Details

Time bar (total: 40.5s)

sample413.0ms

Algorithm
intervals
Results
204.0ms97×body1280valid
104.0ms57×body640valid
54.0ms24×body320valid
18.0ms65×body80valid
8.0ms13×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
17450
218150
365350
4266450
done500050

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
20×times-frac
18×add-cube-cbrt
11×add-exp-log add-cbrt-cube difference-of-squares
9×associate-*r*
8×pow1 sqrt-prod add-log-exp
6×distribute-lft-out--
4×sub-neg unswap-sqr
3×flip3-- prod-exp flip-- cbrt-unprod
2×distribute-rgt-in distribute-lft-in diff-log associate-*r/ pow-prod-down *-commutative
1×cbrt-undiv div-exp associate-*l/ div-inv diff-cos
Counts
4 → 102
Calls
4 calls:
56.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
77.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
12.0ms
(- 3.0 (sqrt 5.0))
10.0ms
(- (cos x) (cos y))

series311.0ms

Counts
4 → 10
Calls
4 calls:
104.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
138.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
68.0ms
(- (cos x) (cos y))

simplify1.4s

Counts
112 → 112
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02471369
15841330
216891232
done50001221

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

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

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
30×*-un-lft-identity
28×associate-*l*
23×times-frac
20×add-cube-cbrt
16×add-exp-log add-cbrt-cube
9×associate-*r* difference-of-squares
8×pow1
7×sqrt-prod
6×associate-*r/ add-log-exp
5×distribute-lft-out--
4×prod-exp associate-/r/ cbrt-unprod unswap-sqr
3×cbrt-undiv sub-neg flip3-+ div-exp associate-*l/ flip-+ associate-/l*
2×distribute-rgt-in flip3-- distribute-lft-in pow-prod-down frac-add *-commutative flip-- div-inv associate-/l/
1×frac-2neg diff-log clear-num associate-/r* diff-cos
Counts
4 → 114
Calls
4 calls:
87.0ms
(/ (+ 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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
79.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
69.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- (cos x) (cos y))

series3.0s

Counts
4 → 12
Calls
4 calls:
2.6s
(/ (+ 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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
124.0ms
(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
113.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
80.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
126 → 126
Iterations

Useful iterations: 2 (859.0ms)

IterNodesCost
03723617
110273530
237323107
done50013107

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(/ 1 (sqrt 2.0))
1.7b
(- (cos x) (cos y))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
28×*-un-lft-identity
24×add-cube-cbrt
22×times-frac
16×sqrt-prod
15×add-exp-log
13×add-cbrt-cube
8×pow1
7×associate-/r*
6×associate-*r/ associate-*r* associate-*l* associate-/l* add-log-exp
4×div-exp associate-/r/
3×cbrt-undiv sub-neg pow-flip flip3-+ flip-+ difference-of-squares
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in associate-*l/ frac-add prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- unswap-sqr
1×rec-exp sqrt-pow1 pow1/2 diff-log 1-exp pow-prod-down *-commutative diff-cos inv-pow
Counts
4 → 118
Calls
4 calls:
71.0ms
(/ (+ 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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
98.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms
(/ 1 (sqrt 2.0))
8.0ms
(- (cos x) (cos y))

series4.1s

Counts
4 → 10
Calls
4 calls:
3.9s
(/ (+ 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 (* (/ 1 (sqrt 2.0)) (* (/ (- (sqrt 5.0) 1.0) (sqrt 2.0)) (cos x)))) (* (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (cos y)))))
122.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(/ 1 (sqrt 2.0))
96.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
128 → 128
Iterations

Useful iterations: done (2.5s)

IterNodesCost
03583755
19523549
234983040
done50002976

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(/ 1 (sqrt 2.0))
1.7b
(- (cos x) (cos y))

rewrite561.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
29×flip3-- *-un-lft-identity flip--
28×frac-times associate-*r/
23×add-cube-cbrt
19×add-exp-log times-frac
17×pow1 add-cbrt-cube
16×sqrt-prod
14×associate-*l/
12×associate-*r*
7×associate-*l* pow-prod-down prod-exp cbrt-unprod
6×associate-/r* add-log-exp
5×sub-neg
4×distribute-rgt-in distribute-lft-in difference-of-squares
3×pow-flip associate-/l* distribute-lft-out--
2×div-exp *-commutative diff-cos unswap-sqr
1×cbrt-undiv rec-exp frac-2neg sqrt-pow1 pow1/2 diff-log 1-exp clear-num div-inv inv-pow
Counts
4 → 145
Calls
4 calls:
460.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
75.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(/ 1 (sqrt 2.0))
12.0ms
(- (cos x) (cos y))

series581.0ms

Counts
4 → 10
Calls
4 calls:
373.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
119.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(/ 1 (sqrt 2.0))
89.0ms
(- (cos x) (cos y))

simplify2.8s

Counts
155 → 155
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
02913534
18393305
239433079
done50013079

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes266.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04064
15264
done5264

end0.0ms

sample14.5s

Algorithm
intervals
Results
7.8s2727×body1280valid
3.8s1787×body640valid
1.2s2248×body80valid
986.0ms853×body320valid
365.0ms385×body160valid