Details

Time bar (total: 1.8m)

sample889.0ms

Algorithm
intervals
Results
266.0ms137×body1280valid
250.0ms35×body5120valid
194.0ms68×body2560valid
112.0ms77×body640valid
18.0ms28×body320valid
14.0ms62×body80valid
4.0ms10×body160valid

simplify2.7s

Counts
1 → 1
Iterations
IterNodes
done5174
43622
3689
2142
144
019

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ l (sin k))
0.3b
(* (pow (/ k t) 2.0) (tan k))
20.4b
(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
34.0b
(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
407×add-exp-log
179×div-exp
173×prod-exp
132×times-frac
89×add-cbrt-cube
72×add-sqr-sqrt
64×*-un-lft-identity add-cube-cbrt
54×pow-exp
47×associate-*l*
42×unpow-prod-down
37×pow-to-exp
34×cbrt-unprod
30×cbrt-undiv
28×associate-/l*
11×sqr-pow
9×pow1
7×div-inv
4×associate-/r* associate-*r* associate-*r/ add-log-exp unswap-sqr
3×pow-prod-down associate-*l/ tan-quot
2×clear-num frac-2neg associate-/r/ *-commutative
1×frac-times associate-/l/
Counts
4 → 274
Calls
4 calls:
4.0ms
(/ l (sin k))
28.0ms
(* (pow (/ k t) 2.0) (tan k))
149.0ms
(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
41.0ms
(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

series1.8s

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ l (sin k))
279.0ms
(* (pow (/ k t) 2.0) (tan k))
954.0ms
(* (/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k))) (* (/ l (sin k)) l))
452.0ms
(/ (/ 2.0 (pow t 3.0)) (* (pow (/ k t) 2.0) (tan k)))

simplify2.8s

Counts
286 → 286
Iterations
IterNodes
done5001
24436
11208
0459

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin k) l) (/ (sin k) l))
0.7b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
10.7b
(* (pow k 2.0) (pow t 1.0))
16.7b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
1292×add-exp-log
790×prod-exp
461×div-exp
367×pow-exp
157×pow-to-exp
80×rec-exp 1-exp
65×add-sqr-sqrt
56×add-cbrt-cube
46×times-frac
41×*-un-lft-identity add-cube-cbrt
31×associate-*l*
23×cbrt-unprod
21×associate-*r*
19×unpow-prod-down
15×cbrt-undiv
13×swap-sqr unswap-sqr
12×pow1
9×sqr-pow
6×div-inv
4×add-log-exp
3×*-commutative associate-/l*
2×associate-*l/ associate-*r/
1×pow2 frac-times clear-num associate-/r* frac-2neg pow-plus pow-prod-down pow-sqr pow-prod-up pow-flip inv-pow
Counts
4 → 418
Calls
4 calls:
21.0ms
(* (/ (sin k) l) (/ (sin k) l))
15.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
15.0ms
(* (pow k 2.0) (pow t 1.0))
150.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (/ (sin k) l) (/ (sin k) l))
483.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
505.0ms
(* (pow k 2.0) (pow t 1.0))
874.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

simplify7.8s

Counts
430 → 430
Iterations
IterNodes
done5029
24346
11387
0507

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.4b

localize82.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.3b
(* (/ (sin k) l) (/ (sin k) l))
0.7b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.7b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

rewrite581.0ms

Algorithm
rewrite-expression-head
Rules
4232×add-exp-log
3008×prod-exp
1373×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
76×add-cbrt-cube
51×add-sqr-sqrt
49×times-frac
39×*-un-lft-identity add-cube-cbrt
28×cbrt-unprod
25×cbrt-undiv
24×associate-*l*
14×associate-*r*
13×swap-sqr
12×pow1
7×unpow-prod-down div-inv
6×associate-/l*
4×add-log-exp unswap-sqr
3×associate-*l/ associate-*r/ associate-/r/
2×frac-times clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-prod-down pow-sqr pow-prod-up pow-flip inv-pow sqr-pow
Counts
4 → 912
Calls
4 calls:
17.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
31.0ms
(* (/ (sin k) l) (/ (sin k) l))
48.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
326.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
59.0ms
(* (/ (sin k) l) (/ (sin k) l))
574.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.0s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))) 2.0))

simplify6.8s

Counts
924 → 924
Iterations
IterNodes
done5000
11688
0649

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0))
0.3b
(* (/ (sin k) l) (/ (sin k) l))
3.7b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) (/ (* 2.0 (cos k)) (* (/ (sin k) l) (/ (sin k) l)))))
12.2b
(* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) (/ (* 2.0 (cos k)) (* (/ (sin k) l) (/ (sin k) l))))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
29536×add-exp-log
16822×div-exp
14668×prod-exp
11901×pow-exp
4335×pow-to-exp
2388×rec-exp 1-exp
766×times-frac
536×unpow-prod-down
438×add-sqr-sqrt
371×*-un-lft-identity
362×add-cube-cbrt
225×associate-*l*
140×add-cbrt-cube
115×sqr-pow
64×cbrt-unprod
43×cbrt-undiv
28×unswap-sqr
25×associate-/l*
23×div-inv
22×associate-*r*
13×swap-sqr
11×pow1
7×associate-/r*
5×associate-*r/
4×add-log-exp
3×associate-/r/ *-commutative
2×frac-times associate-*l/
1×pow2 clear-num frac-2neg pow-plus pow-prod-down pow-sqr pow-prod-up associate-/l/
Counts
4 → 5334
Calls
4 calls:
42.0ms
(/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0))
45.0ms
(* (/ (sin k) l) (/ (sin k) l))
485.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) (/ (* 2.0 (cos k)) (* (/ (sin k) l) (/ (sin k) l)))))
360.0ms
(* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) (/ (* 2.0 (cos k)) (* (/ (sin k) l) (/ (sin k) l))))

series3.0s

Counts
4 → 12
Calls
4 calls:
501.0ms
(/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0))
59.0ms
(* (/ (sin k) l) (/ (sin k) l))
950.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) (/ (* 2.0 (cos k)) (* (/ (sin k) l) (/ (sin k) l)))))
1.5s
(* (pow (/ (/ 1 (pow k (/ 2.0 2))) (pow t 1.0)) 1.0) (/ (* 2.0 (cos k)) (* (/ (sin k) l) (/ (sin k) l))))

simplify34.3s

Counts
5346 → 5346
Iterations
IterNodes
done5000
02622

prune6.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.2b

regimes794.0ms

Accuracy

0% (3.3b remaining)

Error of 8.0b against oracle of 4.6b and baseline of 8.0b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done27
127
022

end0.0ms

sample28.6s

Algorithm
intervals
Results
8.4s4151×body1280valid
6.8s2136×body2560valid
6.6s925×body5120valid
4.2s2536×body640valid
1.3s994×body320valid
449.0ms1977×body80valid
235.0ms454×body160valid