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

Percentage Accurate: 91.1% → 93.3%

Time: 11.4s

Alternatives: 11

Speedup: 0.7×

• 28.4% 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: 91.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x \cdot 0.5, \frac{z}{a} \cdot \left(-4.5 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -1e-39)
   (fma (/ y a) (* x 0.5) (* (/ z a) (* -4.5 t)))
   (* (fma x y (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -1e-39) {
		tmp = fma((y / a), (x * 0.5), ((z / a) * (-4.5 * t)));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -1e-39)
		tmp = fma(Float64(y / a), Float64(x * 0.5), Float64(Float64(z / a) * Float64(-4.5 * t)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -1e-39], N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision] + N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -9.99999999999999929e-40

   1. Initial program 76.3%

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

      1. associate-*l* 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in x around 0 76.4%

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

      1. fma-def 76.3%

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

      2. associate-/l* 83.0%

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

      3. associate-/l* 95.1%

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

      4. associate-/r/ 97.2%

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

   6. Simplified 97.2%

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

      1. fma-udef 97.2%

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

      2. div-inv 97.2%

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

      3. clear-num 97.2%

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

      4. *-commutative 97.2%

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

      5. *-commutative 97.2%

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

      6. associate-*l* 97.2%

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

      7. *-commutative 97.2%

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

      8. associate-*r* 97.0%

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

      9. div-inv 97.0%

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

      10. associate-*r* 97.0%

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

      11. associate-*r* 95.2%

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

      12. associate-/r/ 95.1%

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

      13. *-commutative 95.1%

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

      14. clear-num 95.2%

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

      15. *-commutative 95.2%

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

   8. Applied egg-rr 95.2%

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

      1. +-commutative 95.2%

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

      2. *-un-lft-identity 95.2%

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

      3. associate-*l/ 95.2%

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

      4. fma-def 95.2%

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

      5. associate-*l/ 95.2%

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

      6. *-un-lft-identity 95.2%

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

   10. Applied egg-rr 95.2%

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

   if -9.99999999999999929e-40 < (*.f64 a 2)

   1. Initial program 95.3%

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

      1. associate-*l* 95.2%

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

   3. Simplified 95.2%

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

      1. div-inv 95.2%

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

      2. fma-neg 95.8%

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

      3. distribute-rgt-neg-in 95.8%

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

      4. *-commutative 95.8%

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

      5. distribute-rgt-neg-in 95.8%

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

      6. metadata-eval 95.8%

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

      7. *-commutative 95.8%

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

      8. associate-/r* 96.3%

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

      9. metadata-eval 96.3%

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

   5. Applied egg-rr 96.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x \cdot 0.5, \frac{z}{a} \cdot \left(-4.5 \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -100000000.0)
   (+ (* (/ z a) (* -4.5 t)) (* (/ y a) (* x 0.5)))
   (* (fma x y (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -100000000.0) {
		tmp = ((z / a) * (-4.5 * t)) + ((y / a) * (x * 0.5));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -100000000.0)
		tmp = Float64(Float64(Float64(z / a) * Float64(-4.5 * t)) + Float64(Float64(y / a) * Float64(x * 0.5)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -100000000.0], N[(N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -1e8

   1. Initial program 74.9%

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

      1. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 74.9%

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

      1. fma-def 74.9%

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

      2. associate-/l* 81.9%

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

      3. associate-/l* 94.9%

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

      4. associate-/r/ 97.1%

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

   6. Simplified 97.1%

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

      1. fma-udef 97.1%

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

      2. div-inv 97.0%

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

      3. clear-num 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. associate-*l* 97.0%

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

      7. *-commutative 97.0%

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

      8. associate-*r* 96.9%

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

      9. div-inv 96.8%

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

      10. associate-*r* 96.8%

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

      11. associate-*r* 94.9%

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

      12. associate-/r/ 94.8%

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

      13. *-commutative 94.8%

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

      14. clear-num 94.9%

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

      15. *-commutative 94.9%

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

   8. Applied egg-rr 94.9%

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

   if -1e8 < (*.f64 a 2)

   1. Initial program 95.4%

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

      1. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

      1. div-inv 95.3%

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

      2. fma-neg 95.9%

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

      3. distribute-rgt-neg-in 95.9%

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

      4. *-commutative 95.9%

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

      5. distribute-rgt-neg-in 95.9%

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

      6. metadata-eval 95.9%

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

      7. *-commutative 95.9%

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

      8. associate-/r* 96.4%

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

      9. metadata-eval 96.4%

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

   5. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 3: 94.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+275}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 10^{+211}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{1}{a}\right) \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -2e+275)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* y x) 1e+211)
     (/ (- (* y x) (* z (* t 9.0))) (* a 2.0))
     (* (* y (/ 1.0 a)) (* x 0.5)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+275) {
		tmp = 0.5 * (x / (a / y));
	} else if ((y * x) <= 1e+211) {
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (1.0 / a)) * (x * 0.5);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-2d+275)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((y * x) <= 1d+211) then
        tmp = ((y * x) - (z * (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = (y * (1.0d0 / a)) * (x * 0.5d0)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+275) {
		tmp = 0.5 * (x / (a / y));
	} else if ((y * x) <= 1e+211) {
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (1.0 / a)) * (x * 0.5);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -2e+275:
		tmp = 0.5 * (x / (a / y))
	elif (y * x) <= 1e+211:
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = (y * (1.0 / a)) * (x * 0.5)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= -2e+275)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(y * x) <= 1e+211)
		tmp = Float64(Float64(Float64(y * x) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(1.0 / a)) * Float64(x * 0.5));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -2e+275)
		tmp = 0.5 * (x / (a / y));
	elseif ((y * x) <= 1e+211)
		tmp = ((y * x) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = (y * (1.0 / a)) * (x * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -2e+275], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+211], N[(N[(N[(y * x), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999992e275

   1. Initial program 54.9%

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

      1. associate-*l* 54.9%

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

   3. Simplified 54.9%

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

   4. Taylor expanded in x around inf 54.9%

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

      1. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

   if -1.99999999999999992e275 < (*.f64 x y) < 9.9999999999999996e210

   1. Initial program 95.5%

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

      1. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

   if 9.9999999999999996e210 < (*.f64 x y)

   1. Initial program 70.4%

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

      1. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in x around inf 74.3%

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

      1. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

      1. associate-*r/ 99.4%

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

      2. clear-num 99.4%

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

   8. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{y}}{0.5 \cdot x}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 99.5%

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

   10. Simplified 99.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot \left(0.5 \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-/r/ 99.5%

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

   12. Applied egg-rr 99.5%

       \[\leadsto \color{blue}{\left(\frac{1}{a} \cdot y\right)} \cdot \left(0.5 \cdot x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+275}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 10^{+211}:\\ \;\;\;\;\frac{y \cdot x - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{1}{a}\right) \cdot \left(x \cdot 0.5\right)\\ \end{array} \]

Alternative 4: 94.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+275}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 10^{+211}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{1}{a}\right) \cdot \left(x \cdot 0.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -2e+275)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* y x) 1e+211)
     (/ (- (* y x) (* t (* z 9.0))) (* a 2.0))
     (* (* y (/ 1.0 a)) (* x 0.5)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+275) {
		tmp = 0.5 * (x / (a / y));
	} else if ((y * x) <= 1e+211) {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (1.0 / a)) * (x * 0.5);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-2d+275)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((y * x) <= 1d+211) then
        tmp = ((y * x) - (t * (z * 9.0d0))) / (a * 2.0d0)
    else
        tmp = (y * (1.0d0 / a)) * (x * 0.5d0)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -2e+275) {
		tmp = 0.5 * (x / (a / y));
	} else if ((y * x) <= 1e+211) {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (1.0 / a)) * (x * 0.5);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -2e+275:
		tmp = 0.5 * (x / (a / y))
	elif (y * x) <= 1e+211:
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = (y * (1.0 / a)) * (x * 0.5)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= -2e+275)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(y * x) <= 1e+211)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(1.0 / a)) * Float64(x * 0.5));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -2e+275)
		tmp = 0.5 * (x / (a / y));
	elseif ((y * x) <= 1e+211)
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = (y * (1.0 / a)) * (x * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -2e+275], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1e+211], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.99999999999999992e275

   1. Initial program 54.9%

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

      1. associate-*l* 54.9%

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

   3. Simplified 54.9%

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

   4. Taylor expanded in x around inf 54.9%

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

      1. associate-/l* 92.1%

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

   6. Simplified 92.1%

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

   if -1.99999999999999992e275 < (*.f64 x y) < 9.9999999999999996e210

   1. Initial program 95.5%

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

   if 9.9999999999999996e210 < (*.f64 x y)

   1. Initial program 70.4%

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

      1. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

   4. Taylor expanded in x around inf 74.3%

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

      1. associate-/l* 99.4%

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

   6. Simplified 99.4%

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

      1. associate-*r/ 99.4%

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

      2. clear-num 99.4%

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

   8. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{y}}{0.5 \cdot x}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 99.5%

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

   10. Simplified 99.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot \left(0.5 \cdot x\right)} \]
   11. Step-by-step derivation

       1. associate-/r/ 99.5%

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

   12. Applied egg-rr 99.5%

       \[\leadsto \color{blue}{\left(\frac{1}{a} \cdot y\right)} \cdot \left(0.5 \cdot x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+275}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \cdot x \leq 10^{+211}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \frac{1}{a}\right) \cdot \left(x \cdot 0.5\right)\\ \end{array} \]

Alternative 5: 66.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{z \cdot t}{a}\\ t_2 := 0.5 \cdot \left(\frac{y}{a} \cdot x\right)\\ \mathbf{if}\;x \leq -3 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-55} \lor \neg \left(x \leq 2.7 \cdot 10^{-118}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ (* z t) a))) (t_2 (* 0.5 (* (/ y a) x))))
   (if (<= x -3e+156)
     t_2
     (if (<= x -9.4e+147)
       t_1
       (if (<= x -9.8e+87)
         t_2
         (if (<= x -1.7e-40)
           (* -4.5 (/ t (/ a z)))
           (if (or (<= x -5.2e-55) (not (<= x 2.7e-118))) t_2 t_1)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = 0.5 * ((y / a) * x);
	double tmp;
	if (x <= -3e+156) {
		tmp = t_2;
	} else if (x <= -9.4e+147) {
		tmp = t_1;
	} else if (x <= -9.8e+87) {
		tmp = t_2;
	} else if (x <= -1.7e-40) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x <= -5.2e-55) || !(x <= 2.7e-118)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.5d0) * ((z * t) / a)
    t_2 = 0.5d0 * ((y / a) * x)
    if (x <= (-3d+156)) then
        tmp = t_2
    else if (x <= (-9.4d+147)) then
        tmp = t_1
    else if (x <= (-9.8d+87)) then
        tmp = t_2
    else if (x <= (-1.7d-40)) then
        tmp = (-4.5d0) * (t / (a / z))
    else if ((x <= (-5.2d-55)) .or. (.not. (x <= 2.7d-118))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = 0.5 * ((y / a) * x);
	double tmp;
	if (x <= -3e+156) {
		tmp = t_2;
	} else if (x <= -9.4e+147) {
		tmp = t_1;
	} else if (x <= -9.8e+87) {
		tmp = t_2;
	} else if (x <= -1.7e-40) {
		tmp = -4.5 * (t / (a / z));
	} else if ((x <= -5.2e-55) || !(x <= 2.7e-118)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = -4.5 * ((z * t) / a)
	t_2 = 0.5 * ((y / a) * x)
	tmp = 0
	if x <= -3e+156:
		tmp = t_2
	elif x <= -9.4e+147:
		tmp = t_1
	elif x <= -9.8e+87:
		tmp = t_2
	elif x <= -1.7e-40:
		tmp = -4.5 * (t / (a / z))
	elif (x <= -5.2e-55) or not (x <= 2.7e-118):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(Float64(z * t) / a))
	t_2 = Float64(0.5 * Float64(Float64(y / a) * x))
	tmp = 0.0
	if (x <= -3e+156)
		tmp = t_2;
	elseif (x <= -9.4e+147)
		tmp = t_1;
	elseif (x <= -9.8e+87)
		tmp = t_2;
	elseif (x <= -1.7e-40)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	elseif ((x <= -5.2e-55) || !(x <= 2.7e-118))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * ((z * t) / a);
	t_2 = 0.5 * ((y / a) * x);
	tmp = 0.0;
	if (x <= -3e+156)
		tmp = t_2;
	elseif (x <= -9.4e+147)
		tmp = t_1;
	elseif (x <= -9.8e+87)
		tmp = t_2;
	elseif (x <= -1.7e-40)
		tmp = -4.5 * (t / (a / z));
	elseif ((x <= -5.2e-55) || ~((x <= 2.7e-118)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3e+156], t$95$2, If[LessEqual[x, -9.4e+147], t$95$1, If[LessEqual[x, -9.8e+87], t$95$2, If[LessEqual[x, -1.7e-40], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.2e-55], N[Not[LessEqual[x, 2.7e-118]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3e156 or -9.4000000000000006e147 < x < -9.79999999999999943e87 or -1.69999999999999992e-40 < x < -5.1999999999999998e-55 or 2.69999999999999994e-118 < x

   1. Initial program 87.4%

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

      1. associate-*l* 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around inf 61.5%

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

      1. associate-/l* 68.2%

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

   6. Simplified 68.2%

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

      1. div-inv 68.1%

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

      2. clear-num 68.2%

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

   8. Applied egg-rr 68.2%

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

   if -3e156 < x < -9.4000000000000006e147 or -5.1999999999999998e-55 < x < 2.69999999999999994e-118

   1. Initial program 94.7%

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

      1. associate-*l* 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around 0 72.7%

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

   if -9.79999999999999943e87 < x < -1.69999999999999992e-40

   1. Initial program 77.8%

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

      1. associate-*l* 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around 0 58.5%

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

      1. associate-/l* 74.0%

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

   6. Simplified 74.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+156}:\\ \;\;\;\;0.5 \cdot \left(\frac{y}{a} \cdot x\right)\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{+147}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{+87}:\\ \;\;\;\;0.5 \cdot \left(\frac{y}{a} \cdot x\right)\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-55} \lor \neg \left(x \leq 2.7 \cdot 10^{-118}\right):\\ \;\;\;\;0.5 \cdot \left(\frac{y}{a} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 6: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -100000000.0)
   (+ (* (/ z a) (* -4.5 t)) (* (/ y a) (* x 0.5)))
   (/ (- (* y x) (* t (* z 9.0))) (* a 2.0))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -100000000.0) {
		tmp = ((z / a) * (-4.5 * t)) + ((y / a) * (x * 0.5));
	} else {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 2.0d0) <= (-100000000.0d0)) then
        tmp = ((z / a) * ((-4.5d0) * t)) + ((y / a) * (x * 0.5d0))
    else
        tmp = ((y * x) - (t * (z * 9.0d0))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -100000000.0) {
		tmp = ((z / a) * (-4.5 * t)) + ((y / a) * (x * 0.5));
	} else {
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= -100000000.0:
		tmp = ((z / a) * (-4.5 * t)) + ((y / a) * (x * 0.5))
	else:
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -100000000.0)
		tmp = Float64(Float64(Float64(z / a) * Float64(-4.5 * t)) + Float64(Float64(y / a) * Float64(x * 0.5)));
	else
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 2.0) <= -100000000.0)
		tmp = ((z / a) * (-4.5 * t)) + ((y / a) * (x * 0.5));
	else
		tmp = ((y * x) - (t * (z * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -100000000.0], N[(N[(N[(z / a), $MachinePrecision] * N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -1e8

   1. Initial program 74.9%

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

      1. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

   4. Taylor expanded in x around 0 74.9%

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

      1. fma-def 74.9%

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

      2. associate-/l* 81.9%

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

      3. associate-/l* 94.9%

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

      4. associate-/r/ 97.1%

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

   6. Simplified 97.1%

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

      1. fma-udef 97.1%

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

      2. div-inv 97.0%

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

      3. clear-num 97.1%

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

      4. *-commutative 97.1%

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

      5. *-commutative 97.1%

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

      6. associate-*l* 97.0%

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

      7. *-commutative 97.0%

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

      8. associate-*r* 96.9%

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

      9. div-inv 96.8%

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

      10. associate-*r* 96.8%

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

      11. associate-*r* 94.9%

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

      12. associate-/r/ 94.8%

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

      13. *-commutative 94.8%

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

      14. clear-num 94.9%

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

      15. *-commutative 94.9%

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

   8. Applied egg-rr 94.9%

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

   if -1e8 < (*.f64 a 2)

   1. Initial program 95.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\frac{z}{a} \cdot \left(-4.5 \cdot t\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \cdot x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{1}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -4e-7)
   (* 0.5 (* y (/ x a)))
   (if (<= (* y x) 1.5e+33)
     (* -4.5 (/ (* z t) a))
     (* (* x 0.5) (/ 1.0 (/ a y))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -4e-7) {
		tmp = 0.5 * (y * (x / a));
	} else if ((y * x) <= 1.5e+33) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (x * 0.5) * (1.0 / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-4d-7)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((y * x) <= 1.5d+33) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (x * 0.5d0) * (1.0d0 / (a / y))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -4e-7) {
		tmp = 0.5 * (y * (x / a));
	} else if ((y * x) <= 1.5e+33) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (x * 0.5) * (1.0 / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -4e-7:
		tmp = 0.5 * (y * (x / a))
	elif (y * x) <= 1.5e+33:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = (x * 0.5) * (1.0 / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= -4e-7)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (Float64(y * x) <= 1.5e+33)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(Float64(x * 0.5) * Float64(1.0 / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -4e-7)
		tmp = 0.5 * (y * (x / a));
	elseif ((y * x) <= 1.5e+33)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = (x * 0.5) * (1.0 / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -4e-7], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1.5e+33], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] * N[(1.0 / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.9999999999999998e-7

   1. Initial program 79.6%

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

      1. associate-*l* 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around inf 63.9%

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

      1. associate-/l* 77.6%

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

      2. associate-/r/ 75.3%

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

   6. Simplified 75.3%

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

   if -3.9999999999999998e-7 < (*.f64 x y) < 1.49999999999999992e33

   1. Initial program 96.0%

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

      1. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around 0 77.4%

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

   if 1.49999999999999992e33 < (*.f64 x y)

   1. Initial program 83.5%

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

      1. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around inf 68.4%

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

      1. associate-/l* 72.0%

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

   6. Simplified 72.0%

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

      1. associate-*r/ 72.0%

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

      2. clear-num 72.0%

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

   8. Applied egg-rr 72.0%

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{a}{y}}{0.5 \cdot x}}} \]
   9. Step-by-step derivation

      1. associate-/r/ 71.6%

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

   10. Simplified 71.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot \left(0.5 \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \cdot x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 0.5\right) \cdot \frac{1}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 65.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+176}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;0.5 \cdot \left(\frac{y}{a} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+176)
   (* -4.5 (* z (/ t a)))
   (if (<= z -2e+80)
     (* 0.5 (* y (/ x a)))
     (if (<= z -1.95e-12)
       (* -4.5 (/ (* z t) a))
       (if (<= z 1.8e-44) (* 0.5 (* (/ y a) x)) (* -4.5 (/ t (/ a z))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+176) {
		tmp = -4.5 * (z * (t / a));
	} else if (z <= -2e+80) {
		tmp = 0.5 * (y * (x / a));
	} else if (z <= -1.95e-12) {
		tmp = -4.5 * ((z * t) / a);
	} else if (z <= 1.8e-44) {
		tmp = 0.5 * ((y / a) * x);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+176)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (z <= (-2d+80)) then
        tmp = 0.5d0 * (y * (x / a))
    else if (z <= (-1.95d-12)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (z <= 1.8d-44) then
        tmp = 0.5d0 * ((y / a) * x)
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+176) {
		tmp = -4.5 * (z * (t / a));
	} else if (z <= -2e+80) {
		tmp = 0.5 * (y * (x / a));
	} else if (z <= -1.95e-12) {
		tmp = -4.5 * ((z * t) / a);
	} else if (z <= 1.8e-44) {
		tmp = 0.5 * ((y / a) * x);
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+176:
		tmp = -4.5 * (z * (t / a))
	elif z <= -2e+80:
		tmp = 0.5 * (y * (x / a))
	elif z <= -1.95e-12:
		tmp = -4.5 * ((z * t) / a)
	elif z <= 1.8e-44:
		tmp = 0.5 * ((y / a) * x)
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+176)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (z <= -2e+80)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (z <= -1.95e-12)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (z <= 1.8e-44)
		tmp = Float64(0.5 * Float64(Float64(y / a) * x));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+176)
		tmp = -4.5 * (z * (t / a));
	elseif (z <= -2e+80)
		tmp = 0.5 * (y * (x / a));
	elseif (z <= -1.95e-12)
		tmp = -4.5 * ((z * t) / a);
	elseif (z <= 1.8e-44)
		tmp = 0.5 * ((y / a) * x);
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+176], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2e+80], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-12], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-44], N[(0.5 * N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2e176

   1. Initial program 85.5%

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

      1. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around 0 81.8%

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

      1. fma-def 81.8%

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

      2. associate-/l* 85.5%

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

      3. associate-/l* 82.3%

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

      4. associate-/r/ 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in t around inf 82.5%

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

      1. associate-*l/ 89.3%

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

   9. Simplified 89.3%

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

   if -2e176 < z < -2e80

   1. Initial program 94.0%

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

      1. associate-*l* 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in x around inf 57.4%

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

      1. associate-/l* 63.1%

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

      2. associate-/r/ 57.2%

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

   6. Simplified 57.2%

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

   if -2e80 < z < -1.94999999999999997e-12

   1. Initial program 95.0%

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

      1. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 76.5%

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

   if -1.94999999999999997e-12 < z < 1.7999999999999999e-44

   1. Initial program 90.2%

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

      1. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in x around inf 59.5%

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

      1. associate-/l* 61.8%

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

   6. Simplified 61.8%

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

      1. div-inv 61.1%

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

      2. clear-num 61.2%

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

   8. Applied egg-rr 61.2%

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

   if 1.7999999999999999e-44 < z

   1. Initial program 85.5%

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

      1. associate-*l* 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around 0 51.2%

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

      1. associate-/l* 56.1%

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

   6. Simplified 56.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+176}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;0.5 \cdot \left(\frac{y}{a} \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 73.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \cdot x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y x) -4e-7)
   (* 0.5 (* y (/ x a)))
   (if (<= (* y x) 1.5e+33) (* -4.5 (/ (* z t) a)) (* 0.5 (/ x (/ a y))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -4e-7) {
		tmp = 0.5 * (y * (x / a));
	} else if ((y * x) <= 1.5e+33) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y * x) <= (-4d-7)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((y * x) <= 1.5d+33) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * x) <= -4e-7) {
		tmp = 0.5 * (y * (x / a));
	} else if ((y * x) <= 1.5e+33) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y * x) <= -4e-7:
		tmp = 0.5 * (y * (x / a))
	elif (y * x) <= 1.5e+33:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * x) <= -4e-7)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (Float64(y * x) <= 1.5e+33)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * x) <= -4e-7)
		tmp = 0.5 * (y * (x / a));
	elseif ((y * x) <= 1.5e+33)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * x), $MachinePrecision], -4e-7], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1.5e+33], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.9999999999999998e-7

   1. Initial program 79.6%

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

      1. associate-*l* 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in x around inf 63.9%

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

      1. associate-/l* 77.6%

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

      2. associate-/r/ 75.3%

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

   6. Simplified 75.3%

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

   if -3.9999999999999998e-7 < (*.f64 x y) < 1.49999999999999992e33

   1. Initial program 96.0%

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

      1. associate-*l* 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in x around 0 77.4%

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

   if 1.49999999999999992e33 < (*.f64 x y)

   1. Initial program 83.5%

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

      1. associate-*l* 83.4%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in x around inf 68.4%

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

      1. associate-/l* 72.0%

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

   6. Simplified 72.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \cdot x \leq 1.5 \cdot 10^{+33}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 51.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \left(\frac{z}{a} \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.8e-37) (* -4.5 (* (/ z a) t)) (* -4.5 (/ (* z t) a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e-37) {
		tmp = -4.5 * ((z / a) * t);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-4.8d-37)) then
        tmp = (-4.5d0) * ((z / a) * t)
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e-37) {
		tmp = -4.5 * ((z / a) * t);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.8e-37:
		tmp = -4.5 * ((z / a) * t)
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.8e-37)
		tmp = Float64(-4.5 * Float64(Float64(z / a) * t));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.8e-37)
		tmp = -4.5 * ((z / a) * t);
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.8e-37], N[(-4.5 * N[(N[(z / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999982e-37

   1. Initial program 83.6%

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

      1. associate-*l* 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around 0 38.5%

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

      1. associate-/l* 41.8%

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

   6. Simplified 41.8%

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

   7. Taylor expanded in t around 0 38.5%

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

      1. associate-*r/ 42.9%

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

   9. Simplified 42.9%

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

   if -4.79999999999999982e-37 < x

   1. Initial program 91.5%

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

      1. associate-*l* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 55.0%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-37}:\\ \;\;\;\;-4.5 \cdot \left(\frac{z}{a} \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 11: 51.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

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

   1. associate-*l* 88.9%

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

3. Simplified 88.9%

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

4. Taylor expanded in x around 0 49.7%

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

   1. associate-/l* 49.2%

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

6. Simplified 49.2%

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

7. Taylor expanded in t around 0 49.7%

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

   1. associate-*r/ 48.9%

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

9. Simplified 48.9%

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

10. Final simplification 48.9%

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

Developer target: 93.7% accurate, 0.7× 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 2023274 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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