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

Percentage Accurate: 70.7% → 77.7%

Time: 17.6s

Alternatives: 11

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 70.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 77.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \left(0.3333333333333333 \cdot z\right) \cdot t\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9999999999995739:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(\cos t\_2, \cos y, \sin y \cdot \sin t\_2\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos y - \frac{\frac{1}{b}}{\frac{3}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (* (* 0.3333333333333333 z) t)))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.9999999999995739)
     (- (* t_1 (fma (cos t_2) (cos y) (* (sin y) (sin t_2)))) (/ a (* b 3.0)))
     (- (* t_1 (cos y)) (/ (/ 1.0 b) (/ 3.0 a))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = (0.3333333333333333 * z) * t;
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.9999999999995739) {
		tmp = (t_1 * fma(cos(t_2), cos(y), (sin(y) * sin(t_2)))) - (a / (b * 3.0));
	} else {
		tmp = (t_1 * cos(y)) - ((1.0 / b) / (3.0 / a));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(Float64(0.3333333333333333 * z) * t)
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.9999999999995739)
		tmp = Float64(Float64(t_1 * fma(cos(t_2), cos(y), Float64(sin(y) * sin(t_2)))) - Float64(a / Float64(b * 3.0)));
	else
		tmp = Float64(Float64(t_1 * cos(y)) - Float64(Float64(1.0 / b) / Float64(3.0 / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.3333333333333333 * z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.9999999999995739], N[(N[(t$95$1 * N[(N[Cos[t$95$2], $MachinePrecision] * N[Cos[y], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(1.0 / b), $MachinePrecision] / N[(3.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.9999999999995739

   1. Initial program 70.6%

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

      1. lift--.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y - \frac{z \cdot t}{3}\right)} - \frac{a}{b \cdot 3} \]

      2. sub-neg N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y + \left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{b \cdot 3} \]

      3. +-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\left(\mathsf{neg}\left(\frac{z \cdot t}{3}\right)\right) + y\right)} - \frac{a}{b \cdot 3} \]

      4. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\left(\mathsf{neg}\left(\color{blue}{\frac{z \cdot t}{3}}\right)\right) + y\right) - \frac{a}{b \cdot 3} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\left(\mathsf{neg}\left(\frac{\color{blue}{z \cdot t}}{3}\right)\right) + y\right) - \frac{a}{b \cdot 3} \]

      6. associate-/l* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\left(\mathsf{neg}\left(\color{blue}{z \cdot \frac{t}{3}}\right)\right) + y\right) - \frac{a}{b \cdot 3} \]

      7. *-commutative N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\left(\mathsf{neg}\left(\color{blue}{\frac{t}{3} \cdot z}\right)\right) + y\right) - \frac{a}{b \cdot 3} \]

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

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\color{blue}{\left(\mathsf{neg}\left(\frac{t}{3}\right)\right) \cdot z} + y\right) - \frac{a}{b \cdot 3} \]

      9. lower-fma.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\mathsf{fma}\left(\mathsf{neg}\left(\frac{t}{3}\right), z, y\right)\right)} - \frac{a}{b \cdot 3} \]

      10. div-inv N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{t \cdot \frac{1}{3}}\right), z, y\right)\right) - \frac{a}{b \cdot 3} \]

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

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(\color{blue}{t \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(t \cdot \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3}}\right)\right), z, y\right)\right) - \frac{a}{b \cdot 3} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(t \cdot \color{blue}{\frac{-1}{3}}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

      14. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(t \cdot \color{blue}{\frac{1}{-3}}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(t \cdot \frac{1}{\color{blue}{\mathsf{neg}\left(3\right)}}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

      16. lower-*.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(\color{blue}{t \cdot \frac{1}{\mathsf{neg}\left(3\right)}}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

      17. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(t \cdot \frac{1}{\color{blue}{-3}}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

      18. metadata-eval 70.8

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\mathsf{fma}\left(t \cdot \color{blue}{-0.3333333333333333}, z, y\right)\right) - \frac{a}{b \cdot 3} \]

   4. Applied rewrites 70.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(\mathsf{fma}\left(t \cdot -0.3333333333333333, z, y\right)\right)} - \frac{a}{b \cdot 3} \]

   6. Applied rewrites 73.5%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{fma}\left(\cos \left(\left(0.3333333333333333 \cdot z\right) \cdot t\right), \cos y, \sin y \cdot \sin \left(\left(0.3333333333333333 \cdot z\right) \cdot t\right)\right)} - \frac{a}{b \cdot 3} \]

   if 0.9999999999995739 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 66.8%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   4. Step-by-step derivation

      1. lower-cos.f64 85.8

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

   5. Applied rewrites 85.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

      2. clear-num N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{\frac{b \cdot 3}{a}}} \]

      3. inv-pow N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{\left(\frac{b \cdot 3}{a}\right)}^{-1}} \]

      4. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\left(\frac{\color{blue}{b \cdot 3}}{a}\right)}^{-1} \]

      5. associate-/l* N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\color{blue}{\left(b \cdot \frac{3}{a}\right)}}^{-1} \]

      6. unpow-prod-down N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

      7. inv-pow N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

      9. inv-pow N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

      10. lower-pow.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

      11. lower-pow.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{{\left(\frac{3}{a}\right)}^{-1}} \]

      12. lower-/.f64 85.9

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot {\color{blue}{\left(\frac{3}{a}\right)}}^{-1} \]

   7. Applied rewrites 85.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]
   8. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

      2. lift-pow.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{{\left(\frac{3}{a}\right)}^{-1}} \]

      3. unpow-1 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{\frac{1}{\frac{3}{a}}} \]

      4. un-div-inv N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{{b}^{-1}}{\frac{3}{a}}} \]

      5. frac-2neg N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\mathsf{neg}\left({b}^{-1}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)}} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\mathsf{neg}\left({b}^{-1}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)}} \]

      7. lift-pow.f64 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\mathsf{neg}\left(\color{blue}{{b}^{-1}}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

      8. unpow-1 N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\mathsf{neg}\left(\color{blue}{\frac{1}{b}}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

      9. distribute-neg-frac N/A

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{\mathsf{neg}\left(1\right)}{b}}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

      10. metadata-eval N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{\color{blue}{-1}}{b}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

      11. lower-/.f64 N/A

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{-1}{b}}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

      12. lower-neg.f64 85.9

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{-1}{b}}{\color{blue}{-\frac{3}{a}}} \]

   9. Applied rewrites 85.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9999999999995739:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(\left(0.3333333333333333 \cdot z\right) \cdot t\right), \cos y, \sin y \cdot \sin \left(\left(0.3333333333333333 \cdot z\right) \cdot t\right)\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{1}{b}}{\frac{3}{a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;\frac{a}{-3 \cdot b}\\ \mathbf{elif}\;t\_1 \leq 100000000:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{a}{b}}{-3}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (<= t_1 -5e+71)
     (/ a (* -3.0 b))
     (if (<= t_1 100000000.0)
       (* (* (sqrt x) 2.0) (cos (fma -0.3333333333333333 (* t z) y)))
       (/ (/ a b) -3.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if (t_1 <= -5e+71) {
		tmp = a / (-3.0 * b);
	} else if (t_1 <= 100000000.0) {
		tmp = (sqrt(x) * 2.0) * cos(fma(-0.3333333333333333, (t * z), y));
	} else {
		tmp = (a / b) / -3.0;
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if (t_1 <= -5e+71)
		tmp = Float64(a / Float64(-3.0 * b));
	elseif (t_1 <= 100000000.0)
		tmp = Float64(Float64(sqrt(x) * 2.0) * cos(fma(-0.3333333333333333, Float64(t * z), y)));
	else
		tmp = Float64(Float64(a / b) / -3.0);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+71], N[(a / N[(-3.0 * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 100000000.0], N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(-0.3333333333333333 * N[(t * z), $MachinePrecision] + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(a / b), $MachinePrecision] / -3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -4.99999999999999972e71

   1. Initial program 73.4%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

      2. lower-/.f64 93.5

         \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

   5. Applied rewrites 93.5%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

   7. Applied rewrites 93.7%

      \[\leadsto \frac{a}{\color{blue}{-3 \cdot b}} \]

   if -4.99999999999999972e71 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 1e8

   1. Initial program 58.7%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in x around -inf

      \[\leadsto \color{blue}{-2 \cdot \left(\sqrt{x} \cdot \left(\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right) \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)} \]

   5. Applied rewrites 53.3%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(\mathsf{fma}\left(-0.3333333333333333, t \cdot z, y\right)\right)} \]

   if 1e8 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 85.4%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
   4. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

      2. lower-/.f64 89.6

         \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

   5. Applied rewrites 89.6%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
   6. Step-by-step derivation

   7. Applied rewrites 89.8%

      \[\leadsto \frac{\frac{a}{b}}{\color{blue}{-3}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{1}{b}}{\frac{3}{a}} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ (/ 1.0 b) (/ 3.0 a))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - ((1.0 / b) / (3.0 / a));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - ((1.0d0 / b) / (3.0d0 / a))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - ((1.0 / b) / (3.0 / a));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - ((1.0 / b) / (3.0 / a))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(Float64(1.0 / b) / Float64(3.0 / a)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - ((1.0 / b) / (3.0 / a));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(1.0 / b), $MachinePrecision] / N[(3.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

   2. clear-num N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{\frac{b \cdot 3}{a}}} \]

   3. inv-pow N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{\left(\frac{b \cdot 3}{a}\right)}^{-1}} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\left(\frac{\color{blue}{b \cdot 3}}{a}\right)}^{-1} \]

   5. associate-/l* N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\color{blue}{\left(b \cdot \frac{3}{a}\right)}}^{-1} \]

   6. unpow-prod-down N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

   7. inv-pow N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

   9. inv-pow N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

   10. lower-pow.f64 N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

   11. lower-pow.f64 N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{{\left(\frac{3}{a}\right)}^{-1}} \]

   12. lower-/.f64 77.0

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot {\color{blue}{\left(\frac{3}{a}\right)}}^{-1} \]

7. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

   2. lift-pow.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{{\left(\frac{3}{a}\right)}^{-1}} \]

   3. unpow-1 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{\frac{1}{\frac{3}{a}}} \]

   4. un-div-inv N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{{b}^{-1}}{\frac{3}{a}}} \]

   5. frac-2neg N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\mathsf{neg}\left({b}^{-1}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)}} \]

   6. lower-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\mathsf{neg}\left({b}^{-1}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)}} \]

   7. lift-pow.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\mathsf{neg}\left(\color{blue}{{b}^{-1}}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   8. unpow-1 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\mathsf{neg}\left(\color{blue}{\frac{1}{b}}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   9. distribute-neg-frac N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{\mathsf{neg}\left(1\right)}{b}}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   10. metadata-eval N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{\color{blue}{-1}}{b}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   11. lower-/.f64 N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{-1}{b}}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   12. lower-neg.f64 77.0

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{-1}{b}}{\color{blue}{-\frac{3}{a}}} \]

9. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{-1}{b}}{-\frac{3}{a}}} \]

10. Final simplification 77.0%

    \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{1}{b}}{\frac{3}{a}} \]
11. Add Preprocessing

Alternative 4: 76.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ a (* b 3.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - (a / (b * 3.0));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (a / (b * 3.0d0))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - (a / (b * 3.0));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - (a / (b * 3.0))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(a / Float64(b * 3.0)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (a / (b * 3.0));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Add Preprocessing

Alternative 5: 76.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-0.3333333333333333 \cdot a}{b}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* (cos y) (sqrt x)) 2.0 (/ (* -0.3333333333333333 a) b)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return fma((cos(y) * sqrt(x)), 2.0, ((-0.3333333333333333 * a) / b));
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(cos(y) * sqrt(x)), 2.0, Float64(Float64(-0.3333333333333333 * a) / b))
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[Cos[y], $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 2.0 + N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{a}{b \cdot 3}} \]

   2. clear-num N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{\frac{b \cdot 3}{a}}} \]

   3. inv-pow N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{\left(\frac{b \cdot 3}{a}\right)}^{-1}} \]

   4. lift-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\left(\frac{\color{blue}{b \cdot 3}}{a}\right)}^{-1} \]

   5. associate-/l* N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {\color{blue}{\left(b \cdot \frac{3}{a}\right)}}^{-1} \]

   6. unpow-prod-down N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

   7. inv-pow N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

   8. lower-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

   9. inv-pow N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

   10. lower-pow.f64 N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1}} \cdot {\left(\frac{3}{a}\right)}^{-1} \]

   11. lower-pow.f64 N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{{\left(\frac{3}{a}\right)}^{-1}} \]

   12. lower-/.f64 77.0

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot {\color{blue}{\left(\frac{3}{a}\right)}}^{-1} \]

7. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]
8. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{{b}^{-1} \cdot {\left(\frac{3}{a}\right)}^{-1}} \]

   2. lift-pow.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{{\left(\frac{3}{a}\right)}^{-1}} \]

   3. unpow-1 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - {b}^{-1} \cdot \color{blue}{\frac{1}{\frac{3}{a}}} \]

   4. un-div-inv N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{{b}^{-1}}{\frac{3}{a}}} \]

   5. frac-2neg N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\mathsf{neg}\left({b}^{-1}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)}} \]

   6. lower-/.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\mathsf{neg}\left({b}^{-1}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)}} \]

   7. lift-pow.f64 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\mathsf{neg}\left(\color{blue}{{b}^{-1}}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   8. unpow-1 N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\mathsf{neg}\left(\color{blue}{\frac{1}{b}}\right)}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   9. distribute-neg-frac N/A

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{\mathsf{neg}\left(1\right)}{b}}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   10. metadata-eval N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{\color{blue}{-1}}{b}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   11. lower-/.f64 N/A

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{\frac{-1}{b}}}{\mathsf{neg}\left(\frac{3}{a}\right)} \]

   12. lower-neg.f64 77.0

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{-1}{b}}{\color{blue}{-\frac{3}{a}}} \]

9. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{\frac{-1}{b}}{-\frac{3}{a}}} \]
10. Step-by-step derivation

    1. lift--.f64 N/A

       \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\frac{-1}{b}}{-\frac{3}{a}}} \]

    2. sub-neg N/A

       \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y + \left(\mathsf{neg}\left(\frac{\frac{-1}{b}}{-\frac{3}{a}}\right)\right)} \]

    3. lift-*.f64 N/A

       \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y} + \left(\mathsf{neg}\left(\frac{\frac{-1}{b}}{-\frac{3}{a}}\right)\right) \]

    4. lift-*.f64 N/A

       \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right)} \cdot \cos y + \left(\mathsf{neg}\left(\frac{\frac{-1}{b}}{-\frac{3}{a}}\right)\right) \]

    5. associate-*l* N/A

       \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} + \left(\mathsf{neg}\left(\frac{\frac{-1}{b}}{-\frac{3}{a}}\right)\right) \]

    6. *-commutative N/A

       \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \cos y\right) \cdot 2} + \left(\mathsf{neg}\left(\frac{\frac{-1}{b}}{-\frac{3}{a}}\right)\right) \]

    7. lift-/.f64 N/A

       \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \left(\mathsf{neg}\left(\color{blue}{\frac{\frac{-1}{b}}{-\frac{3}{a}}}\right)\right) \]

    8. lift-/.f64 N/A

       \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \left(\mathsf{neg}\left(\frac{\color{blue}{\frac{-1}{b}}}{-\frac{3}{a}}\right)\right) \]

    9. associate-/l/ N/A

       \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \left(\mathsf{neg}\left(\color{blue}{\frac{-1}{\left(-\frac{3}{a}\right) \cdot b}}\right)\right) \]

    10. distribute-neg-frac N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \color{blue}{\frac{\mathsf{neg}\left(-1\right)}{\left(-\frac{3}{a}\right) \cdot b}} \]

    11. metadata-eval N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{\color{blue}{1}}{\left(-\frac{3}{a}\right) \cdot b} \]

    12. lift-neg.f64 N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{1}{\color{blue}{\left(\mathsf{neg}\left(\frac{3}{a}\right)\right)} \cdot b} \]

    13. lift-/.f64 N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{1}{\left(\mathsf{neg}\left(\color{blue}{\frac{3}{a}}\right)\right) \cdot b} \]

    14. distribute-neg-frac N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{1}{\color{blue}{\frac{\mathsf{neg}\left(3\right)}{a}} \cdot b} \]

    15. metadata-eval N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{1}{\frac{\color{blue}{-3}}{a} \cdot b} \]

    16. associate-*l/ N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{1}{\color{blue}{\frac{-3 \cdot b}{a}}} \]

    17. lift-*.f64 N/A

        \[\leadsto \left(\sqrt{x} \cdot \cos y\right) \cdot 2 + \frac{1}{\frac{\color{blue}{-3 \cdot b}}{a}} \]

11. Applied rewrites 77.0%

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-0.3333333333333333 \cdot a}{b}\right)} \]
12. Add Preprocessing

Alternative 6: 76.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{a}{b} \cdot -0.3333333333333333\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* (cos y) (sqrt x)) 2.0 (* (/ a b) -0.3333333333333333)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return fma((cos(y) * sqrt(x)), 2.0, ((a / b) * -0.3333333333333333));
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(cos(y) * sqrt(x)), 2.0, Float64(Float64(a / b) * -0.3333333333333333))
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[Cos[y], $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * 2.0 + N[(N[(a / b), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
4. Step-by-step derivation

   1. lower-cos.f64 77.0

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]

5. Applied rewrites 77.0%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{b \cdot 3} \]
6. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{b \cdot 3}} \]

   2. sub-neg N/A

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y + \left(\mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right)} \]

   3. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y} + \left(\mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right) \]

   4. lift-*.f64 N/A

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right)} \cdot \cos y + \left(\mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right) \]

   5. associate-*l* N/A

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} + \left(\mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right) \]

   6. *-commutative N/A

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \cos y\right) \cdot 2} + \left(\mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right) \]

   7. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot \cos y, 2, \mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right)} \]

   8. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\cos y \cdot \sqrt{x}}, 2, \mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\cos y \cdot \sqrt{x}}, 2, \mathsf{neg}\left(\frac{a}{b \cdot 3}\right)\right) \]

   10. lift-/.f64 N/A

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \mathsf{neg}\left(\color{blue}{\frac{a}{b \cdot 3}}\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \color{blue}{\frac{\mathsf{neg}\left(a\right)}{b \cdot 3}}\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{\color{blue}{-1 \cdot a}}{b \cdot 3}\right) \]

   13. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1 \cdot a}{\color{blue}{b \cdot 3}}\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{-1 \cdot a}{\color{blue}{3 \cdot b}}\right) \]

7. Applied rewrites 77.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{x}, 2, \frac{a}{b} \cdot -0.3333333333333333\right)} \]
8. Add Preprocessing

Alternative 7: 76.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \frac{a}{b}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (fma (* 2.0 (cos y)) (sqrt x) (* -0.3333333333333333 (/ a b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return fma((2.0 * cos(y)), sqrt(x), (-0.3333333333333333 * (a / b)));
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return fma(Float64(2.0 * cos(y)), sqrt(x), Float64(-0.3333333333333333 * Float64(a / b)))
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Sqrt[x], $MachinePrecision] + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) - \frac{1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. cancel-sign-sub-inv N/A

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \frac{a}{b}} \]

   2. metadata-eval N/A

      \[\leadsto 2 \cdot \left(\sqrt{x} \cdot \cos y\right) + \color{blue}{\frac{-1}{3}} \cdot \frac{a}{b} \]

   3. *-commutative N/A

      \[\leadsto 2 \cdot \color{blue}{\left(\cos y \cdot \sqrt{x}\right)} + \frac{-1}{3} \cdot \frac{a}{b} \]

   4. associate-*r* N/A

      \[\leadsto \color{blue}{\left(2 \cdot \cos y\right) \cdot \sqrt{x}} + \frac{-1}{3} \cdot \frac{a}{b} \]

   5. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, \frac{-1}{3} \cdot \frac{a}{b}\right)} \]

   6. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{2 \cdot \cos y}, \sqrt{x}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   7. lower-cos.f64 N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot \color{blue}{\cos y}, \sqrt{x}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   8. lower-sqrt.f64 N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \color{blue}{\sqrt{x}}, \frac{-1}{3} \cdot \frac{a}{b}\right) \]

   9. lower-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}}\right) \]

   10. lower-/.f64 77.0

       \[\leadsto \mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}}\right) \]

5. Applied rewrites 77.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot \cos y, \sqrt{x}, -0.3333333333333333 \cdot \frac{a}{b}\right)} \]
6. Add Preprocessing

Alternative 8: 50.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{\frac{-1}{b}}{\frac{3}{a}} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (/ (/ -1.0 b) (/ 3.0 a)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return (-1.0 / b) / (3.0 / a);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = ((-1.0d0) / b) / (3.0d0 / a)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return (-1.0 / b) / (3.0 / a);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return (-1.0 / b) / (3.0 / a)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(-1.0 / b) / Float64(3.0 / a))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (-1.0 / b) / (3.0 / a);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(-1.0 / b), $MachinePrecision] / N[(3.0 / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

   2. lower-/.f64 48.3

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

5. Applied rewrites 48.3%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Step-by-step derivation

7. Applied rewrites 48.3%

   \[\leadsto \frac{a}{\color{blue}{-3 \cdot b}} \]
8. Step-by-step derivation

9. Applied rewrites 48.4%

   \[\leadsto \frac{\frac{-1}{b}}{\color{blue}{\frac{3}{a}}} \]
10. Add Preprocessing

Alternative 9: 50.2% accurate, 6.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{\frac{a}{b}}{-3} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (/ (/ a b) -3.0))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return (a / b) / -3.0;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (a / b) / (-3.0d0)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return (a / b) / -3.0;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return (a / b) / -3.0

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(a / b) / -3.0)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (a / b) / -3.0;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(a / b), $MachinePrecision] / -3.0), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

   2. lower-/.f64 48.3

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

5. Applied rewrites 48.3%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Step-by-step derivation

7. Applied rewrites 48.3%

   \[\leadsto \frac{\frac{a}{b}}{\color{blue}{-3}} \]
8. Add Preprocessing

Alternative 10: 50.2% accurate, 9.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{a}{-3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (/ a (* -3.0 b)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return a / (-3.0 * b);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = a / ((-3.0d0) * b)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return a / (-3.0 * b);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return a / (-3.0 * b)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(a / Float64(-3.0 * b))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = a / (-3.0 * b);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(a / N[(-3.0 * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

   2. lower-/.f64 48.3

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

5. Applied rewrites 48.3%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Step-by-step derivation

7. Applied rewrites 48.3%

   \[\leadsto \frac{a}{\color{blue}{-3 \cdot b}} \]
8. Add Preprocessing

Alternative 11: 50.1% accurate, 9.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (-0.3333333333333333d0) * (a / b)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / b);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return -0.3333333333333333 * (a / b)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(-0.3333333333333333 * Float64(a / b))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.1%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]

   2. lower-/.f64 48.3

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{a}{b}} \]

5. Applied rewrites 48.3%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Add Preprocessing

Developer Target 1: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t\_3 \cdot \cos \left(\frac{1}{y} - t\_1\right) - t\_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t\_1\right) \cdot t\_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ 0.3333333333333333 z) t))
        (t_2 (/ (/ a 3.0) b))
        (t_3 (* 2.0 (sqrt x))))
   (if (< z -1.3793337487235141e+129)
     (- (* t_3 (cos (- (/ 1.0 y) t_1))) t_2)
     (if (< z 3.516290613555987e+106)
       (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) t_2)
       (- (* (cos (- y t_1)) t_3) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (0.3333333333333333d0 / z) / t
    t_2 = (a / 3.0d0) / b
    t_3 = 2.0d0 * sqrt(x)
    if (z < (-1.3793337487235141d+129)) then
        tmp = (t_3 * cos(((1.0d0 / y) - t_1))) - t_2
    else if (z < 3.516290613555987d+106) then
        tmp = ((sqrt(x) * 2.0d0) * cos((y - ((t / 3.0d0) * z)))) - t_2
    else
        tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * Math.cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((Math.sqrt(x) * 2.0) * Math.cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (Math.cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.3333333333333333 / z) / t
	t_2 = (a / 3.0) / b
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if z < -1.3793337487235141e+129:
		tmp = (t_3 * math.cos(((1.0 / y) - t_1))) - t_2
	elif z < 3.516290613555987e+106:
		tmp = ((math.sqrt(x) * 2.0) * math.cos((y - ((t / 3.0) * z)))) - t_2
	else:
		tmp = (math.cos((y - t_1)) * t_3) - ((a / b) / 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.3333333333333333 / z) / t)
	t_2 = Float64(Float64(a / 3.0) / b)
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (z < -1.3793337487235141e+129)
		tmp = Float64(Float64(t_3 * cos(Float64(Float64(1.0 / y) - t_1))) - t_2);
	elseif (z < 3.516290613555987e+106)
		tmp = Float64(Float64(Float64(sqrt(x) * 2.0) * cos(Float64(y - Float64(Float64(t / 3.0) * z)))) - t_2);
	else
		tmp = Float64(Float64(cos(Float64(y - t_1)) * t_3) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.3333333333333333 / z) / t;
	t_2 = (a / 3.0) / b;
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (z < -1.3793337487235141e+129)
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	elseif (z < 3.516290613555987e+106)
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	else
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.3333333333333333 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.3793337487235141e+129], N[(N[(t$95$3 * N[Cos[N[(N[(1.0 / y), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[z, 3.516290613555987e+106], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(y - N[(N[(t / 3.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024318 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))