Details

sample428.0ms

Algorithm

intervals

Results

132.0ms	42×	body	2560	valid
104.0ms	86×	body	1280	valid
89.0ms	68×	body	640	valid
16.0ms	33×	body	320	valid
5.0ms	18×	body	160	valid
2.0ms	9×	body	80	valid

simplify22.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize94.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite61.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
14.0ms	(- x (sin x))

series265.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(/ (- x (sin x)) (- x (tan x)))
92.0ms	(- x (tan x))
71.0ms	(- x (sin x))

simplify1.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune399.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.8b	(- x (tan x))
0.8b	(- x (sin x))
0.8b	(- x (sin x))
0.8b	(- x (sin x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

5.0ms	(- x (tan x))
5.0ms	(- x (sin x))
5.0ms	(- x (sin x))
8.0ms	(- x (sin x))

series238.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- x (tan x))
53.0ms	(- x (sin x))
45.0ms	(- x (sin x))
61.0ms	(- x (sin x))

simplify1.7s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
4	2687
3	881
2	359
1	153
0	76

prune417.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (tan x)) (- x (sin x)))
0.8b	(- x (tan x))
0.8b	(- x (sin x))

rewrite30.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

18.0ms	(/ (- x (tan x)) (- x (sin x)))
4.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series261.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(/ (- x (tan x)) (- x (sin x)))
74.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify1.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1329
1	366
0	155

prune388.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* (* x x) 27/2800))
0.1b	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
0.2b	(* (* x x) 27/2800)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-l` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 56

Calls

3 calls:

8.0ms	(- 9/40 (* (* x x) 27/2800))
48.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
28.0ms	(* (* x x) 27/2800)

series291.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(- 9/40 (* (* x x) 27/2800))
143.0ms	(* (* x x) (- 9/40 (* (* x x) 27/2800)))
52.0ms	(* (* x x) 27/2800)

simplify1.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5002
2	1743
1	258
0	87

prune206.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes76.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch136.0ms

Steps

Iters	Range		Point
11	1.9534460235190362e-22	53640.016154094046	0.02985439976441334
10	-17239113253358.373	-4.96108325192681e-05	-0.026748202540908116

simplify6.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample13.3s

Algorithm

intervals

Results

6.1s	1666×	body	2560	valid
4.5s	2699×	body	1280	valid
1.3s	1879×	body	640	valid
901.0ms	944×	body	320	valid
137.0ms	474×	body	160	valid
55.0ms	338×	body	80	valid