Details

sample263.0ms

Algorithm

intervals

Results

120.0ms	1769×	body	80	nan
19.0ms	256×	body	80	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	16
1	27	16
2	58	16
3	121	16
4	296	16
5	687	16
6	1204	16
7	2061	16
8	2393	16
9	2562	16
10	2718	16
11	2846	16
12	3015	16
13	3171	16
14	3299	16
15	3468	16
16	3624	16
17	3752	16
18	3921	16
19	4077	16
20	4205	16
21	4375	16
22	4531	16
23	4659	16
24	4829	16
25	4985	16
done	5000	16

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (log (+ x y)) (log z)) t)
0.1b	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.5b	(+ (log (+ x y)) (log z))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
19×	`log-prod`
18×	`add-sqr-sqrt`
15×	`pow1`
14×	`add-log-exp`
12×	`add-cube-cbrt`
9×	`associate-+r+` `log-pow` `distribute-lft-out`
7×	`associate-+l+`
6×	`add-exp-log` `distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `sum-log` `add-cbrt-cube` `flip--` `distribute-lft-out--`
5×	`associate-+l-` `associate-l`
4×	`log-div` `flip3-+` `diff-log` `associate-r` `frac-add` `flip-+`
2×	`+-commutative` `associate--l-` `sub-neg` `associate--l+` `difference-of-squares`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

9.0ms	(- (+ (log (+ x y)) (log z)) t)
20.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
7.0ms	(* (- a 0.5) (log t))
8.0ms	(+ (log (+ x y)) (log z))

series120.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (+ (log (+ x y)) (log z)) t)
59.0ms	(+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t)))
10.0ms	(* (- a 0.5) (log t))
16.0ms	(+ (log (+ x y)) (log z))

simplify619.0ms

Counts

114 → 114

Iterations

Useful iterations: done (615.0ms)

Iter	Nodes	Cost
0	254	1890
1	684	1765
2	2359	1634
done	5000	1629

prune422.0ms

Filtered

84 candidates to 114 candidates (-35.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	7	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 0b

Counts

115 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
0.1b	(* (- a 0.5) (log t))
0.4b	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
0.4b	(+ (log (+ x y)) (log (sqrt z)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
28×	`log-prod`
24×	`pow1`
23×	`distribute-lft-out`
19×	`add-sqr-sqrt`
18×	`associate-+r+` `log-pow`
15×	`add-cube-cbrt` `add-log-exp`
11×	`sum-log`
8×	`associate-+l+`
7×	`associate-+l-`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sqrt-prod` `add-cbrt-cube`
5×	`flip3--` `flip3-+` `associate-l` `flip--` `flip-+`
4×	`log-div` `associate-r` `frac-add`
3×	`+-commutative` `diff-log`
1×	`sub-neg` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

20.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
8.0ms	(* (- a 0.5) (log t))
12.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
9.0ms	(+ (log (+ x y)) (log (sqrt z)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(+ (- (+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z))) t) (* (- a 0.5) (log t)))
10.0ms	(* (- a 0.5) (log t))
25.0ms	(+ (+ (log (+ x y)) (log (sqrt z))) (log (sqrt z)))
27.0ms	(+ (log (+ x y)) (log (sqrt z)))

simplify704.0ms

Counts

127 → 127

Iterations

Useful iterations: done (700.0ms)

Iter	Nodes	Cost
0	308	2493
1	837	2217
2	2941	2014
done	5000	2010

prune183.0ms

Filtered

88 candidates to 127 candidates (-44.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	127	7	134

Merged error: 0b

Counts

134 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))
0.6b	(* (cbrt (+ x y)) (cbrt (+ x y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
38×	`pow1`
35×	`distribute-lft-out`
32×	`cbrt-prod`
30×	`cbrt-div`
22×	`add-sqr-sqrt` `log-pow`
16×	`flip3-+` `flip-+`
14×	`add-cube-cbrt`
10×	`associate-+l-` `log-div`
9×	`swap-sqr`
8×	`frac-times` `pow1/3`
7×	`associate-r` `associate-l` `pow-prod-down`
6×	`add-exp-log`
5×	`add-log-exp`
4×	`associate-r/` `associate-l/` `add-cbrt-cube` `unswap-sqr`
3×	`sum-log`
2×	`associate-+r-` `pow-sqr` `pow-prod-up`
1×	`+-commutative` `pow2` `associate-+l+` `associate-+r+` `log-prod` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

3.0ms	(cbrt (+ x y))
3.0ms	(cbrt (+ x y))
25.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))
11.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

series173.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (+ x y))
33.0ms	(cbrt (+ x y))
65.0ms	(+ (log (* (cbrt (+ x y)) (cbrt (+ x y)))) (+ (log (cbrt (+ x y))) (log z)))
42.0ms	(* (cbrt (+ x y)) (cbrt (+ x y)))

simplify1.0s

Counts

132 → 132

Iterations

Useful iterations: 3 (418.0ms)

Iter	Nodes	Cost
0	195	2149
1	465	1910
2	1305	1565
3	4702	1423
done	5000	1423

prune207.0ms

Filtered

93 candidates to 132 candidates (-41.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	132	7	139

Merged error: 0b

Counts

139 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (+ (- (log z) t) (log (+ x y))) (* (* 2 (log (cbrt t))) (- a 0.5))) (* (- a 0.5) (log (cbrt t))))
0.3b	(+ (- (log z) t) (log (+ x y)))
0.6b	(cbrt t)
0.6b	(cbrt t)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`frac-add`
19×	`log-prod`
17×	`add-log-exp`
16×	`associate-+r+`
12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `associate-*l/`
11×	`sum-log`
10×	`flip3--` `flip3-+` `flip--` `flip-+`
9×	`pow1`
8×	`associate-+l-` `associate-*r/`
7×	`distribute-lft-out`
6×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
5×	`log-pow`
4×	`add-exp-log` `associate-+r-` `log-div` `add-cbrt-cube` `distribute-lft-out--`
3×	`associate--l+`
2×	`+-commutative` `pow1/3` `diff-log`
1×	`sub-neg`

Counts

4 → 94

Calls

4 calls:

19.0ms	(+ (+ (+ (- (log z) t) (log (+ x y))) (* (* 2 (log (cbrt t))) (- a 0.5))) (* (- a 0.5) (log (cbrt t))))
11.0ms	(+ (- (log z) t) (log (+ x y)))
1.0ms	(cbrt t)
1.0ms	(cbrt t)

series170.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (+ (+ (- (log z) t) (log (+ x y))) (* (* 2 (log (cbrt t))) (- a 0.5))) (* (- a 0.5) (log (cbrt t))))
20.0ms	(+ (- (log z) t) (log (+ x y)))
31.0ms	(cbrt t)
24.0ms	(cbrt t)

simplify957.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (314.0ms)

Iter	Nodes	Cost
0	306	3386
1	1019	3166
2	4107	2842
done	5000	2842

prune173.0ms

Filtered

85 candidates to 106 candidates (-24.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	106	7	113

Merged error: 0b

Counts

113 → 7

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	21
1	22	21
done	22	21

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.9s	56874×	body	80	nan
601.0ms	8028×	body	80	valid

Details

sample263.0ms

simplify4.8s

prune5.0ms

localize15.0ms

rewrite48.0ms

series120.0ms

simplify619.0ms

prune422.0ms

localize18.0ms

rewrite53.0ms

series130.0ms

simplify704.0ms

prune183.0ms

localize21.0ms

rewrite49.0ms

series173.0ms

simplify1.0s

prune207.0ms

localize25.0ms

rewrite38.0ms

series170.0ms

simplify957.0ms

prune173.0ms

regimes1.0s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.3s

Profiling