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

Percentage Accurate: 90.9% → 96.5%

Time: 10.2s

Alternatives: 11

Speedup: 0.6×

• Unsound rule application detected in e-graph. Results may not be sound.

• 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: 90.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right) + \left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+287)))
     (+ (* -4.5 (* z (/ t a))) (* (* x (/ y a)) 0.5))
     (/ (fma x y (* z (* t -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 t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+287)) {
		tmp = (-4.5 * (z * (t / a))) + ((x * (y / a)) * 0.5);
	} else {
		tmp = fma(x, y, (z * (t * -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)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+287))
		tmp = Float64(Float64(-4.5 * Float64(z * Float64(t / a))) + Float64(Float64(x * Float64(y / a)) * 0.5));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+287]], $MachinePrecision]], N[(N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 2.0000000000000002e287 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 59.3%

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

      1. sub-neg 59.3%

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

      2. +-commutative 59.3%

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

      3. neg-sub0 59.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 59.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 59.3%

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

      6. neg-mul-1 59.3%

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

      7. associate-/l* 59.3%

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

      8. associate-/r/ 59.3%

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

      9. *-commutative 59.3%

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

      10. sub-neg 59.3%

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

      11. +-commutative 59.3%

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

      12. neg-sub0 59.3%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 59.3%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 59.3%

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

      15. distribute-lft-neg-out 59.3%

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

      16. distribute-rgt-neg-in 59.3%

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

   3. Simplified 62.7%

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

      1. clear-num 62.7%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

      2. div-inv 62.7%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

      3. metadata-eval 62.7%

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

      4. div-inv 62.7%

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

      5. *-commutative 62.7%

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

      6. metadata-eval 62.7%

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

      7. distribute-lft-neg-in 62.7%

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

      8. distribute-rgt-neg-in 62.7%

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

      9. fma-neg 59.3%

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

      10. div-sub 56.0%

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

      11. frac-sub 54.9%

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

      12. associate-*r* 54.9%

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

      13. *-commutative 54.9%

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

      14. swap-sqr 54.9%

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

      15. metadata-eval 54.9%

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

   5. Applied egg-rr 54.9%

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

   6. Taylor expanded in x around 0 56.0%

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

      1. fma-def 56.0%

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

      2. associate-/l* 71.4%

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

      3. associate-*r/ 71.4%

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

      4. associate-*r* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-*l/ 86.7%

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

      7. *-commutative 86.7%

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

      8. associate-*r/ 86.7%

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

      9. associate-*l* 86.7%

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

   8. Simplified 86.7%

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

      1. fma-udef 86.7%

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

      2. associate-/r/ 83.4%

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

      3. *-commutative 83.4%

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

   10. Applied egg-rr 83.4%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 2.0000000000000002e287

   1. Initial program 97.7%

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

      1. div-sub 95.7%

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

      2. +-rgt-identity 95.7%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 97.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 97.7%

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

      5. fma-neg 97.7%

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

      6. associate-*l* 97.7%

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

      7. distribute-rgt-neg-in 97.7%

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

      8. *-commutative 97.7%

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

      9. distribute-rgt-neg-in 97.7%

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

      10. metadata-eval 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right) + \left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right) + \left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+287)))
     (+ (* -4.5 (* z (/ t a))) (* (* x (/ y a)) 0.5))
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+287)) {
		tmp = (-4.5 * (z * (t / a))) + ((x * (y / a)) * 0.5);
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+287)) {
		tmp = (-4.5 * (z * (t / a))) + ((x * (y / a)) * 0.5);
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+287):
		tmp = (-4.5 * (z * (t / a))) + ((x * (y / a)) * 0.5)
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+287))
		tmp = Float64(Float64(-4.5 * Float64(z * Float64(t / a))) + Float64(Float64(x * Float64(y / a)) * 0.5));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / 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)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+287)))
		tmp = (-4.5 * (z * (t / a))) + ((x * (y / a)) * 0.5);
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+287]], $MachinePrecision]], N[(N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 2.0000000000000002e287 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 59.3%

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

      1. sub-neg 59.3%

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

      2. +-commutative 59.3%

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

      3. neg-sub0 59.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 59.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 59.3%

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

      6. neg-mul-1 59.3%

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

      7. associate-/l* 59.3%

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

      8. associate-/r/ 59.3%

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

      9. *-commutative 59.3%

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

      10. sub-neg 59.3%

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

      11. +-commutative 59.3%

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

      12. neg-sub0 59.3%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 59.3%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 59.3%

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

      15. distribute-lft-neg-out 59.3%

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

      16. distribute-rgt-neg-in 59.3%

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

   3. Simplified 62.7%

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

      1. clear-num 62.7%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

      2. div-inv 62.7%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

      3. metadata-eval 62.7%

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

      4. div-inv 62.7%

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

      5. *-commutative 62.7%

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

      6. metadata-eval 62.7%

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

      7. distribute-lft-neg-in 62.7%

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

      8. distribute-rgt-neg-in 62.7%

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

      9. fma-neg 59.3%

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

      10. div-sub 56.0%

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

      11. frac-sub 54.9%

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

      12. associate-*r* 54.9%

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

      13. *-commutative 54.9%

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

      14. swap-sqr 54.9%

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

      15. metadata-eval 54.9%

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

   5. Applied egg-rr 54.9%

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

   6. Taylor expanded in x around 0 56.0%

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

      1. fma-def 56.0%

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

      2. associate-/l* 71.4%

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

      3. associate-*r/ 71.4%

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

      4. associate-*r* 71.4%

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

      5. *-commutative 71.4%

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

      6. associate-*l/ 86.7%

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

      7. *-commutative 86.7%

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

      8. associate-*r/ 86.7%

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

      9. associate-*l* 86.7%

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

   8. Simplified 86.7%

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

      1. fma-udef 86.7%

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

      2. associate-/r/ 83.4%

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

      3. *-commutative 83.4%

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

   10. Applied egg-rr 83.4%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 2.0000000000000002e287

   1. Initial program 97.7%

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

      1. associate-*l* 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+287}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right) + \left(x \cdot \frac{y}{a}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 3: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* -4.5 (* z (/ t a)))
     (if (<= t_1 2e+296)
       (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
       (* z (* -4.5 (/ t a)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.5 * (z * (t / a));
	} else if (t_1 <= 2e+296) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = z * (-4.5 * (t / a));
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -4.5 * (z * (t / a));
	} else if (t_1 <= 2e+296) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = z * (-4.5 * (t / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -4.5 * (z * (t / a))
	elif t_1 <= 2e+296:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = z * (-4.5 * (t / a))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (t_1 <= 2e+296)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(z * Float64(-4.5 * Float64(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)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -4.5 * (z * (t / a));
	elseif (t_1 <= 2e+296)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = z * (-4.5 * (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_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+296], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 49.7%

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

      1. div-sub 49.7%

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

      2. +-rgt-identity 49.7%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 49.7%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 49.7%

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

      5. fma-neg 49.7%

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

      6. associate-*l* 49.7%

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

      7. distribute-rgt-neg-in 49.7%

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

      8. *-commutative 49.7%

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

      9. distribute-rgt-neg-in 49.7%

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

      10. metadata-eval 49.7%

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

   3. Simplified 49.7%

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

   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* 87.9%

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

      2. associate-/r/ 88.0%

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

   6. Simplified 88.0%

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

   if -inf.0 < (*.f64 (*.f64 z 9) t) < 1.99999999999999996e296

   1. Initial program 94.2%

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

      1. associate-*l* 94.2%

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

   3. Simplified 94.2%

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

   if 1.99999999999999996e296 < (*.f64 (*.f64 z 9) t)

   1. Initial program 56.5%

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

      1. sub-neg 56.5%

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

      2. +-commutative 56.5%

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

      3. neg-sub0 56.5%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 56.5%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 56.5%

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

      6. neg-mul-1 56.5%

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

      7. associate-/l* 56.5%

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

      8. associate-/r/ 56.5%

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

      9. *-commutative 56.5%

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

      10. sub-neg 56.5%

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

      11. +-commutative 56.5%

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

      12. neg-sub0 56.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 56.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 56.5%

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

      15. distribute-lft-neg-out 56.5%

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

      16. distribute-rgt-neg-in 56.5%

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

   3. Simplified 67.9%

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

      1. *-commutative 67.9%

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

      2. metadata-eval 67.9%

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

      3. distribute-lft-neg-in 67.9%

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

      4. distribute-rgt-neg-in 67.9%

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

      5. fma-neg 56.5%

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

      6. associate-*r* 56.5%

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

      7. *-commutative 56.5%

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

   5. Applied egg-rr 56.5%

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

   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. *-commutative 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*r/ 94.3%

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

      4. associate-*l* 94.3%

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

   8. Simplified 94.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;\left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 4: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

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 (<= (* x y) (- INFINITY))
   (* x (* y (/ 0.5 a)))
   (if (<= (* x y) 2e+287)
     (* (- (* x y) (* (* z 9.0) t)) (/ 0.5 a))
     (* x (/ (* y 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 ((x * y) <= -((double) INFINITY)) {
		tmp = x * (y * (0.5 / a));
	} else if ((x * y) <= 2e+287) {
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / a);
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

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 * y) <= -Double.POSITIVE_INFINITY) {
		tmp = x * (y * (0.5 / a));
	} else if ((x * y) <= 2e+287) {
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / a);
	} else {
		tmp = x * ((y * 0.5) / 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 * y) <= -math.inf:
		tmp = x * (y * (0.5 / a))
	elif (x * y) <= 2e+287:
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / a)
	else:
		tmp = x * ((y * 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(x * y) <= Float64(-Inf))
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (Float64(x * y) <= 2e+287)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) * Float64(0.5 / a));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / 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 * y) <= -Inf)
		tmp = x * (y * (0.5 / a));
	elseif ((x * y) <= 2e+287)
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / a);
	else
		tmp = x * ((y * 0.5) / 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[N[(x * y), $MachinePrecision], (-Infinity)], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+287], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 69.9%

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

      1. div-sub 69.9%

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

      2. +-rgt-identity 69.9%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 69.9%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 69.9%

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

      5. fma-neg 69.9%

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

      6. associate-*l* 69.9%

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

      7. distribute-rgt-neg-in 69.9%

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

      8. *-commutative 69.9%

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

      9. distribute-rgt-neg-in 69.9%

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

      10. metadata-eval 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in x around inf 70.6%

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

      1. associate-*r/ 70.6%

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

      2. *-commutative 70.6%

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

      3. *-commutative 70.6%

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

      4. associate-/l* 70.6%

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

      5. *-commutative 70.6%

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

   6. Simplified 70.6%

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

      1. div-inv 70.6%

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

      2. metadata-eval 70.6%

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

      3. div-inv 70.6%

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

      4. *-commutative 70.6%

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

      5. metadata-eval 70.6%

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

      6. div-inv 70.6%

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

      7. clear-num 70.6%

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

      8. associate-*l* 95.5%

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

   8. Applied egg-rr 95.5%

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

   if -inf.0 < (*.f64 x y) < 2.0000000000000002e287

   1. Initial program 93.7%

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

      1. sub-neg 93.7%

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

      2. +-commutative 93.7%

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

      3. neg-sub0 93.7%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 93.7%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 93.7%

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

      6. neg-mul-1 93.7%

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

      7. associate-/l* 93.1%

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

      8. associate-/r/ 93.6%

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

      9. *-commutative 93.6%

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

      10. sub-neg 93.6%

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

      11. +-commutative 93.6%

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

      12. neg-sub0 93.6%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 93.6%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 93.6%

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

      15. distribute-lft-neg-out 93.6%

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

      16. distribute-rgt-neg-in 93.6%

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

   3. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. metadata-eval 93.6%

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

      3. distribute-lft-neg-in 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

      5. fma-neg 93.6%

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

      6. associate-*r* 93.6%

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

      7. *-commutative 93.6%

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

   5. Applied egg-rr 93.6%

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

   if 2.0000000000000002e287 < (*.f64 x y)

   1. Initial program 49.6%

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

      1. div-sub 44.8%

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

      2. +-rgt-identity 44.8%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 49.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 49.6%

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

      5. fma-neg 59.4%

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

      6. associate-*l* 59.4%

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

      7. distribute-rgt-neg-in 59.4%

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

      8. *-commutative 59.4%

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

      9. distribute-rgt-neg-in 59.4%

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

      10. metadata-eval 59.4%

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

   3. Simplified 59.4%

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

   4. Taylor expanded in x around inf 54.4%

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

      1. associate-*r/ 54.4%

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

      2. *-commutative 54.4%

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

      3. *-commutative 54.4%

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

      4. associate-/l* 54.4%

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

      5. *-commutative 54.4%

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

   6. Simplified 54.4%

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

      1. div-inv 54.4%

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

      2. metadata-eval 54.4%

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

      3. div-inv 54.4%

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

      4. *-commutative 54.4%

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

      5. metadata-eval 54.4%

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

      6. div-inv 54.4%

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

      7. clear-num 54.4%

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

      8. associate-*l* 81.1%

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

   8. Applied egg-rr 81.1%

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

      1. associate-*r/ 81.1%

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

   10. Applied egg-rr 81.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]

Alternative 5: 67.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-72} \lor \neg \left(y \leq 8.6 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

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 (or (<= y -2.6e-72) (not (<= y 8.6e-16)))
   (* x (* y (/ 0.5 a)))
   (* t (* -4.5 (/ z a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e-72) || !(y <= 8.6e-16)) {
		tmp = x * (y * (0.5 / a));
	} else {
		tmp = t * (-4.5 * (z / 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 ((y <= (-2.6d-72)) .or. (.not. (y <= 8.6d-16))) then
        tmp = x * (y * (0.5d0 / a))
    else
        tmp = t * ((-4.5d0) * (z / 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 ((y <= -2.6e-72) || !(y <= 8.6e-16)) {
		tmp = x * (y * (0.5 / a));
	} else {
		tmp = t * (-4.5 * (z / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.6e-72) or not (y <= 8.6e-16):
		tmp = x * (y * (0.5 / a))
	else:
		tmp = t * (-4.5 * (z / 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 ((y <= -2.6e-72) || !(y <= 8.6e-16))
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	else
		tmp = Float64(t * Float64(-4.5 * Float64(z / 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 ((y <= -2.6e-72) || ~((y <= 8.6e-16)))
		tmp = x * (y * (0.5 / a));
	else
		tmp = t * (-4.5 * (z / 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[Or[LessEqual[y, -2.6e-72], N[Not[LessEqual[y, 8.6e-16]], $MachinePrecision]], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999996e-72 or 8.5999999999999997e-16 < y

   1. Initial program 85.0%

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

      1. div-sub 82.9%

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

      2. +-rgt-identity 82.9%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 85.0%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 85.0%

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

      5. fma-neg 86.5%

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

      6. associate-*l* 86.4%

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

      7. distribute-rgt-neg-in 86.4%

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

      8. *-commutative 86.4%

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

      9. distribute-rgt-neg-in 86.4%

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

      10. metadata-eval 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in x around inf 59.2%

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

      1. associate-*r/ 59.2%

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

      2. *-commutative 59.2%

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

      3. *-commutative 59.2%

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

      4. associate-/l* 59.2%

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

      5. *-commutative 59.2%

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

   6. Simplified 59.2%

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

      1. div-inv 59.2%

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

      2. metadata-eval 59.2%

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

      3. div-inv 59.2%

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

      4. *-commutative 59.2%

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

      5. metadata-eval 59.2%

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

      6. div-inv 59.2%

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

      7. clear-num 59.2%

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

      8. associate-*l* 63.8%

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

   8. Applied egg-rr 63.8%

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

   if -2.59999999999999996e-72 < y < 8.5999999999999997e-16

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. +-commutative 93.0%

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

      3. neg-sub0 93.0%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 93.0%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 93.0%

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

      6. neg-mul-1 93.0%

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

      7. associate-/l* 92.0%

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

      8. associate-/r/ 93.0%

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

      9. *-commutative 93.0%

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

      10. sub-neg 93.0%

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

      11. +-commutative 93.0%

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

      12. neg-sub0 93.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 93.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 93.0%

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

      15. distribute-lft-neg-out 93.0%

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

      16. distribute-rgt-neg-in 93.0%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

      2. div-inv 93.0%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

      3. metadata-eval 93.0%

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

      4. div-inv 93.0%

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

      5. *-commutative 93.0%

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

      6. metadata-eval 93.0%

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

      7. distribute-lft-neg-in 93.0%

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

      8. distribute-rgt-neg-in 93.0%

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

      9. fma-neg 93.0%

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

      10. div-sub 90.4%

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

      11. frac-sub 67.8%

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

      12. associate-*r* 67.9%

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

      13. *-commutative 67.9%

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

      14. swap-sqr 67.8%

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

      15. metadata-eval 67.8%

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

   5. Applied egg-rr 67.8%

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

   6. Taylor expanded in x around 0 90.2%

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

      1. fma-def 90.3%

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

      2. associate-/l* 87.3%

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

      3. associate-*r/ 87.3%

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

      4. associate-*r* 87.3%

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

      5. *-commutative 87.3%

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

      6. associate-*l/ 85.8%

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

      7. *-commutative 85.8%

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

      8. associate-*r/ 85.8%

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

      9. associate-*l* 85.8%

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

   8. Simplified 85.8%

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

   9. Taylor expanded in t around inf 71.2%

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

       1. associate-/l* 69.1%

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

       2. associate-*r/ 69.2%

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

       3. *-rgt-identity 69.2%

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

       4. associate-*r/ 68.7%

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

       5. *-commutative 68.7%

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

       6. associate-*l* 68.8%

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

       7. associate-/r/ 69.3%

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

       8. associate-*l/ 69.4%

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

       9. *-lft-identity 69.4%

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

   11. Simplified 69.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-72} \lor \neg \left(y \leq 8.6 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \end{array} \]

Alternative 6: 67.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \end{array} \]

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 (<= y -3.2e-72)
   (* x (* y (/ 0.5 a)))
   (if (<= y 1.1e-15) (* t (* -4.5 (/ z a))) (* x (/ (* y 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 (y <= -3.2e-72) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.1e-15) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = x * ((y * 0.5) / 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 (y <= (-3.2d-72)) then
        tmp = x * (y * (0.5d0 / a))
    else if (y <= 1.1d-15) then
        tmp = t * ((-4.5d0) * (z / a))
    else
        tmp = x * ((y * 0.5d0) / 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 (y <= -3.2e-72) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1.1e-15) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = x * ((y * 0.5) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e-72:
		tmp = x * (y * (0.5 / a))
	elif y <= 1.1e-15:
		tmp = t * (-4.5 * (z / a))
	else:
		tmp = x * ((y * 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 (y <= -3.2e-72)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (y <= 1.1e-15)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	else
		tmp = Float64(x * Float64(Float64(y * 0.5) / 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 (y <= -3.2e-72)
		tmp = x * (y * (0.5 / a));
	elseif (y <= 1.1e-15)
		tmp = t * (-4.5 * (z / a));
	else
		tmp = x * ((y * 0.5) / 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[y, -3.2e-72], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-15], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * 0.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.19999999999999999e-72

   1. Initial program 86.0%

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

      1. div-sub 83.6%

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

      2. +-rgt-identity 83.6%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 86.0%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 86.0%

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

      5. fma-neg 87.2%

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

      6. associate-*l* 87.2%

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

      7. distribute-rgt-neg-in 87.2%

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

      8. *-commutative 87.2%

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

      9. distribute-rgt-neg-in 87.2%

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

      10. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around inf 51.4%

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

      1. associate-*r/ 51.4%

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

      2. *-commutative 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-/l* 51.4%

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

      5. *-commutative 51.4%

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

   6. Simplified 51.4%

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

      1. div-inv 51.4%

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

      2. metadata-eval 51.4%

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

      3. div-inv 51.4%

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

      4. *-commutative 51.4%

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

      5. metadata-eval 51.4%

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

      6. div-inv 51.4%

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

      7. clear-num 51.4%

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

      8. associate-*l* 57.0%

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

   8. Applied egg-rr 57.0%

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

   if -3.19999999999999999e-72 < y < 1.09999999999999993e-15

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. +-commutative 93.0%

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

      3. neg-sub0 93.0%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 93.0%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 93.0%

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

      6. neg-mul-1 93.0%

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

      7. associate-/l* 92.0%

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

      8. associate-/r/ 93.0%

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

      9. *-commutative 93.0%

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

      10. sub-neg 93.0%

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

      11. +-commutative 93.0%

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

      12. neg-sub0 93.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 93.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 93.0%

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

      15. distribute-lft-neg-out 93.0%

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

      16. distribute-rgt-neg-in 93.0%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

      2. div-inv 93.0%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

      3. metadata-eval 93.0%

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

      4. div-inv 93.0%

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

      5. *-commutative 93.0%

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

      6. metadata-eval 93.0%

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

      7. distribute-lft-neg-in 93.0%

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

      8. distribute-rgt-neg-in 93.0%

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

      9. fma-neg 93.0%

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

      10. div-sub 90.4%

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

      11. frac-sub 67.8%

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

      12. associate-*r* 67.9%

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

      13. *-commutative 67.9%

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

      14. swap-sqr 67.8%

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

      15. metadata-eval 67.8%

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

   5. Applied egg-rr 67.8%

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

   6. Taylor expanded in x around 0 90.2%

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

      1. fma-def 90.3%

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

      2. associate-/l* 87.3%

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

      3. associate-*r/ 87.3%

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

      4. associate-*r* 87.3%

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

      5. *-commutative 87.3%

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

      6. associate-*l/ 85.8%

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

      7. *-commutative 85.8%

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

      8. associate-*r/ 85.8%

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

      9. associate-*l* 85.8%

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

   8. Simplified 85.8%

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

   9. Taylor expanded in t around inf 71.2%

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

       1. associate-/l* 69.1%

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

       2. associate-*r/ 69.2%

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

       3. *-rgt-identity 69.2%

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

       4. associate-*r/ 68.7%

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

       5. *-commutative 68.7%

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

       6. associate-*l* 68.8%

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

       7. associate-/r/ 69.3%

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

       8. associate-*l/ 69.4%

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

       9. *-lft-identity 69.4%

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

   11. Simplified 69.4%

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

   if 1.09999999999999993e-15 < y

   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. div-sub 82.0%

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

      2. +-rgt-identity 82.0%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 83.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 83.6%

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

      5. fma-neg 85.4%

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

      6. associate-*l* 85.4%

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

      7. distribute-rgt-neg-in 85.4%

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

      8. *-commutative 85.4%

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

      9. distribute-rgt-neg-in 85.4%

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

      10. metadata-eval 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. *-commutative 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-/l* 69.9%

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

      5. *-commutative 69.9%

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

   6. Simplified 69.9%

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

      1. div-inv 69.9%

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

      2. metadata-eval 69.9%

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

      3. div-inv 69.8%

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

      4. *-commutative 69.8%

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

      5. metadata-eval 69.8%

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

      6. div-inv 69.8%

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

      7. clear-num 69.8%

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

      8. associate-*l* 73.2%

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

   8. Applied egg-rr 73.2%

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

      1. associate-*r/ 73.3%

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

   10. Applied egg-rr 73.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]

Alternative 7: 66.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

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 (<= y -1.05e-72)
   (* x (* y (/ 0.5 a)))
   (if (<= y 8.6e-16) (* t (* -4.5 (/ z a))) (* (* x y) (/ 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 (y <= -1.05e-72) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 8.6e-16) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = (x * y) * (0.5 / 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 (y <= (-1.05d-72)) then
        tmp = x * (y * (0.5d0 / a))
    else if (y <= 8.6d-16) then
        tmp = t * ((-4.5d0) * (z / a))
    else
        tmp = (x * y) * (0.5d0 / 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 (y <= -1.05e-72) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 8.6e-16) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = (x * y) * (0.5 / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e-72:
		tmp = x * (y * (0.5 / a))
	elif y <= 8.6e-16:
		tmp = t * (-4.5 * (z / a))
	else:
		tmp = (x * y) * (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 (y <= -1.05e-72)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (y <= 8.6e-16)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	else
		tmp = Float64(Float64(x * y) * Float64(0.5 / 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 (y <= -1.05e-72)
		tmp = x * (y * (0.5 / a));
	elseif (y <= 8.6e-16)
		tmp = t * (-4.5 * (z / a));
	else
		tmp = (x * y) * (0.5 / 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[y, -1.05e-72], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6e-16], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-72

   1. Initial program 86.0%

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

      1. div-sub 83.6%

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

      2. +-rgt-identity 83.6%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 86.0%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 86.0%

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

      5. fma-neg 87.2%

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

      6. associate-*l* 87.2%

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

      7. distribute-rgt-neg-in 87.2%

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

      8. *-commutative 87.2%

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

      9. distribute-rgt-neg-in 87.2%

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

      10. metadata-eval 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around inf 51.4%

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

      1. associate-*r/ 51.4%

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

      2. *-commutative 51.4%

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

      3. *-commutative 51.4%

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

      4. associate-/l* 51.4%

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

      5. *-commutative 51.4%

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

   6. Simplified 51.4%

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

      1. div-inv 51.4%

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

      2. metadata-eval 51.4%

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

      3. div-inv 51.4%

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

      4. *-commutative 51.4%

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

      5. metadata-eval 51.4%

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

      6. div-inv 51.4%

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

      7. clear-num 51.4%

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

      8. associate-*l* 57.0%

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

   8. Applied egg-rr 57.0%

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

   if -1.05e-72 < y < 8.5999999999999997e-16

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. +-commutative 93.0%

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

      3. neg-sub0 93.0%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 93.0%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 93.0%

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

      6. neg-mul-1 93.0%

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

      7. associate-/l* 92.0%

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

      8. associate-/r/ 93.0%

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

      9. *-commutative 93.0%

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

      10. sub-neg 93.0%

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

      11. +-commutative 93.0%

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

      12. neg-sub0 93.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 93.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 93.0%

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

      15. distribute-lft-neg-out 93.0%

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

      16. distribute-rgt-neg-in 93.0%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

      2. div-inv 93.0%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

      3. metadata-eval 93.0%

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

      4. div-inv 93.0%

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

      5. *-commutative 93.0%

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

      6. metadata-eval 93.0%

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

      7. distribute-lft-neg-in 93.0%

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

      8. distribute-rgt-neg-in 93.0%

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

      9. fma-neg 93.0%

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

      10. div-sub 90.4%

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

      11. frac-sub 67.8%

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

      12. associate-*r* 67.9%

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

      13. *-commutative 67.9%

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

      14. swap-sqr 67.8%

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

      15. metadata-eval 67.8%

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

   5. Applied egg-rr 67.8%

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

   6. Taylor expanded in x around 0 90.2%

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

      1. fma-def 90.3%

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

      2. associate-/l* 87.3%

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

      3. associate-*r/ 87.3%

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

      4. associate-*r* 87.3%

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

      5. *-commutative 87.3%

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

      6. associate-*l/ 85.8%

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

      7. *-commutative 85.8%

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

      8. associate-*r/ 85.8%

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

      9. associate-*l* 85.8%

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

   8. Simplified 85.8%

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

   9. Taylor expanded in t around inf 71.2%

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

       1. associate-/l* 69.1%

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

       2. associate-*r/ 69.2%

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

       3. *-rgt-identity 69.2%

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

       4. associate-*r/ 68.7%

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

       5. *-commutative 68.7%

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

       6. associate-*l* 68.8%

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

       7. associate-/r/ 69.3%

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

       8. associate-*l/ 69.4%

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

       9. *-lft-identity 69.4%

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

   11. Simplified 69.4%

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

   if 8.5999999999999997e-16 < y

   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. sub-neg 83.6%

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

      2. +-commutative 83.6%

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

      3. neg-sub0 83.6%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 83.6%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 83.6%

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

      6. neg-mul-1 83.6%

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

      7. associate-/l* 83.5%

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

      8. associate-/r/ 83.5%

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

      9. *-commutative 83.5%

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

      10. sub-neg 83.5%

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

      11. +-commutative 83.5%

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

      12. neg-sub0 83.5%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 83.5%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 83.5%

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

      15. distribute-lft-neg-out 83.5%

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

      16. distribute-rgt-neg-in 83.5%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in x around inf 69.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-16}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 8: 66.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 10^{-15}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{\frac{a}{0.5}}\\ \end{array} \end{array} \]

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 -5.4e-76)
   (* x (* y (/ 0.5 a)))
   (if (<= y 1e-15) (* t (* -4.5 (/ z a))) (/ (* x y) (/ a 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 <= -5.4e-76) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1e-15) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = (x * y) / (a / 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 <= (-5.4d-76)) then
        tmp = x * (y * (0.5d0 / a))
    else if (y <= 1d-15) then
        tmp = t * ((-4.5d0) * (z / a))
    else
        tmp = (x * y) / (a / 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 <= -5.4e-76) {
		tmp = x * (y * (0.5 / a));
	} else if (y <= 1e-15) {
		tmp = t * (-4.5 * (z / a));
	} else {
		tmp = (x * y) / (a / 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 <= -5.4e-76:
		tmp = x * (y * (0.5 / a))
	elif y <= 1e-15:
		tmp = t * (-4.5 * (z / a))
	else:
		tmp = (x * y) / (a / 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 (y <= -5.4e-76)
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	elseif (y <= 1e-15)
		tmp = Float64(t * Float64(-4.5 * Float64(z / a)));
	else
		tmp = Float64(Float64(x * y) / Float64(a / 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 <= -5.4e-76)
		tmp = x * (y * (0.5 / a));
	elseif (y <= 1e-15)
		tmp = t * (-4.5 * (z / a));
	else
		tmp = (x * y) / (a / 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[y, -5.4e-76], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-15], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / N[(a / 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4000000000000001e-76

   1. Initial program 86.2%

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

      1. div-sub 83.8%

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

      2. +-rgt-identity 83.8%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 86.2%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 86.2%

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

      5. fma-neg 87.4%

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

      6. associate-*l* 87.4%

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

      7. distribute-rgt-neg-in 87.4%

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

      8. *-commutative 87.4%

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

      9. distribute-rgt-neg-in 87.4%

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

      10. metadata-eval 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in x around inf 50.8%

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

      1. associate-*r/ 50.8%

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

      2. *-commutative 50.8%

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

      3. *-commutative 50.8%

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

      4. associate-/l* 50.8%

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

      5. *-commutative 50.8%

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

   6. Simplified 50.8%

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

      1. div-inv 50.8%

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

      2. metadata-eval 50.8%

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

      3. div-inv 50.8%

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

      4. *-commutative 50.8%

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

      5. metadata-eval 50.8%

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

      6. div-inv 50.8%

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

      7. clear-num 50.8%

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

      8. associate-*l* 56.3%

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

   8. Applied egg-rr 56.3%

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

   if -5.4000000000000001e-76 < y < 1.0000000000000001e-15

   1. Initial program 92.9%

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

      1. sub-neg 92.9%

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

      2. +-commutative 92.9%

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

      3. neg-sub0 92.9%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 92.9%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 92.9%

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

      6. neg-mul-1 92.9%

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

      7. associate-/l* 92.0%

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

      8. associate-/r/ 92.9%

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

      9. *-commutative 92.9%

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

      10. sub-neg 92.9%

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

      11. +-commutative 92.9%

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

      12. neg-sub0 92.9%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 92.9%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 92.9%

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

      15. distribute-lft-neg-out 92.9%

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

      16. distribute-rgt-neg-in 92.9%

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

   3. Simplified 92.9%

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

      1. clear-num 92.9%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

      2. div-inv 92.9%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

      3. metadata-eval 92.9%

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

      4. div-inv 92.9%

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

      5. *-commutative 92.9%

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

      6. metadata-eval 92.9%

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

      7. distribute-lft-neg-in 92.9%

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

      8. distribute-rgt-neg-in 92.9%

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

      9. fma-neg 92.9%

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

      10. div-sub 90.3%

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

      11. frac-sub 68.4%

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

      12. associate-*r* 68.5%

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

      13. *-commutative 68.5%

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

      14. swap-sqr 68.4%

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

      15. metadata-eval 68.4%

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

   5. Applied egg-rr 68.4%

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

   6. Taylor expanded in x around 0 90.1%

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

      1. fma-def 90.2%

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

      2. associate-/l* 87.2%

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

      3. associate-*r/ 87.2%

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

      4. associate-*r* 87.2%

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

      5. *-commutative 87.2%

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

      6. associate-*l/ 85.7%

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

      7. *-commutative 85.7%

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

      8. associate-*r/ 85.7%

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

      9. associate-*l* 85.7%

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

   8. Simplified 85.7%

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

   9. Taylor expanded in t around inf 71.0%

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

       1. associate-/l* 68.8%

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

       2. associate-*r/ 68.9%

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

       3. *-rgt-identity 68.9%

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

       4. associate-*r/ 68.5%

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

       5. *-commutative 68.5%

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

       6. associate-*l* 68.5%

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

       7. associate-/r/ 69.0%

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

       8. associate-*l/ 69.1%

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

       9. *-lft-identity 69.1%

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

   11. Simplified 69.1%

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

   if 1.0000000000000001e-15 < y

   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. div-sub 82.0%

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

      2. +-rgt-identity 82.0%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 83.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 83.6%

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

      5. fma-neg 85.4%

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

      6. associate-*l* 85.4%

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

      7. distribute-rgt-neg-in 85.4%

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

      8. *-commutative 85.4%

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

      9. distribute-rgt-neg-in 85.4%

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

      10. metadata-eval 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around inf 69.9%

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

      1. associate-*r/ 69.9%

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

      2. *-commutative 69.9%

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

      3. *-commutative 69.9%

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

      4. associate-/l* 69.9%

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

      5. *-commutative 69.9%

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

   6. Simplified 69.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{elif}\;y \leq 10^{-15}:\\ \;\;\;\;t \cdot \left(-4.5 \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{\frac{a}{0.5}}\\ \end{array} \]

Alternative 9: 51.1% accurate, 1.9× speedup

Math

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

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 (/ t a))))

C

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

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

Python

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

Julia

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

Derivation

1. Initial program 88.6%

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

   1. div-sub 86.2%

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

   2. +-rgt-identity 86.2%

      \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   3. div-sub 88.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

   4. +-rgt-identity 88.6%

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

   5. fma-neg 89.4%

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

   6. associate-*l* 89.4%

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

   7. distribute-rgt-neg-in 89.4%

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

   8. *-commutative 89.4%

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

   9. distribute-rgt-neg-in 89.4%

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

   10. metadata-eval 89.4%

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

3. Simplified 89.4%

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

4. Taylor expanded in x around 0 51.1%

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

   1. associate-/l* 53.0%

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

   2. associate-/r/ 52.9%

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

6. Simplified 52.9%

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

7. Final simplification 52.9%

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

Alternative 10: 51.1% accurate, 1.9× speedup

Math

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

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 (/ t (/ a z))))

C

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

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

Python

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

Julia

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

Derivation

1. Initial program 88.6%

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

   1. div-sub 86.2%

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

   2. +-rgt-identity 86.2%

      \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   3. div-sub 88.6%

      \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

   4. +-rgt-identity 88.6%

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

   5. fma-neg 89.4%

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

   6. associate-*l* 89.4%

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

   7. distribute-rgt-neg-in 89.4%

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

   8. *-commutative 89.4%

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

   9. distribute-rgt-neg-in 89.4%

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

   10. metadata-eval 89.4%

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

3. Simplified 89.4%

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

4. Taylor expanded in x around 0 51.1%

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

   1. associate-/l* 53.0%

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

6. Simplified 53.0%

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

7. Final simplification 53.0%

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

Alternative 11: 51.2% accurate, 1.9× speedup

Math

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

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 (* t (* -4.5 (/ z a))))

C

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

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 = t * ((-4.5d0) * (z / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 88.6%

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

   1. sub-neg 88.6%

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

   2. +-commutative 88.6%

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

   3. neg-sub0 88.6%

      \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

   4. associate-+l- 88.6%

      \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

   5. sub0-neg 88.6%

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

   6. neg-mul-1 88.6%

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

   7. associate-/l* 88.1%

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

   8. associate-/r/ 88.5%

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

   9. *-commutative 88.5%

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

   10. sub-neg 88.5%

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

   11. +-commutative 88.5%

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

   12. neg-sub0 88.5%

       \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

   13. associate-+l- 88.5%

       \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

   14. sub0-neg 88.5%

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

   15. distribute-lft-neg-out 88.5%

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

   16. distribute-rgt-neg-in 88.5%

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

3. Simplified 89.3%

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

   1. clear-num 89.3%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \color{blue}{\frac{1}{\frac{a}{0.5}}} \]

   2. div-inv 89.3%

      \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{a \cdot \frac{1}{0.5}}} \]

   3. metadata-eval 89.3%

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

   4. div-inv 89.4%

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

   5. *-commutative 89.4%

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

   6. metadata-eval 89.4%

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

   7. distribute-lft-neg-in 89.4%

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

   8. distribute-rgt-neg-in 89.4%

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

   9. fma-neg 88.6%

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

   10. div-sub 86.2%

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

   11. frac-sub 60.6%

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

   12. associate-*r* 60.6%

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

   13. *-commutative 60.6%

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

   14. swap-sqr 60.5%

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

   15. metadata-eval 60.5%

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

5. Applied egg-rr 60.5%

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

6. Taylor expanded in x around 0 86.1%

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

   1. fma-def 86.2%

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

   2. associate-/l* 85.7%

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

   3. associate-*r/ 85.7%

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

   4. associate-*r* 85.7%

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

   5. *-commutative 85.7%

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

   6. associate-*l/ 85.6%

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

   7. *-commutative 85.6%

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

   8. associate-*r/ 85.3%

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

   9. associate-*l* 85.3%

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

8. Simplified 85.3%

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

9. Taylor expanded in t around inf 51.1%

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

    1. associate-/l* 53.0%

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

    2. associate-*r/ 53.1%

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

    3. *-rgt-identity 53.1%

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

    4. associate-*r/ 52.9%

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

    5. *-commutative 52.9%

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

    6. associate-*l* 52.9%

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

    7. associate-/r/ 53.1%

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

    8. associate-*l/ 53.2%

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

    9. *-lft-identity 53.2%

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

11. Simplified 53.2%

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

12. Final simplification 53.2%

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

Developer target: 93.0% 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 2023173 
(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)))