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

Percentage Accurate: 91.1% → 95.0%

Time: 9.3s

Alternatives: 11

Speedup: 0.6×

• 28.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;2 \cdot a\_m \leq 10^{-18}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a\_m}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-4.5 \cdot z}{a\_m}, 0.5 \cdot \left(\frac{y}{a\_m} \cdot x\right)\right)\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* 2.0 a_m) 1e-18)
    (/ (- (* y x) (* t (* 9.0 z))) (* 2.0 a_m))
    (fma t (/ (* -4.5 z) a_m) (* 0.5 (* (/ y a_m) x))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((2.0 * a_m) <= 1e-18) {
		tmp = ((y * x) - (t * (9.0 * z))) / (2.0 * a_m);
	} else {
		tmp = fma(t, ((-4.5 * z) / a_m), (0.5 * ((y / a_m) * x)));
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(2.0 * a_m) <= 1e-18)
		tmp = Float64(Float64(Float64(y * x) - Float64(t * Float64(9.0 * z))) / Float64(2.0 * a_m));
	else
		tmp = fma(t, Float64(Float64(-4.5 * z) / a_m), Float64(0.5 * Float64(Float64(y / a_m) * x)));
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(2.0 * a$95$m), $MachinePrecision], 1e-18], N[(N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a$95$m), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(-4.5 * z), $MachinePrecision] / a$95$m), $MachinePrecision] + N[(0.5 * N[(N[(y / a$95$m), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1.0000000000000001e-18

   1. Initial program 92.5%

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

   if 1.0000000000000001e-18 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 84.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. div-sub N/A

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

      4. sub-neg N/A

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

      5. +-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. times-frac N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-/l* N/A

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

      16. lower-*.f64 N/A

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

      17. metadata-eval N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. associate-/l* N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 N/A

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

   4. Applied rewrites 94.8%

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

      1. lift-fma.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 94.9

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

      7. lift-neg.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. distribute-lft-neg-in N/A

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

      11. lower-*.f64 N/A

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

      12. metadata-eval 94.9

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-*l* N/A

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

      16. *-commutative N/A

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

      17. lift-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. *-commutative N/A

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

      20. associate-*l/ N/A

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

      21. lift-/.f64 N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

      24. associate-*r* N/A

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

      25. lower-*.f64 N/A

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

   6. Applied rewrites 96.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot a \leq 10^{-18}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{-4.5 \cdot z}{a}, 0.5 \cdot \left(\frac{y}{a} \cdot x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \mathsf{fma}\left(0.5 \cdot y, \frac{x}{z}, -4.5 \cdot t\right) \cdot \frac{z}{a\_m}\\ t_2 := y \cdot x - t \cdot \left(9 \cdot z\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{t\_2}{2 \cdot a\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (fma (* 0.5 y) (/ x z) (* -4.5 t)) (/ z a_m)))
        (t_2 (- (* y x) (* t (* 9.0 z)))))
   (*
    a_s
    (if (<= t_2 (- INFINITY))
      t_1
      (if (<= t_2 5e+297) (/ t_2 (* 2.0 a_m)) t_1)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = fma((0.5 * y), (x / z), (-4.5 * t)) * (z / a_m);
	double t_2 = (y * x) - (t * (9.0 * z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+297) {
		tmp = t_2 / (2.0 * a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(fma(Float64(0.5 * y), Float64(x / z), Float64(-4.5 * t)) * Float64(z / a_m))
	t_2 = Float64(Float64(y * x) - Float64(t * Float64(9.0 * z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+297)
		tmp = Float64(t_2 / Float64(2.0 * a_m));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(0.5 * y), $MachinePrecision] * N[(x / z), $MachinePrecision] + N[(-4.5 * t), $MachinePrecision]), $MachinePrecision] * N[(z / a$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+297], N[(t$95$2 / N[(2.0 * a$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < -inf.0 or 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 67.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 82.8%

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

   7. Applied rewrites 89.1%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 4.9999999999999998e297

   1. Initial program 99.7%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(0.5 \cdot y, \frac{x}{z}, -4.5 \cdot t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;y \cdot x - t \cdot \left(9 \cdot z\right) \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.5 \cdot y, \frac{x}{z}, -4.5 \cdot t\right) \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ t_2 := t \cdot \left(9 \cdot z\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+231}:\\ \;\;\;\;\frac{y \cdot x - t\_2}{2 \cdot a\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (* (/ t a_m) z) -4.5)) (t_2 (* t (* 9.0 z))))
   (*
    a_s
    (if (<= t_2 (- INFINITY))
      t_1
      (if (<= t_2 1e+231) (/ (- (* y x) t_2) (* 2.0 a_m)) t_1)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((t / a_m) * z) * -4.5;
	double t_2 = t * (9.0 * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 1e+231) {
		tmp = ((y * x) - t_2) / (2.0 * a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((t / a_m) * z) * -4.5;
	double t_2 = t * (9.0 * z);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= 1e+231) {
		tmp = ((y * x) - t_2) / (2.0 * a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = ((t / a_m) * z) * -4.5
	t_2 = t * (9.0 * z)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= 1e+231:
		tmp = ((y * x) - t_2) / (2.0 * a_m)
	else:
		tmp = t_1
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(Float64(t / a_m) * z) * -4.5)
	t_2 = Float64(t * Float64(9.0 * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 1e+231)
		tmp = Float64(Float64(Float64(y * x) - t_2) / Float64(2.0 * a_m));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = ((t / a_m) * z) * -4.5;
	t_2 = t * (9.0 * z);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= 1e+231)
		tmp = ((y * x) - t_2) / (2.0 * a_m);
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 1e+231], N[(N[(N[(y * x), $MachinePrecision] - t$95$2), $MachinePrecision] / N[(2.0 * a$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0 or 1.0000000000000001e231 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 71.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 95.6

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

   5. Applied rewrites 95.6%

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

   7. Applied rewrites 97.4%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.0000000000000001e231

   1. Initial program 94.9%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -\infty:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 10^{+231}:\\ \;\;\;\;\frac{y \cdot x - t \cdot \left(9 \cdot z\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ t_2 := t \cdot \left(9 \cdot z\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, -9 \cdot \left(t \cdot z\right)\right)}{2 \cdot a\_m}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (* (/ t a_m) z) -4.5)) (t_2 (* t (* 9.0 z))))
   (*
    a_s
    (if (<= t_2 (- INFINITY))
      t_1
      (if (<= t_2 5e+253) (/ (fma y x (* -9.0 (* t z))) (* 2.0 a_m)) t_1)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((t / a_m) * z) * -4.5;
	double t_2 = t * (9.0 * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+253) {
		tmp = fma(y, x, (-9.0 * (t * z))) / (2.0 * a_m);
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(Float64(t / a_m) * z) * -4.5)
	t_2 = Float64(t * Float64(9.0 * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+253)
		tmp = Float64(fma(y, x, Float64(-9.0 * Float64(t * z))) / Float64(2.0 * a_m));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+253], N[(N[(y * x + N[(-9.0 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 * a$95$m), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0 or 4.9999999999999997e253 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 97.5

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

   5. Applied rewrites 97.5%

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

   7. Applied rewrites 97.4%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999997e253

   1. Initial program 94.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r* N/A

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

      10. distribute-rgt-neg-in N/A

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

      11. lower-*.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. metadata-eval 94.8

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

   4. Applied rewrites 94.8%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -\infty:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, -9 \cdot \left(t \cdot z\right)\right)}{2 \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ t_2 := t \cdot \left(9 \cdot z\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{0.5}{a\_m} \cdot \mathsf{fma}\left(t \cdot z, -9, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (* (/ t a_m) z) -4.5)) (t_2 (* t (* 9.0 z))))
   (*
    a_s
    (if (<= t_2 (- INFINITY))
      t_1
      (if (<= t_2 5e+253) (* (/ 0.5 a_m) (fma (* t z) -9.0 (* y x))) t_1)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((t / a_m) * z) * -4.5;
	double t_2 = t * (9.0 * z);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= 5e+253) {
		tmp = (0.5 / a_m) * fma((t * z), -9.0, (y * x));
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(Float64(t / a_m) * z) * -4.5)
	t_2 = Float64(t * Float64(9.0 * z))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= 5e+253)
		tmp = Float64(Float64(0.5 / a_m) * fma(Float64(t * z), -9.0, Float64(y * x)));
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, 5e+253], N[(N[(0.5 / a$95$m), $MachinePrecision] * N[(N[(t * z), $MachinePrecision] * -9.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -inf.0 or 4.9999999999999997e253 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 97.5

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

   5. Applied rewrites 97.5%

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

   7. Applied rewrites 97.4%

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

   if -inf.0 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 4.9999999999999997e253

   1. Initial program 94.9%

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

      1. lift-/.f64 N/A

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

      2. div-inv N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lift-*.f64 N/A

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

      10. associate-*r* N/A

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

      11. distribute-rgt-neg-in N/A

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

      12. lower-fma.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. metadata-eval N/A

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

      15. lift-*.f64 N/A

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

      16. *-commutative N/A

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

      17. lower-*.f64 N/A

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

      18. lift-*.f64 N/A

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

      19. *-commutative N/A

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

      20. associate-/r* N/A

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

      21. lower-/.f64 N/A

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

      22. metadata-eval 94.7

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

   4. Applied rewrites 94.7%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -\infty:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{0.5}{a} \cdot \mathsf{fma}\left(t \cdot z, -9, y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(9 \cdot z\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\left(-4.5 \cdot z\right) \cdot \frac{t}{a\_m}\\ \mathbf{elif}\;t\_1 \leq 10^{+91}:\\ \;\;\;\;\frac{0.5 \cdot x}{\frac{a\_m}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* t (* 9.0 z))))
   (*
    a_s
    (if (<= t_1 -5e+34)
      (* (* -4.5 z) (/ t a_m))
      (if (<= t_1 1e+91) (/ (* 0.5 x) (/ a_m y)) (* (* (/ t a_m) z) -4.5))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (9.0 * z);
	double tmp;
	if (t_1 <= -5e+34) {
		tmp = (-4.5 * z) * (t / a_m);
	} else if (t_1 <= 1e+91) {
		tmp = (0.5 * x) / (a_m / y);
	} else {
		tmp = ((t / a_m) * z) * -4.5;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (9.0d0 * z)
    if (t_1 <= (-5d+34)) then
        tmp = ((-4.5d0) * z) * (t / a_m)
    else if (t_1 <= 1d+91) then
        tmp = (0.5d0 * x) / (a_m / y)
    else
        tmp = ((t / a_m) * z) * (-4.5d0)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (9.0 * z);
	double tmp;
	if (t_1 <= -5e+34) {
		tmp = (-4.5 * z) * (t / a_m);
	} else if (t_1 <= 1e+91) {
		tmp = (0.5 * x) / (a_m / y);
	} else {
		tmp = ((t / a_m) * z) * -4.5;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = t * (9.0 * z)
	tmp = 0
	if t_1 <= -5e+34:
		tmp = (-4.5 * z) * (t / a_m)
	elif t_1 <= 1e+91:
		tmp = (0.5 * x) / (a_m / y)
	else:
		tmp = ((t / a_m) * z) * -4.5
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(t * Float64(9.0 * z))
	tmp = 0.0
	if (t_1 <= -5e+34)
		tmp = Float64(Float64(-4.5 * z) * Float64(t / a_m));
	elseif (t_1 <= 1e+91)
		tmp = Float64(Float64(0.5 * x) / Float64(a_m / y));
	else
		tmp = Float64(Float64(Float64(t / a_m) * z) * -4.5);
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = t * (9.0 * z);
	tmp = 0.0;
	if (t_1 <= -5e+34)
		tmp = (-4.5 * z) * (t / a_m);
	elseif (t_1 <= 1e+91)
		tmp = (0.5 * x) / (a_m / y);
	else
		tmp = ((t / a_m) * z) * -4.5;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, -5e+34], N[(N[(-4.5 * z), $MachinePrecision] * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+91], N[(N[(0.5 * x), $MachinePrecision] / N[(a$95$m / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -4.9999999999999998e34

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   7. Applied rewrites 85.6%

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

   if -4.9999999999999998e34 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.00000000000000008e91

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 73.2

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

   5. Applied rewrites 73.2%

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

   7. Applied rewrites 73.1%

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

   9. Applied rewrites 74.0%

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

   if 1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 70.5

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

   5. Applied rewrites 70.5%

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

   7. Applied rewrites 72.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\left(-4.5 \cdot z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 10^{+91}:\\ \;\;\;\;\frac{0.5 \cdot x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := t \cdot \left(9 \cdot z\right)\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\left(-4.5 \cdot z\right) \cdot \frac{t}{a\_m}\\ \mathbf{elif}\;t\_1 \leq 10^{+91}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* t (* 9.0 z))))
   (*
    a_s
    (if (<= t_1 -5e+34)
      (* (* -4.5 z) (/ t a_m))
      (if (<= t_1 1e+91) (* (* 0.5 x) (/ y a_m)) (* (* (/ t a_m) z) -4.5))))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (9.0 * z);
	double tmp;
	if (t_1 <= -5e+34) {
		tmp = (-4.5 * z) * (t / a_m);
	} else if (t_1 <= 1e+91) {
		tmp = (0.5 * x) * (y / a_m);
	} else {
		tmp = ((t / a_m) * z) * -4.5;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (9.0d0 * z)
    if (t_1 <= (-5d+34)) then
        tmp = ((-4.5d0) * z) * (t / a_m)
    else if (t_1 <= 1d+91) then
        tmp = (0.5d0 * x) * (y / a_m)
    else
        tmp = ((t / a_m) * z) * (-4.5d0)
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = t * (9.0 * z);
	double tmp;
	if (t_1 <= -5e+34) {
		tmp = (-4.5 * z) * (t / a_m);
	} else if (t_1 <= 1e+91) {
		tmp = (0.5 * x) * (y / a_m);
	} else {
		tmp = ((t / a_m) * z) * -4.5;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = t * (9.0 * z)
	tmp = 0
	if t_1 <= -5e+34:
		tmp = (-4.5 * z) * (t / a_m)
	elif t_1 <= 1e+91:
		tmp = (0.5 * x) * (y / a_m)
	else:
		tmp = ((t / a_m) * z) * -4.5
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(t * Float64(9.0 * z))
	tmp = 0.0
	if (t_1 <= -5e+34)
		tmp = Float64(Float64(-4.5 * z) * Float64(t / a_m));
	elseif (t_1 <= 1e+91)
		tmp = Float64(Float64(0.5 * x) * Float64(y / a_m));
	else
		tmp = Float64(Float64(Float64(t / a_m) * z) * -4.5);
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = t * (9.0 * z);
	tmp = 0.0;
	if (t_1 <= -5e+34)
		tmp = (-4.5 * z) * (t / a_m);
	elseif (t_1 <= 1e+91)
		tmp = (0.5 * x) * (y / a_m);
	else
		tmp = ((t / a_m) * z) * -4.5;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(t * N[(9.0 * z), $MachinePrecision]), $MachinePrecision]}, N[(a$95$s * If[LessEqual[t$95$1, -5e+34], N[(N[(-4.5 * z), $MachinePrecision] * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+91], N[(N[(0.5 * x), $MachinePrecision] * N[(y / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -4.9999999999999998e34

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 85.5

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

   5. Applied rewrites 85.5%

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

   7. Applied rewrites 85.6%

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

   if -4.9999999999999998e34 < (*.f64 (*.f64 z #s(literal 9 binary64)) t) < 1.00000000000000008e91

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 73.2

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

   5. Applied rewrites 73.2%

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

   7. Applied rewrites 74.0%

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

   if 1.00000000000000008e91 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 70.5

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

   5. Applied rewrites 70.5%

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

   7. Applied rewrites 72.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \left(9 \cdot z\right) \leq -5 \cdot 10^{+34}:\\ \;\;\;\;\left(-4.5 \cdot z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;t \cdot \left(9 \cdot z\right) \leq 10^{+91}:\\ \;\;\;\;\left(0.5 \cdot x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{+73}:\\ \;\;\;\;\left(\frac{x}{a\_m} \cdot 0.5\right) \cdot y\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(-4.5 \cdot z\right) \cdot \frac{t}{a\_m}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a\_m} \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* y x) -4e+73)
    (* (* (/ x a_m) 0.5) y)
    (if (<= (* y x) 2e+74) (* (* -4.5 z) (/ t a_m)) (* (* (/ 0.5 a_m) x) y)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((y * x) <= -4e+73) {
		tmp = ((x / a_m) * 0.5) * y;
	} else if ((y * x) <= 2e+74) {
		tmp = (-4.5 * z) * (t / a_m);
	} else {
		tmp = ((0.5 / a_m) * x) * y;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: tmp
    if ((y * x) <= (-4d+73)) then
        tmp = ((x / a_m) * 0.5d0) * y
    else if ((y * x) <= 2d+74) then
        tmp = ((-4.5d0) * z) * (t / a_m)
    else
        tmp = ((0.5d0 / a_m) * x) * y
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((y * x) <= -4e+73) {
		tmp = ((x / a_m) * 0.5) * y;
	} else if ((y * x) <= 2e+74) {
		tmp = (-4.5 * z) * (t / a_m);
	} else {
		tmp = ((0.5 / a_m) * x) * y;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (y * x) <= -4e+73:
		tmp = ((x / a_m) * 0.5) * y
	elif (y * x) <= 2e+74:
		tmp = (-4.5 * z) * (t / a_m)
	else:
		tmp = ((0.5 / a_m) * x) * y
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(y * x) <= -4e+73)
		tmp = Float64(Float64(Float64(x / a_m) * 0.5) * y);
	elseif (Float64(y * x) <= 2e+74)
		tmp = Float64(Float64(-4.5 * z) * Float64(t / a_m));
	else
		tmp = Float64(Float64(Float64(0.5 / a_m) * x) * y);
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((y * x) <= -4e+73)
		tmp = ((x / a_m) * 0.5) * y;
	elseif ((y * x) <= 2e+74)
		tmp = (-4.5 * z) * (t / a_m);
	else
		tmp = ((0.5 / a_m) * x) * y;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(y * x), $MachinePrecision], -4e+73], N[(N[(N[(x / a$95$m), $MachinePrecision] * 0.5), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 2e+74], N[(N[(-4.5 * z), $MachinePrecision] * N[(t / a$95$m), $MachinePrecision]), $MachinePrecision], N[(N[(N[(0.5 / a$95$m), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999993e73

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if -3.99999999999999993e73 < (*.f64 x y) < 1.9999999999999999e74

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 69.2

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

   5. Applied rewrites 69.2%

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

   7. Applied rewrites 72.5%

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

   if 1.9999999999999999e74 < (*.f64 x y)

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.9

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

   5. Applied rewrites 85.9%

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

   7. Applied rewrites 85.9%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{+73}:\\ \;\;\;\;\left(\frac{x}{a} \cdot 0.5\right) \cdot y\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(-4.5 \cdot z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{+73}:\\ \;\;\;\;\left(\frac{x}{a\_m} \cdot 0.5\right) \cdot y\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a\_m} \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (*
  a_s
  (if (<= (* y x) -4e+73)
    (* (* (/ x a_m) 0.5) y)
    (if (<= (* y x) 2e+74) (* (* (/ t a_m) z) -4.5) (* (* (/ 0.5 a_m) x) y)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((y * x) <= -4e+73) {
		tmp = ((x / a_m) * 0.5) * y;
	} else if ((y * x) <= 2e+74) {
		tmp = ((t / a_m) * z) * -4.5;
	} else {
		tmp = ((0.5 / a_m) * x) * y;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: tmp
    if ((y * x) <= (-4d+73)) then
        tmp = ((x / a_m) * 0.5d0) * y
    else if ((y * x) <= 2d+74) then
        tmp = ((t / a_m) * z) * (-4.5d0)
    else
        tmp = ((0.5d0 / a_m) * x) * y
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double tmp;
	if ((y * x) <= -4e+73) {
		tmp = ((x / a_m) * 0.5) * y;
	} else if ((y * x) <= 2e+74) {
		tmp = ((t / a_m) * z) * -4.5;
	} else {
		tmp = ((0.5 / a_m) * x) * y;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	tmp = 0
	if (y * x) <= -4e+73:
		tmp = ((x / a_m) * 0.5) * y
	elif (y * x) <= 2e+74:
		tmp = ((t / a_m) * z) * -4.5
	else:
		tmp = ((0.5 / a_m) * x) * y
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	tmp = 0.0
	if (Float64(y * x) <= -4e+73)
		tmp = Float64(Float64(Float64(x / a_m) * 0.5) * y);
	elseif (Float64(y * x) <= 2e+74)
		tmp = Float64(Float64(Float64(t / a_m) * z) * -4.5);
	else
		tmp = Float64(Float64(Float64(0.5 / a_m) * x) * y);
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	tmp = 0.0;
	if ((y * x) <= -4e+73)
		tmp = ((x / a_m) * 0.5) * y;
	elseif ((y * x) <= 2e+74)
		tmp = ((t / a_m) * z) * -4.5;
	else
		tmp = ((0.5 / a_m) * x) * y;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := N[(a$95$s * If[LessEqual[N[(y * x), $MachinePrecision], -4e+73], N[(N[(N[(x / a$95$m), $MachinePrecision] * 0.5), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 2e+74], N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision], N[(N[(N[(0.5 / a$95$m), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999993e73

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if -3.99999999999999993e73 < (*.f64 x y) < 1.9999999999999999e74

   1. Initial program 93.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 69.2

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

   5. Applied rewrites 69.2%

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

   7. Applied rewrites 72.5%

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

   if 1.9999999999999999e74 < (*.f64 x y)

   1. Initial program 82.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.9

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

   5. Applied rewrites 85.9%

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

   7. Applied rewrites 85.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4 \cdot 10^{+73}:\\ \;\;\;\;\left(\frac{x}{a} \cdot 0.5\right) \cdot y\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ \begin{array}{l} t_1 := \left(\frac{0.5}{a\_m} \cdot x\right) \cdot y\\ a\_s \cdot \begin{array}{l} \mathbf{if}\;y \cdot x \leq -6 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(\frac{t}{a\_m} \cdot z\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m)
 :precision binary64
 (let* ((t_1 (* (* (/ 0.5 a_m) x) y)))
   (*
    a_s
    (if (<= (* y x) -6e+60)
      t_1
      (if (<= (* y x) 2e+74) (* (* (/ t a_m) z) -4.5) t_1)))))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((0.5 / a_m) * x) * y;
	double tmp;
	if ((y * x) <= -6e+60) {
		tmp = t_1;
	} else if ((y * x) <= 2e+74) {
		tmp = ((t / a_m) * z) * -4.5;
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((0.5d0 / a_m) * x) * y
    if ((y * x) <= (-6d+60)) then
        tmp = t_1
    else if ((y * x) <= 2d+74) then
        tmp = ((t / a_m) * z) * (-4.5d0)
    else
        tmp = t_1
    end if
    code = a_s * tmp
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	double t_1 = ((0.5 / a_m) * x) * y;
	double tmp;
	if ((y * x) <= -6e+60) {
		tmp = t_1;
	} else if ((y * x) <= 2e+74) {
		tmp = ((t / a_m) * z) * -4.5;
	} else {
		tmp = t_1;
	}
	return a_s * tmp;
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	t_1 = ((0.5 / a_m) * x) * y
	tmp = 0
	if (y * x) <= -6e+60:
		tmp = t_1
	elif (y * x) <= 2e+74:
		tmp = ((t / a_m) * z) * -4.5
	else:
		tmp = t_1
	return a_s * tmp

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	t_1 = Float64(Float64(Float64(0.5 / a_m) * x) * y)
	tmp = 0.0
	if (Float64(y * x) <= -6e+60)
		tmp = t_1;
	elseif (Float64(y * x) <= 2e+74)
		tmp = Float64(Float64(Float64(t / a_m) * z) * -4.5);
	else
		tmp = t_1;
	end
	return Float64(a_s * tmp)
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp_2 = code(a_s, x, y, z, t, a_m)
	t_1 = ((0.5 / a_m) * x) * y;
	tmp = 0.0;
	if ((y * x) <= -6e+60)
		tmp = t_1;
	elseif ((y * x) <= 2e+74)
		tmp = ((t / a_m) * z) * -4.5;
	else
		tmp = t_1;
	end
	tmp_2 = a_s * tmp;
end

Wolfram

a\_m = N[Abs[a], $MachinePrecision]
a\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[a]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
code[a$95$s_, x_, y_, z_, t_, a$95$m_] := Block[{t$95$1 = N[(N[(N[(0.5 / a$95$m), $MachinePrecision] * x), $MachinePrecision] * y), $MachinePrecision]}, N[(a$95$s * If[LessEqual[N[(y * x), $MachinePrecision], -6e+60], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 2e+74], N[(N[(N[(t / a$95$m), $MachinePrecision] * z), $MachinePrecision] * -4.5), $MachinePrecision], t$95$1]]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.9999999999999997e60 or 1.9999999999999999e74 < (*.f64 x y)

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
   4. Step-by-step derivation

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 81.2

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

   5. Applied rewrites 81.2%

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

   7. Applied rewrites 81.2%

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

   if -5.9999999999999997e60 < (*.f64 x y) < 1.9999999999999999e74

   1. Initial program 93.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-9}{2} \cdot \frac{t \cdot z}{a}} \]
   4. Step-by-step derivation

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 70.1

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

   5. Applied rewrites 70.1%

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

   7. Applied rewrites 73.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -6 \cdot 10^{+60}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot x\right) \cdot y\\ \mathbf{elif}\;y \cdot x \leq 2 \cdot 10^{+74}:\\ \;\;\;\;\left(\frac{t}{a} \cdot z\right) \cdot -4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.5}{a} \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} a\_m = \left|a\right| \\ a\_s = \mathsf{copysign}\left(1, a\right) \\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\\\ [x, y, z, t, a_m] = \mathsf{sort}([x, y, z, t, a_m])\\ \\ a\_s \cdot \left(\left(\frac{0.5}{a\_m} \cdot x\right) \cdot y\right) \end{array} \]

FPCore

a\_m = (fabs.f64 a)
a\_s = (copysign.f64 #s(literal 1 binary64) a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
(FPCore (a_s x y z t a_m) :precision binary64 (* a_s (* (* (/ 0.5 a_m) x) y)))

C

a\_m = fabs(a);
a\_s = copysign(1.0, a);
assert(x < y && y < z && z < t && t < a_m);
assert(x < y && y < z && z < t && t < a_m);
double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (((0.5 / a_m) * x) * y);
}

Fortran

a\_m = abs(a)
a\_s = copysign(1.0d0, a)
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a_m should be sorted in increasing order before calling this function.
real(8) function code(a_s, x, y, z, t, a_m)
    real(8), intent (in) :: a_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a_m
    code = a_s * (((0.5d0 / a_m) * x) * y)
end function

Java

a\_m = Math.abs(a);
a\_s = Math.copySign(1.0, a);
assert x < y && y < z && z < t && t < a_m;
assert x < y && y < z && z < t && t < a_m;
public static double code(double a_s, double x, double y, double z, double t, double a_m) {
	return a_s * (((0.5 / a_m) * x) * y);
}

Python

a\_m = math.fabs(a)
a\_s = math.copysign(1.0, a)
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
[x, y, z, t, a_m] = sort([x, y, z, t, a_m])
def code(a_s, x, y, z, t, a_m):
	return a_s * (((0.5 / a_m) * x) * y)

Julia

a\_m = abs(a)
a\_s = copysign(1.0, a)
x, y, z, t, a_m = sort([x, y, z, t, a_m])
x, y, z, t, a_m = sort([x, y, z, t, a_m])
function code(a_s, x, y, z, t, a_m)
	return Float64(a_s * Float64(Float64(Float64(0.5 / a_m) * x) * y))
end

MATLAB

a\_m = abs(a);
a\_s = sign(a) * abs(1.0);
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
x, y, z, t, a_m = num2cell(sort([x, y, z, t, a_m])){:}
function tmp = code(a_s, x, y, z, t, a_m)
	tmp = a_s * (((0.5 / a_m) * x) * y);
end

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x \cdot y}{a}} \]
4. Step-by-step derivation

   1. associate-*l/ N/A

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

   2. associate-*l* N/A

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

   3. lower-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 52.3

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

5. Applied rewrites 52.3%

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

7. Applied rewrites 52.2%

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

8. Final simplification 52.2%

   \[\leadsto \left(\frac{0.5}{a} \cdot x\right) \cdot y \]
9. Add Preprocessing

Developer Target 1: 94.3% accurate, 0.6× 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 2024294 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< a -209046455797670900000000000000000000000000000000000000000000000000000000000000000000000) (- (* 1/2 (/ (* y x) a)) (* 9/2 (/ t (/ a z)))) (if (< a 2144030707833976000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 1/2)) (* (/ t a) (* z 9/2))))))

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