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

Percentage Accurate: 91.2% → 94.8%

Time: 9.8s

Alternatives: 11

Speedup: 0.6×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a\_m} \cdot \left(y \cdot 0.5\right) - \frac{z}{a\_m} \cdot \left(t \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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+73)
    (/ (fma x y (* z (* t -9.0))) (* a_m 2.0))
    (- (* (/ x a_m) (* y 0.5)) (* (/ z a_m) (* t 4.5))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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+73) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x / a_m) * (y * 0.5)) - ((z / a_m) * (t * 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+73)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(Float64(x / a_m) * Float64(y * 0.5)) - Float64(Float64(z / a_m) * Float64(t * 4.5)));
	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.
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+73], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a$95$m), $MachinePrecision] * N[(t * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 9.99999999999999983e72

   1. Initial program 93.1%

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

      1. div-sub 90.8%

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

      2. *-commutative 90.8%

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

      3. div-sub 93.1%

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

      4. cancel-sign-sub-inv 93.1%

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

      5. *-commutative 93.1%

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

      6. fma-define 93.6%

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

      7. distribute-rgt-neg-in 93.6%

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

      8. associate-*r* 94.0%

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

      9. distribute-lft-neg-in 94.0%

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

      10. *-commutative 94.0%

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

      11. distribute-rgt-neg-in 94.0%

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

      12. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   if 9.99999999999999983e72 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 75.1%

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

   3. Taylor expanded in z around 0 75.0%

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

      1. associate-*r* 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

   5. Simplified 75.1%

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

      1. div-sub 75.0%

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

      2. times-frac 86.3%

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

      3. div-inv 86.3%

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

      4. metadata-eval 86.3%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. times-frac 86.2%

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

      8. associate-/l* 92.7%

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

      9. metadata-eval 92.7%

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

   7. Applied egg-rr 92.7%

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

   8. Taylor expanded in t around 0 86.2%

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

      1. associate-*r/ 92.7%

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

      2. associate-*r* 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

   10. Simplified 92.9%

       \[\leadsto \frac{x}{a} \cdot \left(y \cdot 0.5\right) - \color{blue}{\frac{z}{a} \cdot \left(t \cdot 4.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right) - \frac{z}{a} \cdot \left(t \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a\_m} \cdot \left(y \cdot 0.5\right) - \frac{z}{a\_m} \cdot \left(t \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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+73)
    (* (fma x y (* t (* z -9.0))) (/ 0.5 a_m))
    (- (* (/ x a_m) (* y 0.5)) (* (/ z a_m) (* t 4.5))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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+73) {
		tmp = fma(x, y, (t * (z * -9.0))) * (0.5 / a_m);
	} else {
		tmp = ((x / a_m) * (y * 0.5)) - ((z / a_m) * (t * 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+73)
		tmp = Float64(fma(x, y, Float64(t * Float64(z * -9.0))) * Float64(0.5 / a_m));
	else
		tmp = Float64(Float64(Float64(x / a_m) * Float64(y * 0.5)) - Float64(Float64(z / a_m) * Float64(t * 4.5)));
	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.
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+73], N[(N[(x * y + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a$95$m), $MachinePrecision] * N[(t * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 9.99999999999999983e72

   1. Initial program 93.1%

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

      1. div-inv 93.1%

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

      2. fma-neg 93.6%

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

      3. *-commutative 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

      5. distribute-rgt-neg-in 93.6%

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

      6. metadata-eval 93.6%

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

      7. *-commutative 93.6%

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

      8. associate-/r* 93.6%

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

      9. metadata-eval 93.6%

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

   4. Applied egg-rr 93.6%

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

   if 9.99999999999999983e72 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 75.1%

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

   3. Taylor expanded in z around 0 75.0%

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

      1. associate-*r* 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

   5. Simplified 75.1%

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

      1. div-sub 75.0%

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

      2. times-frac 86.3%

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

      3. div-inv 86.3%

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

      4. metadata-eval 86.3%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. times-frac 86.2%

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

      8. associate-/l* 92.7%

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

      9. metadata-eval 92.7%

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

   7. Applied egg-rr 92.7%

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

   8. Taylor expanded in t around 0 86.2%

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

      1. associate-*r/ 92.7%

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

      2. associate-*r* 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

   10. Simplified 92.9%

       \[\leadsto \frac{x}{a} \cdot \left(y \cdot 0.5\right) - \color{blue}{\frac{z}{a} \cdot \left(t \cdot 4.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right) - \frac{z}{a} \cdot \left(t \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \frac{x}{a\_m} \cdot \left(y \cdot 0.5\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \mathbf{elif}\;x \cdot y \leq 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{a\_m \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(\frac{z}{a\_m} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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 a_m) (* y 0.5))))
   (*
    a_s
    (if (<= (* x y) -4e+72)
      t_1
      (if (<= (* x y) 5e-57)
        (* (* z t) (/ -4.5 a_m))
        (if (<= (* x y) 1e+79)
          (/ (* x y) (* a_m 2.0))
          (if (<= (* x y) 2e+148) (* t (* (/ z a_m) -4.5)) t_1)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 / a_m) * (y * 0.5);
	double tmp;
	if ((x * y) <= -4e+72) {
		tmp = t_1;
	} else if ((x * y) <= 5e-57) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if ((x * y) <= 1e+79) {
		tmp = (x * y) / (a_m * 2.0);
	} else if ((x * y) <= 2e+148) {
		tmp = t * ((z / a_m) * -4.5);
	} 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.
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 / a_m) * (y * 0.5d0)
    if ((x * y) <= (-4d+72)) then
        tmp = t_1
    else if ((x * y) <= 5d-57) then
        tmp = (z * t) * ((-4.5d0) / a_m)
    else if ((x * y) <= 1d+79) then
        tmp = (x * y) / (a_m * 2.0d0)
    else if ((x * y) <= 2d+148) then
        tmp = t * ((z / a_m) * (-4.5d0))
    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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = (x / a_m) * (y * 0.5);
	double tmp;
	if ((x * y) <= -4e+72) {
		tmp = t_1;
	} else if ((x * y) <= 5e-57) {
		tmp = (z * t) * (-4.5 / a_m);
	} else if ((x * y) <= 1e+79) {
		tmp = (x * y) / (a_m * 2.0);
	} else if ((x * y) <= 2e+148) {
		tmp = t * ((z / a_m) * -4.5);
	} 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])
def code(a_s, x, y, z, t, a_m):
	t_1 = (x / a_m) * (y * 0.5)
	tmp = 0
	if (x * y) <= -4e+72:
		tmp = t_1
	elif (x * y) <= 5e-57:
		tmp = (z * t) * (-4.5 / a_m)
	elif (x * y) <= 1e+79:
		tmp = (x * y) / (a_m * 2.0)
	elif (x * y) <= 2e+148:
		tmp = t * ((z / a_m) * -4.5)
	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])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(x / a_m) * Float64(y * 0.5))
	tmp = 0.0
	if (Float64(x * y) <= -4e+72)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-57)
		tmp = Float64(Float64(z * t) * Float64(-4.5 / a_m));
	elseif (Float64(x * y) <= 1e+79)
		tmp = Float64(Float64(x * y) / Float64(a_m * 2.0));
	elseif (Float64(x * y) <= 2e+148)
		tmp = Float64(t * Float64(Float64(z / a_m) * -4.5));
	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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = (x / a_m) * (y * 0.5);
	tmp = 0.0;
	if ((x * y) <= -4e+72)
		tmp = t_1;
	elseif ((x * y) <= 5e-57)
		tmp = (z * t) * (-4.5 / a_m);
	elseif ((x * y) <= 1e+79)
		tmp = (x * y) / (a_m * 2.0);
	elseif ((x * y) <= 2e+148)
		tmp = t * ((z / a_m) * -4.5);
	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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], -4e+72], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+79], N[(N[(x * y), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+148], N[(t * N[(N[(z / a$95$m), $MachinePrecision] * -4.5), $MachinePrecision]), $MachinePrecision], t$95$1]]]]), $MachinePrecision]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -3.99999999999999978e72 or 2.0000000000000001e148 < (*.f64 x y)

   1. Initial program 82.6%

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

   3. Taylor expanded in x around inf 70.4%

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

      1. times-frac 83.6%

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

      2. div-inv 83.6%

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

      3. metadata-eval 83.6%

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

   5. Applied egg-rr 83.6%

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

   if -3.99999999999999978e72 < (*.f64 x y) < 5.0000000000000002e-57

   1. Initial program 94.7%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. associate-/l* 80.7%

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

      2. associate-*r* 80.7%

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

      3. *-commutative 80.7%

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

      4. associate-*l/ 81.3%

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

      5. *-commutative 81.3%

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

   5. Applied egg-rr 81.3%

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

      1. associate-*r* 81.2%

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

      2. associate-/l* 81.3%

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

      3. *-commutative 81.3%

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

   7. Applied egg-rr 81.3%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 9.99999999999999967e78

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 62.8%

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

   if 9.99999999999999967e78 < (*.f64 x y) < 2.0000000000000001e148

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 83.9%

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

      1. associate-*r* 83.7%

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

      2. *-commutative 83.7%

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

      3. *-commutative 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in x around 0 67.9%

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

      1. associate-*r/ 83.7%

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

      2. associate-*r* 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-*r* 83.7%

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

   8. Simplified 83.7%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+79}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-29} \lor \neg \left(x \leq 9000000000000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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 (/ (* y 0.5) a_m))))
   (*
    a_s
    (if (<= x -7.2e+134)
      t_1
      (if (<= x -3.1e+82)
        (* (* t (/ z a_m)) -4.5)
        (if (or (<= x -5e-29) (not (<= x 9000000000000.0)))
          t_1
          (* -4.5 (/ (* z t) a_m))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 * ((y * 0.5) / a_m);
	double tmp;
	if (x <= -7.2e+134) {
		tmp = t_1;
	} else if (x <= -3.1e+82) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x <= -5e-29) || !(x <= 9000000000000.0)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / 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.
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 * ((y * 0.5d0) / a_m)
    if (x <= (-7.2d+134)) then
        tmp = t_1
    else if (x <= (-3.1d+82)) then
        tmp = (t * (z / a_m)) * (-4.5d0)
    else if ((x <= (-5d-29)) .or. (.not. (x <= 9000000000000.0d0))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = x * ((y * 0.5) / a_m);
	double tmp;
	if (x <= -7.2e+134) {
		tmp = t_1;
	} else if (x <= -3.1e+82) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x <= -5e-29) || !(x <= 9000000000000.0)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / 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])
def code(a_s, x, y, z, t, a_m):
	t_1 = x * ((y * 0.5) / a_m)
	tmp = 0
	if x <= -7.2e+134:
		tmp = t_1
	elif x <= -3.1e+82:
		tmp = (t * (z / a_m)) * -4.5
	elif (x <= -5e-29) or not (x <= 9000000000000.0):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / 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])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a_m))
	tmp = 0.0
	if (x <= -7.2e+134)
		tmp = t_1;
	elseif (x <= -3.1e+82)
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	elseif ((x <= -5e-29) || !(x <= 9000000000000.0))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = x * ((y * 0.5) / a_m);
	tmp = 0.0;
	if (x <= -7.2e+134)
		tmp = t_1;
	elseif (x <= -3.1e+82)
		tmp = (t * (z / a_m)) * -4.5;
	elseif ((x <= -5e-29) || ~((x <= 9000000000000.0)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[x, -7.2e+134], t$95$1, If[LessEqual[x, -3.1e+82], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[Or[LessEqual[x, -5e-29], N[Not[LessEqual[x, 9000000000000.0]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999976e134 or -3.10000000000000032e82 < x < -4.99999999999999986e-29 or 9e12 < x

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-/l* 69.2%

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

      3. associate-*r* 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-*r/ 69.2%

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

   5. Simplified 69.2%

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

   if -7.19999999999999976e134 < x < -3.10000000000000032e82

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. associate-/l* 56.4%

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

   5. Applied egg-rr 56.4%

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

   if -4.99999999999999986e-29 < x < 9e12

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 70.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{+82}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-29} \lor \neg \left(x \leq 9000000000000\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a\_m}\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-32} \lor \neg \left(x \leq 9.6 \cdot 10^{+30}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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 (/ (* y 0.5) a_m))))
   (*
    a_s
    (if (<= x -7.2e+134)
      t_1
      (if (<= x -2.6e+82)
        (* (* t (/ z a_m)) -4.5)
        (if (or (<= x -1.85e-32) (not (<= x 9.6e+30)))
          t_1
          (* (* z t) (/ -4.5 a_m))))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 * ((y * 0.5) / a_m);
	double tmp;
	if (x <= -7.2e+134) {
		tmp = t_1;
	} else if (x <= -2.6e+82) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x <= -1.85e-32) || !(x <= 9.6e+30)) {
		tmp = t_1;
	} else {
		tmp = (z * t) * (-4.5 / 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.
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 * ((y * 0.5d0) / a_m)
    if (x <= (-7.2d+134)) then
        tmp = t_1
    else if (x <= (-2.6d+82)) then
        tmp = (t * (z / a_m)) * (-4.5d0)
    else if ((x <= (-1.85d-32)) .or. (.not. (x <= 9.6d+30))) then
        tmp = t_1
    else
        tmp = (z * t) * ((-4.5d0) / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = x * ((y * 0.5) / a_m);
	double tmp;
	if (x <= -7.2e+134) {
		tmp = t_1;
	} else if (x <= -2.6e+82) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x <= -1.85e-32) || !(x <= 9.6e+30)) {
		tmp = t_1;
	} else {
		tmp = (z * t) * (-4.5 / 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])
def code(a_s, x, y, z, t, a_m):
	t_1 = x * ((y * 0.5) / a_m)
	tmp = 0
	if x <= -7.2e+134:
		tmp = t_1
	elif x <= -2.6e+82:
		tmp = (t * (z / a_m)) * -4.5
	elif (x <= -1.85e-32) or not (x <= 9.6e+30):
		tmp = t_1
	else:
		tmp = (z * t) * (-4.5 / 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])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(x * Float64(Float64(y * 0.5) / a_m))
	tmp = 0.0
	if (x <= -7.2e+134)
		tmp = t_1;
	elseif (x <= -2.6e+82)
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	elseif ((x <= -1.85e-32) || !(x <= 9.6e+30))
		tmp = t_1;
	else
		tmp = Float64(Float64(z * t) * Float64(-4.5 / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = x * ((y * 0.5) / a_m);
	tmp = 0.0;
	if (x <= -7.2e+134)
		tmp = t_1;
	elseif (x <= -2.6e+82)
		tmp = (t * (z / a_m)) * -4.5;
	elseif ((x <= -1.85e-32) || ~((x <= 9.6e+30)))
		tmp = t_1;
	else
		tmp = (z * t) * (-4.5 / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(x * N[(N[(y * 0.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[x, -7.2e+134], t$95$1, If[LessEqual[x, -2.6e+82], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[Or[LessEqual[x, -1.85e-32], N[Not[LessEqual[x, 9.6e+30]], $MachinePrecision]], t$95$1, N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if x < -7.19999999999999976e134 or -2.5999999999999998e82 < x < -1.85e-32 or 9.5999999999999997e30 < x

   1. Initial program 84.9%

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

   3. Taylor expanded in x around inf 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-/l* 70.0%

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

      3. associate-*r* 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-*r/ 70.0%

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

   5. Simplified 70.0%

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

   if -7.19999999999999976e134 < x < -2.5999999999999998e82

   1. Initial program 82.9%

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

   3. Taylor expanded in x around 0 56.5%

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

      1. associate-/l* 56.4%

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

   5. Applied egg-rr 56.4%

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

   if -1.85e-32 < x < 9.5999999999999997e30

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 69.7%

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

      1. associate-/l* 69.9%

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

      2. associate-*r* 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*l/ 69.7%

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

      5. *-commutative 69.7%

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

   5. Applied egg-rr 69.7%

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

      1. associate-*r* 69.7%

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

      2. associate-/l* 69.8%

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

      3. *-commutative 69.8%

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

   7. Applied egg-rr 69.8%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-32} \lor \neg \left(x \leq 9.6 \cdot 10^{+30}\right):\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a\_m}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;\left(t \cdot \frac{z}{a\_m}\right) \cdot -4.5\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-31} \lor \neg \left(x \leq 1.6 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{a\_m} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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 (<= x -1.12e+135)
    (* x (/ (* y 0.5) a_m))
    (if (<= x -2.5e+83)
      (* (* t (/ z a_m)) -4.5)
      (if (or (<= x -1.8e-31) (not (<= x 1.6e+31)))
        (* (/ x a_m) (* y 0.5))
        (* (* z t) (/ -4.5 a_m)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 (x <= -1.12e+135) {
		tmp = x * ((y * 0.5) / a_m);
	} else if (x <= -2.5e+83) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x <= -1.8e-31) || !(x <= 1.6e+31)) {
		tmp = (x / a_m) * (y * 0.5);
	} else {
		tmp = (z * t) * (-4.5 / 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.
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 (x <= (-1.12d+135)) then
        tmp = x * ((y * 0.5d0) / a_m)
    else if (x <= (-2.5d+83)) then
        tmp = (t * (z / a_m)) * (-4.5d0)
    else if ((x <= (-1.8d-31)) .or. (.not. (x <= 1.6d+31))) then
        tmp = (x / a_m) * (y * 0.5d0)
    else
        tmp = (z * t) * ((-4.5d0) / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (x <= -1.12e+135) {
		tmp = x * ((y * 0.5) / a_m);
	} else if (x <= -2.5e+83) {
		tmp = (t * (z / a_m)) * -4.5;
	} else if ((x <= -1.8e-31) || !(x <= 1.6e+31)) {
		tmp = (x / a_m) * (y * 0.5);
	} else {
		tmp = (z * t) * (-4.5 / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if x <= -1.12e+135:
		tmp = x * ((y * 0.5) / a_m)
	elif x <= -2.5e+83:
		tmp = (t * (z / a_m)) * -4.5
	elif (x <= -1.8e-31) or not (x <= 1.6e+31):
		tmp = (x / a_m) * (y * 0.5)
	else:
		tmp = (z * t) * (-4.5 / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (x <= -1.12e+135)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a_m));
	elseif (x <= -2.5e+83)
		tmp = Float64(Float64(t * Float64(z / a_m)) * -4.5);
	elseif ((x <= -1.8e-31) || !(x <= 1.6e+31))
		tmp = Float64(Float64(x / a_m) * Float64(y * 0.5));
	else
		tmp = Float64(Float64(z * t) * Float64(-4.5 / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (x <= -1.12e+135)
		tmp = x * ((y * 0.5) / a_m);
	elseif (x <= -2.5e+83)
		tmp = (t * (z / a_m)) * -4.5;
	elseif ((x <= -1.8e-31) || ~((x <= 1.6e+31)))
		tmp = (x / a_m) * (y * 0.5);
	else
		tmp = (z * t) * (-4.5 / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[x, -1.12e+135], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e+83], N[(N[(t * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision] * -4.5), $MachinePrecision], If[Or[LessEqual[x, -1.8e-31], N[Not[LessEqual[x, 1.6e+31]], $MachinePrecision]], N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if x < -1.1199999999999999e135

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/l* 80.4%

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

      3. associate-*r* 80.4%

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

      4. *-commutative 80.4%

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

      5. associate-*r/ 80.4%

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

   5. Simplified 80.4%

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

   if -1.1199999999999999e135 < x < -2.50000000000000014e83

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 52.0%

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

   5. Applied egg-rr 52.0%

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

   if -2.50000000000000014e83 < x < -1.80000000000000002e-31 or 1.6e31 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in x around inf 49.1%

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

      1. times-frac 62.1%

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

      2. div-inv 62.1%

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

      3. metadata-eval 62.1%

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

   5. Applied egg-rr 62.1%

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

   if -1.80000000000000002e-31 < x < 1.6e31

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 69.7%

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

      1. associate-/l* 69.9%

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

      2. associate-*r* 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*l/ 69.7%

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

      5. *-commutative 69.7%

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

   5. Applied egg-rr 69.7%

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

      1. associate-*r* 69.7%

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

      2. associate-/l* 69.8%

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

      3. *-commutative 69.8%

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

   7. Applied egg-rr 69.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;\left(t \cdot \frac{z}{a}\right) \cdot -4.5\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-31} \lor \neg \left(x \leq 1.6 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a\_m}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a\_m}{z}}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-29} \lor \neg \left(x \leq 2.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{a\_m} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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 (<= x -7.2e+134)
    (* x (/ (* y 0.5) a_m))
    (if (<= x -2.5e+83)
      (/ (* t -4.5) (/ a_m z))
      (if (or (<= x -1.05e-29) (not (<= x 2.5e+27)))
        (* (/ x a_m) (* y 0.5))
        (* (* z t) (/ -4.5 a_m)))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 (x <= -7.2e+134) {
		tmp = x * ((y * 0.5) / a_m);
	} else if (x <= -2.5e+83) {
		tmp = (t * -4.5) / (a_m / z);
	} else if ((x <= -1.05e-29) || !(x <= 2.5e+27)) {
		tmp = (x / a_m) * (y * 0.5);
	} else {
		tmp = (z * t) * (-4.5 / 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.
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 (x <= (-7.2d+134)) then
        tmp = x * ((y * 0.5d0) / a_m)
    else if (x <= (-2.5d+83)) then
        tmp = (t * (-4.5d0)) / (a_m / z)
    else if ((x <= (-1.05d-29)) .or. (.not. (x <= 2.5d+27))) then
        tmp = (x / a_m) * (y * 0.5d0)
    else
        tmp = (z * t) * ((-4.5d0) / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if (x <= -7.2e+134) {
		tmp = x * ((y * 0.5) / a_m);
	} else if (x <= -2.5e+83) {
		tmp = (t * -4.5) / (a_m / z);
	} else if ((x <= -1.05e-29) || !(x <= 2.5e+27)) {
		tmp = (x / a_m) * (y * 0.5);
	} else {
		tmp = (z * t) * (-4.5 / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if x <= -7.2e+134:
		tmp = x * ((y * 0.5) / a_m)
	elif x <= -2.5e+83:
		tmp = (t * -4.5) / (a_m / z)
	elif (x <= -1.05e-29) or not (x <= 2.5e+27):
		tmp = (x / a_m) * (y * 0.5)
	else:
		tmp = (z * t) * (-4.5 / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (x <= -7.2e+134)
		tmp = Float64(x * Float64(Float64(y * 0.5) / a_m));
	elseif (x <= -2.5e+83)
		tmp = Float64(Float64(t * -4.5) / Float64(a_m / z));
	elseif ((x <= -1.05e-29) || !(x <= 2.5e+27))
		tmp = Float64(Float64(x / a_m) * Float64(y * 0.5));
	else
		tmp = Float64(Float64(z * t) * Float64(-4.5 / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if (x <= -7.2e+134)
		tmp = x * ((y * 0.5) / a_m);
	elseif (x <= -2.5e+83)
		tmp = (t * -4.5) / (a_m / z);
	elseif ((x <= -1.05e-29) || ~((x <= 2.5e+27)))
		tmp = (x / a_m) * (y * 0.5);
	else
		tmp = (z * t) * (-4.5 / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[x, -7.2e+134], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e+83], N[(N[(t * -4.5), $MachinePrecision] / N[(a$95$m / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.05e-29], N[Not[LessEqual[x, 2.5e+27]], $MachinePrecision]], N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(z * t), $MachinePrecision] * N[(-4.5 / a$95$m), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]

Derivation

1. Split input into 4 regimes

2. if x < -7.19999999999999976e134

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 74.8%

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

      1. *-commutative 74.8%

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

      2. associate-/l* 80.4%

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

      3. associate-*r* 80.4%

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

      4. *-commutative 80.4%

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

      5. associate-*r/ 80.4%

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

   5. Simplified 80.4%

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

   if -7.19999999999999976e134 < x < -2.50000000000000014e83

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 52.2%

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

      1. associate-/l* 52.0%

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

      2. associate-*r* 51.9%

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

      3. clear-num 51.9%

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

      4. un-div-inv 51.6%

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

      5. *-commutative 51.6%

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

   5. Applied egg-rr 51.6%

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

   if -2.50000000000000014e83 < x < -1.04999999999999995e-29 or 2.4999999999999999e27 < x

   1. Initial program 80.6%

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

   3. Taylor expanded in x around inf 49.1%

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

      1. times-frac 62.1%

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

      2. div-inv 62.1%

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

      3. metadata-eval 62.1%

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

   5. Applied egg-rr 62.1%

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

   if -1.04999999999999995e-29 < x < 2.4999999999999999e27

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0 69.7%

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

      1. associate-/l* 69.9%

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

      2. associate-*r* 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-*l/ 69.7%

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

      5. *-commutative 69.7%

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

   5. Applied egg-rr 69.7%

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

      1. associate-*r* 69.7%

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

      2. associate-/l* 69.8%

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

      3. *-commutative 69.8%

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

   7. Applied egg-rr 69.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-29} \lor \neg \left(x \leq 2.5 \cdot 10^{+27}\right):\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot \frac{-4.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a\_m} \cdot \left(y \cdot 0.5\right) - 4.5 \cdot \left(t \cdot \frac{z}{a\_m}\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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+73)
    (/ (- (* x y) (* z (* t 9.0))) (* a_m 2.0))
    (- (* (/ x a_m) (* y 0.5)) (* 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);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((a_m * 2.0) <= 1e+73) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x / a_m) * (y * 0.5)) - (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.
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) <= 1d+73) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = ((x / a_m) * (y * 0.5d0)) - (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;
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) <= 1e+73) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x / a_m) * (y * 0.5)) - (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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (a_m * 2.0) <= 1e+73:
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0)
	else:
		tmp = ((x / a_m) * (y * 0.5)) - (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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+73)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(Float64(x / a_m) * Float64(y * 0.5)) - 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((a_m * 2.0) <= 1e+73)
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	else
		tmp = ((x / a_m) * (y * 0.5)) - (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.
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+73], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $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 #s(literal 2 binary64)) < 9.99999999999999983e72

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 93.6%

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

      1. associate-*r* 93.6%

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

      2. *-commutative 93.6%

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

      3. *-commutative 93.6%

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

   5. Simplified 93.6%

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

   if 9.99999999999999983e72 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 75.1%

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

   3. Taylor expanded in z around 0 75.0%

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

      1. associate-*r* 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

   5. Simplified 75.1%

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

      1. div-sub 75.0%

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

      2. times-frac 86.3%

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

      3. div-inv 86.3%

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

      4. metadata-eval 86.3%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. times-frac 86.2%

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

      8. associate-/l* 92.7%

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

      9. metadata-eval 92.7%

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

   7. Applied egg-rr 92.7%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(y \cdot 0.5\right) - \left(t \cdot \frac{z}{a}\right) \cdot 4.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right) - 4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;a\_m \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a\_m} \cdot \left(y \cdot 0.5\right) - \frac{z}{a\_m} \cdot \left(t \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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+73)
    (/ (- (* x y) (* z (* t 9.0))) (* a_m 2.0))
    (- (* (/ x a_m) (* y 0.5)) (* (/ z a_m) (* t 4.5))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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+73) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x / a_m) * (y * 0.5)) - ((z / a_m) * (t * 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.
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) <= 1d+73) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = ((x / a_m) * (y * 0.5d0)) - ((z / a_m) * (t * 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;
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) <= 1e+73) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = ((x / a_m) * (y * 0.5)) - ((z / a_m) * (t * 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (a_m * 2.0) <= 1e+73:
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0)
	else:
		tmp = ((x / a_m) * (y * 0.5)) - ((z / a_m) * (t * 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(a_m * 2.0) <= 1e+73)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(Float64(Float64(x / a_m) * Float64(y * 0.5)) - Float64(Float64(z / a_m) * Float64(t * 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((a_m * 2.0) <= 1e+73)
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	else
		tmp = ((x / a_m) * (y * 0.5)) - ((z / a_m) * (t * 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.
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+73], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a$95$m), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(z / a$95$m), $MachinePrecision] * N[(t * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 9.99999999999999983e72

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 93.6%

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

      1. associate-*r* 93.6%

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

      2. *-commutative 93.6%

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

      3. *-commutative 93.6%

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

   5. Simplified 93.6%

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

   if 9.99999999999999983e72 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 75.1%

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

   3. Taylor expanded in z around 0 75.0%

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

      1. associate-*r* 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

   5. Simplified 75.1%

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

      1. div-sub 75.0%

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

      2. times-frac 86.3%

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

      3. div-inv 86.3%

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

      4. metadata-eval 86.3%

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

      5. associate-*r* 86.3%

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

      6. *-commutative 86.3%

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

      7. times-frac 86.2%

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

      8. associate-/l* 92.7%

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

      9. metadata-eval 92.7%

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

   7. Applied egg-rr 92.7%

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

   8. Taylor expanded in t around 0 86.2%

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

      1. associate-*r/ 92.7%

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

      2. associate-*r* 92.9%

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

      3. *-commutative 92.9%

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

      4. *-commutative 92.9%

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

   10. Simplified 92.9%

       \[\leadsto \frac{x}{a} \cdot \left(y \cdot 0.5\right) - \color{blue}{\frac{z}{a} \cdot \left(t \cdot 4.5\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+73}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \left(y \cdot 0.5\right) - \frac{z}{a} \cdot \left(t \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a\_m}\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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 (<= (* x y) 2e+277)
    (/ (- (* x y) (* z (* t 9.0))) (* a_m 2.0))
    (* x (/ (* y 0.5) a_m)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
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 ((x * y) <= 2e+277) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = x * ((y * 0.5) / 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.
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 ((x * y) <= 2d+277) then
        tmp = ((x * y) - (z * (t * 9.0d0))) / (a_m * 2.0d0)
    else
        tmp = x * ((y * 0.5d0) / 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;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((x * y) <= 2e+277) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	} else {
		tmp = x * ((y * 0.5) / 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])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (x * y) <= 2e+277:
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0)
	else:
		tmp = x * ((y * 0.5) / 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])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(x * y) <= 2e+277)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a_m * 2.0));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / 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])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((x * y) <= 2e+277)
		tmp = ((x * y) - (z * (t * 9.0))) / (a_m * 2.0);
	else
		tmp = x * ((y * 0.5) / 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.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(x * y), $MachinePrecision], 2e+277], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 2.00000000000000001e277

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 94.1%

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

      1. associate-*r* 94.1%

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

      2. *-commutative 94.1%

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

      3. *-commutative 94.1%

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

   5. Simplified 94.1%

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

   if 2.00000000000000001e277 < (*.f64 x y)

   1. Initial program 50.9%

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

   3. Taylor expanded in x around inf 50.9%

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

      1. *-commutative 50.9%

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

      2. associate-/l* 99.8%

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

      3. associate-*r* 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r/ 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+277}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.3% accurate, 1.9× speedup

Math

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

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
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);
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.
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;
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])
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])
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])){:}
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.
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 90.2%

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

3. Taylor expanded in x around 0 54.3%

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

   1. associate-/l* 54.9%

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

5. Applied egg-rr 54.9%

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

6. Final simplification 54.9%

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

Developer target: 94.5% 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 2024071 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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