Details

Time bar (total: 41.1s)

sample355.0ms

Algorithm
intervals
Results
187.0ms88×body1280valid
86.0ms61×body640valid
22.0ms23×body320valid
22.0ms72×body80valid
6.0ms12×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0321087
1741087
21811087
36551087
431411087
done50001087

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize100.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
15×*-un-lft-identity
11×add-cbrt-cube add-exp-log
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*r* associate-*l* associate-*r/
5×sqrt-prod difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-+ flip3-- flip-+ flip-- associate-/l* distribute-lft-out--
2×distribute-rgt-in cbrt-undiv distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod unswap-sqr associate-/l/
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv diff-cos
Counts
4 → 88
Calls
4 calls:
63.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
78.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- 3.0 (sqrt 5.0))
6.0ms
(- (cos x) (cos y))

series2.1s

Counts
4 → 10
Calls
4 calls:
1.9s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
128.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
73.0ms
(- (cos x) (cos y))

simplify3.8s

Counts
98 → 98
Iterations

Useful iterations: 2 (1.7s)

IterNodesCost
032460596
191856563
2412956243
done500056283

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize109.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
0.3b
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
16×*-un-lft-identity
13×sqrt-prod
11×add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×associate-*l*
8×add-log-exp
6×pow1 associate-*r* associate-*r/
5×difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-+ flip3-- flip-+ flip-- associate-/l* distribute-lft-out-- unswap-sqr
2×distribute-rgt-in cbrt-undiv distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/
1×clear-num associate-/r* frac-2neg pow-prod-down *-commutative div-inv diff-cos
Counts
4 → 92
Calls
4 calls:
68.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
81.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
10.0ms
(- 3.0 (sqrt 5.0))
11.0ms
(- (cos x) (cos y))

series2.5s

Counts
4 → 10
Calls
4 calls:
163.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
2.3s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.0ms
(- 3.0 (sqrt 5.0))
77.0ms
(- (cos x) (cos y))

simplify4.1s

Counts
102 → 102
Iterations

Useful iterations: 2 (2.0s)

IterNodesCost
033065533
192361500
2408658900
done500058900

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.3b
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
0.3b
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
1.7b
(- (cos x) (cos y))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×sqrt-prod
18×associate-*l*
17×*-un-lft-identity
16×add-cbrt-cube add-exp-log
13×add-cube-cbrt
11×pow1
10×distribute-rgt-in distribute-lft-in associate-*r/
7×sub-neg associate-*r*
6×add-log-exp
5×prod-exp cbrt-unprod
4×times-frac pow-prod-down associate-/r/
3×flip3-+ flip3-- flip-+ flip-- associate-/l* difference-of-squares unswap-sqr
2×cbrt-undiv div-exp associate-*l/ frac-add *-commutative distribute-lft-out-- associate-/l/
1×clear-num associate-/r* frac-2neg diff-log div-inv diff-cos
Counts
4 → 111
Calls
4 calls:
117.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
92.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
90.0ms
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
11.0ms
(- (cos x) (cos y))

series3.6s

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
176.0ms
(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
3.2s
(/ (+ 2.0 (* (* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
90.0ms
(- (cos x) (cos y))

simplify2.2s

Counts
123 → 123
Iterations

Useful iterations: done (2.2s)

IterNodesCost
034881847
1102177603
done500072242

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize162.0ms

Local error

Found 4 expressions with local error:

1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))
1.7b
(- (cos x) (cos y))
1.7b
(- (cos x) (cos y))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-log-exp
5×difference-of-squares
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip-- distribute-lft-out--
3×diff-cos
1×sqrt-prod
Counts
4 → 60
Calls
4 calls:
7.0ms
(- 3.0 (sqrt 5.0))
7.0ms
(- (cos x) (cos y))
6.0ms
(- (cos x) (cos y))
6.0ms
(- (cos x) (cos y))

series237.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(- 3.0 (sqrt 5.0))
78.0ms
(- (cos x) (cos y))
91.0ms
(- (cos x) (cos y))
68.0ms
(- (cos x) (cos y))

simplify1.6s

Counts
70 → 70
Iterations

Useful iterations: 3 (651.0ms)

IterNodesCost
010220992
122017852
259317852
3227617692
done500117692

prune578.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes269.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0361247
1451247
done451247

end0.0ms

sample12.5s

Algorithm
intervals
Results
7.4s2697×body1280valid
3.2s1941×body640valid
764.0ms2244×body80valid
620.0ms732×body320valid
285.0ms386×body160valid