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

      1. *-commutative 73.9%

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

      2. associate-*r/ 75.7%

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

      3. *-commutative 75.7%

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

      4. associate-*l* 75.6%

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

      5. associate-*l/ 75.7%

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

      6. *-commutative 75.7%

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

   9. Simplified 75.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+140}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+51}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{elif}\;x \cdot y \leq -0.05:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+77}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 9\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a\_m}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* t (* z 9.0))))
   (*
    a_s
    (if (<= t_1 (- INFINITY))
      (* z (/ (* t -4.5) a_m))
      (if (<= t_1 2e+263)
        (/ (- (* x y) t_1) (* a_m 2.0))
        (* (* t (/ z a_m)) -4.5))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * ((t * -4.5) / a_m);
	} else if (t_1 <= 2e+263) {
		tmp = ((x * y) - t_1) / (a_m * 2.0);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (z * 9.0);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((t * -4.5) / a_m);
	} else if (t_1 <= 2e+263) {
		tmp = ((x * y) - t_1) / (a_m * 2.0);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = t * (z * 9.0)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * ((t * -4.5) / a_m)
	elif t_1 <= 2e+263:
		tmp = ((x * y) - t_1) / (a_m * 2.0)
	else:
		tmp = (t * (z / a_m)) * -4.5
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(t * Float64(z * 9.0))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(t * -4.5) / a_m));
	elseif (t_1 <= 2e+263)
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = t * (z * 9.0);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * ((t * -4.5) / a_m);
	elseif (t_1 <= 2e+263)
		tmp = ((x * y) - t_1) / (a_m * 2.0);
	else
		tmp = (t * (z / a_m)) * -4.5;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+263], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z 9) t) < -inf.0

   1. Initial program 55.1%

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

      1. div-sub 49.2%

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

      2. associate-/l* 43.3%

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

      3. associate-/l* 82.1%

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

   4. Applied egg-rr 82.1%

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

      1. associate-*r/ 88.0%

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

      2. clear-num 88.0%

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

      3. *-commutative 88.0%

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

      4. *-commutative 88.0%

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

      5. times-frac 88.0%

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

   6. Applied egg-rr 88.0%

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

   7. Taylor expanded in y around 0 55.1%

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

      1. *-commutative 55.1%

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

      2. associate-*r/ 93.9%

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

      3. *-commutative 93.9%

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

      4. associate-*l* 93.8%

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

      5. associate-*l/ 93.8%

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

      6. *-commutative 93.8%

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

   9. Simplified 93.8%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < 2.00000000000000003e263

   1. Initial program 94.0%

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

   if 2.00000000000000003e263 < (*.f64 (*.f64 z 9) t)

   1. Initial program 52.2%

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

   3. Taylor expanded in x around 0 56.8%

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

      1. associate-/l* 94.2%

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

   5. Simplified 94.2%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(z \cdot 9\right) \leq -\infty:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{elif}\;t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{+263}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-159} \lor \neg \left(t \leq 1.8 \cdot 10^{-96} \lor \neg \left(t \leq 2.8 \cdot 10^{-12}\right) \land t \leq 1.05 \cdot 10^{+117}\right):\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (or (<= t -2.5e-159)
          (not
           (or (<= t 1.8e-96) (and (not (<= t 2.8e-12)) (<= t 1.05e+117)))))
    (* z (/ (* t -4.5) a_m))
    (* (* x 0.5) (/ y a_m)))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((t <= -2.5e-159) || !((t <= 1.8e-96) || (!(t <= 2.8e-12) && (t <= 1.05e+117)))) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = (x * 0.5) * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((t <= (-2.5d-159)) .or. (.not. (t <= 1.8d-96) .or. (.not. (t <= 2.8d-12)) .and. (t <= 1.05d+117))) then
        tmp = z * ((t * (-4.5d0)) / a_m)
    else
        tmp = (x * 0.5d0) * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((t <= -2.5e-159) || !((t <= 1.8e-96) || (!(t <= 2.8e-12) && (t <= 1.05e+117)))) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = (x * 0.5) * (y / a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (t <= -2.5e-159) or not ((t <= 1.8e-96) or (not (t <= 2.8e-12) and (t <= 1.05e+117))):
		tmp = z * ((t * -4.5) / a_m)
	else:
		tmp = (x * 0.5) * (y / a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if ((t <= -2.5e-159) || !((t <= 1.8e-96) || (!(t <= 2.8e-12) && (t <= 1.05e+117))))
		tmp = Float64(z * Float64(Float64(t * -4.5) / a_m));
	else
		tmp = Float64(Float64(x * 0.5) * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((t <= -2.5e-159) || ~(((t <= 1.8e-96) || (~((t <= 2.8e-12)) && (t <= 1.05e+117)))))
		tmp = z * ((t * -4.5) / a_m);
	else
		tmp = (x * 0.5) * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[Or[LessEqual[t, -2.5e-159], N[Not[Or[LessEqual[t, 1.8e-96], And[N[Not[LessEqual[t, 2.8e-12]], $MachinePrecision], LessEqual[t, 1.05e+117]]]], $MachinePrecision]], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000016e-159 or 1.80000000000000004e-96 < t < 2.8000000000000002e-12 or 1.0500000000000001e117 < t

   1. Initial program 85.3%

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

      1. div-sub 83.5%

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

      2. associate-/l* 83.9%

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

      3. associate-/l* 89.1%

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

   4. Applied egg-rr 89.1%

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

      1. associate-*r/ 88.1%

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

      2. clear-num 88.0%

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

      3. *-commutative 88.0%

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

      4. *-commutative 88.0%

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

      5. times-frac 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in y around 0 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*r/ 67.4%

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

      3. *-commutative 67.4%

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

      4. associate-*l* 67.4%

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

      5. associate-*l/ 67.4%

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

      6. *-commutative 67.4%

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

   9. Simplified 67.4%

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

   if -2.50000000000000016e-159 < t < 1.80000000000000004e-96 or 2.8000000000000002e-12 < t < 1.0500000000000001e117

   1. Initial program 92.5%

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

   3. Taylor expanded in x around inf 68.9%

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

      1. associate-/l* 71.7%

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

      2. associate-*r* 71.7%

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

   5. Simplified 71.7%

      \[\leadsto \color{blue}{\left(0.5 \cdot x\right) \cdot \frac{y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-159} \lor \neg \left(t \leq 1.8 \cdot 10^{-96} \lor \neg \left(t \leq 2.8 \cdot 10^{-12}\right) \land t \leq 1.05 \cdot 10^{+117}\right):\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := z \cdot \frac{t \cdot -4.5}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-96}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a\_m}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-12} \lor \neg \left(t \leq 2 \cdot 10^{+117}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* z (/ (* t -4.5) a_m))))
   (*
    a_s
    (if (<= t -1.3e-164)
      t_1
      (if (<= t 1.65e-96)
        (* (* y 0.5) (/ x a_m))
        (if (or (<= t 1.2e-12) (not (<= t 2e+117)))
          t_1
          (* (* x 0.5) (/ y a_m))))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = z * ((t * -4.5) / a_m);
	double tmp;
	if (t <= -1.3e-164) {
		tmp = t_1;
	} else if (t <= 1.65e-96) {
		tmp = (y * 0.5) * (x / a_m);
	} else if ((t <= 1.2e-12) || !(t <= 2e+117)) {
		tmp = t_1;
	} else {
		tmp = (x * 0.5) * (y / a_m);
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((t * (-4.5d0)) / a_m)
    if (t <= (-1.3d-164)) then
        tmp = t_1
    else if (t <= 1.65d-96) then
        tmp = (y * 0.5d0) * (x / a_m)
    else if ((t <= 1.2d-12) .or. (.not. (t <= 2d+117))) then
        tmp = t_1
    else
        tmp = (x * 0.5d0) * (y / a_m)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = z * ((t * -4.5) / a_m);
	double tmp;
	if (t <= -1.3e-164) {
		tmp = t_1;
	} else if (t <= 1.65e-96) {
		tmp = (y * 0.5) * (x / a_m);
	} else if ((t <= 1.2e-12) || !(t <= 2e+117)) {
		tmp = t_1;
	} else {
		tmp = (x * 0.5) * (y / a_m);
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = z * ((t * -4.5) / a_m)
	tmp = 0
	if t <= -1.3e-164:
		tmp = t_1
	elif t <= 1.65e-96:
		tmp = (y * 0.5) * (x / a_m)
	elif (t <= 1.2e-12) or not (t <= 2e+117):
		tmp = t_1
	else:
		tmp = (x * 0.5) * (y / a_m)
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(z * Float64(Float64(t * -4.5) / a_m))
	tmp = 0.0
	if (t <= -1.3e-164)
		tmp = t_1;
	elseif (t <= 1.65e-96)
		tmp = Float64(Float64(y * 0.5) * Float64(x / a_m));
	elseif ((t <= 1.2e-12) || !(t <= 2e+117))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 0.5) * Float64(y / a_m));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = z * ((t * -4.5) / a_m);
	tmp = 0.0;
	if (t <= -1.3e-164)
		tmp = t_1;
	elseif (t <= 1.65e-96)
		tmp = (y * 0.5) * (x / a_m);
	elseif ((t <= 1.2e-12) || ~((t <= 2e+117)))
		tmp = t_1;
	else
		tmp = (x * 0.5) * (y / a_m);
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(z * N[(N[(t * -4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t, -1.3e-164], t$95$1, If[LessEqual[t, 1.65e-96], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a$95$m), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.2e-12], N[Not[LessEqual[t, 2e+117]], $MachinePrecision]], t$95$1, N[(N[(x * 0.5), $MachinePrecision] * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3000000000000001e-164 or 1.64999999999999995e-96 < t < 1.19999999999999994e-12 or 2.0000000000000001e117 < t

   1. Initial program 85.4%

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

      1. div-sub 83.6%

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

      2. associate-/l* 84.0%

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

      3. associate-/l* 89.1%

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

   4. Applied egg-rr 89.1%

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

      1. associate-*r/ 88.1%

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

      2. clear-num 88.1%

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

      3. *-commutative 88.1%

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

      4. *-commutative 88.1%

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

      5. times-frac 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in y around 0 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-*r/ 67.1%

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

      3. *-commutative 67.1%

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

      4. associate-*l* 67.0%

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

      5. associate-*l/ 67.1%

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

      6. *-commutative 67.1%

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

   9. Simplified 67.1%

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

   if -1.3000000000000001e-164 < t < 1.64999999999999995e-96

   1. Initial program 92.3%

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

   3. Taylor expanded in x around inf 72.7%

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

      1. times-frac 72.7%

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

      2. div-inv 72.7%

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

      3. metadata-eval 72.7%

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

   5. Applied egg-rr 72.7%

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

   if 1.19999999999999994e-12 < t < 2.0000000000000001e117

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf 58.8%

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

      1. associate-/l* 62.4%

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

      2. associate-*r* 62.4%

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

   5. Simplified 62.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-164}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-96}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-12} \lor \neg \left(t \leq 2 \cdot 10^{+117}\right):\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 4 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2}{y} \cdot \frac{a\_m}{x}} - \left(z \cdot 9\right) \cdot \frac{t}{a\_m \cdot 2}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* a_m 2.0) 4e-59)
    (/ (- (* x y) (* t (* z 9.0))) (* a_m 2.0))
    (- (/ 1.0 (* (/ 2.0 y) (/ a_m x))) (* (* z 9.0) (/ t (* a_m 2.0)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 4e-59) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	} else {
		tmp = (1.0 / ((2.0 / y) * (a_m / x))) - ((z * 9.0) * (t / (a_m * 2.0)));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((a_m * 2.0d0) <= 4d-59) then
        tmp = ((x * y) - (t * (z * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = (1.0d0 / ((2.0d0 / y) * (a_m / x))) - ((z * 9.0d0) * (t / (a_m * 2.0d0)))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 4e-59) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	} else {
		tmp = (1.0 / ((2.0 / y) * (a_m / x))) - ((z * 9.0) * (t / (a_m * 2.0)));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (a_m * 2.0) <= 4e-59:
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0)
	else:
		tmp = (1.0 / ((2.0 / y) * (a_m / x))) - ((z * 9.0) * (t / (a_m * 2.0)))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 4e-59)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(1.0 / Float64(Float64(2.0 / y) * Float64(a_m / x))) - Float64(Float64(z * 9.0) * Float64(t / Float64(a_m * 2.0))));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((a_m * 2.0) <= 4e-59)
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	else
		tmp = (1.0 / ((2.0 / y) * (a_m / x))) - ((z * 9.0) * (t / (a_m * 2.0)));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 4e-59], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(N[(2.0 / y), $MachinePrecision] * N[(a$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 4.0000000000000001e-59

   1. Initial program 91.7%

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

   if 4.0000000000000001e-59 < (*.f64 a 2)

   1. Initial program 78.9%

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

      1. div-sub 78.9%

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

      2. associate-/l* 82.5%

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

      3. associate-/l* 93.4%

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

   4. Applied egg-rr 93.4%

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

      1. associate-*r/ 88.6%

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

      2. clear-num 88.4%

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

      3. *-commutative 88.4%

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

      4. *-commutative 88.4%

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

      5. times-frac 93.2%

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

   6. Applied egg-rr 93.2%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-59}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{2}{y} \cdot \frac{a}{x}} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a\_m \cdot 2}\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* a_m 2.0) 5e+45)
    (/ (- (* x y) (* t (* z 9.0))) (* a_m 2.0))
    (- (* x (/ y (* a_m 2.0))) (* (* z 9.0) (/ t (* a_m 2.0)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 5e+45) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	} else {
		tmp = (x * (y / (a_m * 2.0))) - ((z * 9.0) * (t / (a_m * 2.0)));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((a_m * 2.0d0) <= 5d+45) then
        tmp = ((x * y) - (t * (z * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = (x * (y / (a_m * 2.0d0))) - ((z * 9.0d0) * (t / (a_m * 2.0d0)))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 5e+45) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	} else {
		tmp = (x * (y / (a_m * 2.0))) - ((z * 9.0) * (t / (a_m * 2.0)));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (a_m * 2.0) <= 5e+45:
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0)
	else:
		tmp = (x * (y / (a_m * 2.0))) - ((z * 9.0) * (t / (a_m * 2.0)))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 5e+45)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a_m * 2.0))) - Float64(Float64(z * 9.0) * Float64(t / Float64(a_m * 2.0))));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((a_m * 2.0) <= 5e+45)
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	else
		tmp = (x * (y / (a_m * 2.0))) - ((z * 9.0) * (t / (a_m * 2.0)));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 5e+45], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 5e45

   1. Initial program 92.4%

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

   if 5e45 < (*.f64 a 2)

   1. Initial program 73.0%

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

      1. div-sub 73.0%

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

      2. associate-/l* 77.6%

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

      3. associate-/l* 91.7%

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

   4. Applied egg-rr 91.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a\_m \cdot 2} - 4.5 \cdot \left(t \cdot \frac{z}{a\_m}\right)\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* a_m 2.0) 5e+131)
    (/ (- (* x y) (* t (* z 9.0))) (* a_m 2.0))
    (- (* x (/ y (* a_m 2.0))) (* 4.5 (* t (/ z a_m)))))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 5e+131) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	} else {
		tmp = (x * (y / (a_m * 2.0))) - (4.5 * (t * (z / a_m)));
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if ((a_m * 2.0d0) <= 5d+131) then
        tmp = ((x * y) - (t * (z * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = (x * (y / (a_m * 2.0d0))) - (4.5d0 * (t * (z / a_m)))
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 5e+131) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	} else {
		tmp = (x * (y / (a_m * 2.0))) - (4.5 * (t * (z / a_m)));
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (a_m * 2.0) <= 5e+131:
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0)
	else:
		tmp = (x * (y / (a_m * 2.0))) - (4.5 * (t * (z / a_m)))
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 5e+131)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a_m * 2.0))) - Float64(4.5 * Float64(t * Float64(z / a_m))));
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((a_m * 2.0) <= 5e+131)
		tmp = ((x * y) - (t * (z * 9.0))) / (a_m * 2.0);
	else
		tmp = (x * (y / (a_m * 2.0))) - (4.5 * (t * (z / a_m)));
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(a$95$m * 2.0), $MachinePrecision], 5e+131], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 4.99999999999999995e131

   1. Initial program 92.2%

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

   if 4.99999999999999995e131 < (*.f64 a 2)

   1. Initial program 64.5%

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

      1. div-sub 64.5%

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

      2. associate-/l* 69.1%

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

      3. associate-/l* 92.5%

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

   4. Applied egg-rr 92.5%

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

   5. Taylor expanded in z around 0 69.2%

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

      1. associate-*r/ 90.2%

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

   7. Simplified 90.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-263}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= y 2.7e-263) (* -4.5 (/ (* t z) a_m)) (* (* t (/ z a_m)) -4.5))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (y <= 2.7e-263) {
		tmp = -4.5 * ((t * z) / a_m);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (y <= 2.7d-263) then
        tmp = (-4.5d0) * ((t * z) / a_m)
    else
        tmp = (t * (z / a_m)) * (-4.5d0)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (y <= 2.7e-263) {
		tmp = -4.5 * ((t * z) / a_m);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if y <= 2.7e-263:
		tmp = -4.5 * ((t * z) / a_m)
	else:
		tmp = (t * (z / a_m)) * -4.5
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (y <= 2.7e-263)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a_m));
	else
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (y <= 2.7e-263)
		tmp = -4.5 * ((t * z) / a_m);
	else
		tmp = (t * (z / a_m)) * -4.5;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[y, 2.7e-263], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 2.70000000000000003e-263

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0 50.7%

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

   if 2.70000000000000003e-263 < y

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 50.8%

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

      1. associate-/l* 59.1%

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

   5. Simplified 59.1%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-263}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= y 2.05e-85) (* z (/ (* t -4.5) a_m)) (* (* t (/ z a_m)) -4.5))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (y <= 2.05e-85) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (y <= 2.05d-85) then
        tmp = z * ((t * (-4.5d0)) / a_m)
    else
        tmp = (t * (z / a_m)) * (-4.5d0)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (y <= 2.05e-85) {
		tmp = z * ((t * -4.5) / a_m);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if y <= 2.05e-85:
		tmp = z * ((t * -4.5) / a_m)
	else:
		tmp = (t * (z / a_m)) * -4.5
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (y <= 2.05e-85)
		tmp = Float64(z * Float64(Float64(t * -4.5) / a_m));
	else
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (y <= 2.05e-85)
		tmp = z * ((t * -4.5) / a_m);
	else
		tmp = (t * (z / a_m)) * -4.5;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[y, 2.05e-85], N[(z * N[(N[(t * -4.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 2.04999999999999997e-85

   1. Initial program 89.0%

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

      1. div-sub 86.8%

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

      2. associate-/l* 87.7%

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

      3. associate-/l* 89.3%

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

   4. Applied egg-rr 89.3%

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

      1. associate-*r/ 87.8%

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

      2. clear-num 87.7%

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

      3. *-commutative 87.7%

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

      4. *-commutative 87.7%

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

      5. times-frac 86.0%

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

   6. Applied egg-rr 86.0%

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

   7. Taylor expanded in y around 0 52.7%

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

      1. *-commutative 52.7%

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

      2. associate-*r/ 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-*l* 55.5%

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

      5. associate-*l/ 55.5%

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

      6. *-commutative 55.5%

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

   9. Simplified 55.5%

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

   if 2.04999999999999997e-85 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 46.3%

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

      1. associate-/l* 51.2%

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

   5. Simplified 51.2%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \frac{t \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-83}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (* a_s (if (<= y 2.9e-83) (* (* z -4.5) (/ t a_m)) (* (* t (/ z a_m)) -4.5))))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (y <= 2.9e-83) {
		tmp = (z * -4.5) * (t / a_m);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    real(8) :: tmp
    if (y <= 2.9d-83) then
        tmp = (z * (-4.5d0)) * (t / a_m)
    else
        tmp = (t * (z / a_m)) * (-4.5d0)
    end if
    code = a_s * tmp
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (y <= 2.9e-83) {
		tmp = (z * -4.5) * (t / a_m);
	} else {
		tmp = (t * (z / a_m)) * -4.5;
	}
	return a_s * tmp;
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if y <= 2.9e-83:
		tmp = (z * -4.5) * (t / a_m)
	else:
		tmp = (t * (z / a_m)) * -4.5
	return a_s * tmp

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (y <= 2.9e-83)
		tmp = Float64(Float64(z * -4.5) * Float64(t / a_m));
	else
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	end
	return Float64(a_s * tmp)
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (y <= 2.9e-83)
		tmp = (z * -4.5) * (t / a_m);
	else
		tmp = (t * (z / a_m)) * -4.5;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[y, 2.9e-83], N[(N[(z * -4.5), $MachinePrecision] * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 2.8999999999999999e-83

   1. Initial program 89.0%

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

   3. Taylor expanded in x around 0 52.7%

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

      1. associate-/l* 57.9%

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

   5. Simplified 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-*r/ 52.7%

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

      3. associate-*l/ 52.7%

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

      4. *-commutative 52.7%

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

   7. Applied egg-rr 52.7%

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

      1. *-commutative 52.7%

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

      2. associate-*r/ 52.7%

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

      3. associate-/l* 55.5%

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

      4. associate-*r* 55.5%

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

   9. Applied egg-rr 55.5%

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

   if 2.8999999999999999e-83 < y

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 46.3%

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

      1. associate-/l* 51.2%

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

   5. Simplified 51.2%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{-83}:\\ \;\;\;\;\left(z \cdot -4.5\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ a_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\right) \end{array} \]

FPCore

a_m = (fabs.f64 a)
a_s = (copysign.f64 1 a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* (* t (/ z a_m)) -4.5)))

C

a_m = fabs(a);
a_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * ((t * (z / a_m)) * -4.5);
}

Fortran

a_m = abs(a)
a_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    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_m
    code = a_s * ((t * (z / a_m)) * (-4.5d0))
end function

Java

a_m = Math.abs(a);
a_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * ((t * (z / a_m)) * -4.5);
}

Python

a_m = math.fabs(a)
a_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * ((t * (z / a_m)) * -4.5)

Julia

a_m = abs(a)
a_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(Float64(t * Float64(z / a_m)) * -4.5))
end

MATLAB

a_m = abs(a);
a_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * ((t * (z / a_m)) * -4.5);
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
a_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.8%

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

3. Taylor expanded in x around 0 50.7%

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

   1. associate-/l* 55.8%

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

5. Simplified 55.8%

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

6. Final simplification 55.8%

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

Developer target: 94.3% 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 2024044 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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