Details

sample554.0ms

Algorithm

intervals

Results

134.0ms	60×	body	2560	valid
89.0ms	103×	body	1280	valid
15.0ms	47×	body	640	valid
6.0ms	26×	body	320	valid
2.0ms	9×	body	160	valid
1.0ms	11×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5
done	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.6b	(- x (tan x))
0.6b	(- x (sin x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify147.0ms

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685
done	5001	685

prune201.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- x (tan x))
0.6b	(- x (tan x))
0.6b	(- x (sin x))
0.6b	(- x (sin x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

6.0ms	(- x (tan x))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))
7.0ms	(- x (sin x))

series172.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- x (tan x))
54.0ms	(- x (tan x))
32.0ms	(- x (sin x))
32.0ms	(- x (sin x))

simplify65.0ms

Counts

68 → 68

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	150	314
1	342	294
2	774	294
3	2023	294
4	5001	294
done	5001	294

prune185.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
18.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

12.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
20.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series114.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
49.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify39.0ms

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315
done	5001	315

prune141.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(log (exp (* 27/2800 (pow x 4))))
0.3b	(* 9/40 (pow x 2))
18.6b	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`pow1`
4×	`sqr-pow`
3×	`log-prod` `log-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `sum-log` `flip--` `associate--r+`

Counts

4 → 80

Calls

4 calls:

12.0ms	(* 27/2800 (pow x 4))
3.0ms	(log (exp (* 27/2800 (pow x 4))))
12.0ms	(* 9/40 (pow x 2))
24.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

series148.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 27/2800 (pow x 4))
39.0ms	(log (exp (* 27/2800 (pow x 4))))
25.0ms	(* 9/40 (pow x 2))
47.0ms	(- (* 9/40 (pow x 2)) (+ (log (exp (* 27/2800 (pow x 4)))) 1/2))

simplify42.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	300	448
1	1183	390
2	5001	385
done	5001	385

prune212.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes63.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch84.0ms

Steps

Iters	Range		Point
8	0.02319676823116778	7.055123656280252	1.5807919572689517
10	-1.8070707071506563e+17	-0.15939393977811658	-1.5845262208940065

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	21
1	33	21
done	33	21

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.4s	1575×	body	2560	valid
1.9s	2776×	body	1280	valid
701.0ms	1962×	body	640	valid
200.0ms	904×	body	320	valid
68.0ms	439×	body	160	valid
30.0ms	344×	body	80	valid