Details

sample468.0ms

Algorithm

intervals

Results

213.0ms	48×	body	2560	valid
106.0ms	89×	body	1280	valid
44.0ms	62×	body	640	valid
11.0ms	27×	body	320	valid
6.0ms	18×	body	160	valid
2.0ms	12×	body	80	valid

simplify60.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite35.0ms

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:

20.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series252.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (- x (sin x)) (- x (tan x)))
104.0ms	(- x (tan x))
56.0ms	(- x (sin x))

simplify789.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
2	1382
1	372
0	157

prune431.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.7b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

12.0ms	(/ (sin x) (- x (tan x)))
75.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
9.0ms	(- x (tan x))
16.0ms	(- x (tan x))

series490.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (sin x) (- x (tan x)))
234.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
74.0ms	(- x (tan x))
77.0ms	(- x (tan x))

simplify677.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1452
1	389
0	177

prune525.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 9/40 (* x x)) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (* x x))
14.8b	(- (- (* 9/40 (* x x)) 1/2) (* 27/2800 (pow x 4)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

15.0ms	(- (* 9/40 (* x x)) 1/2)
9.0ms	(* 27/2800 (pow x 4))
13.0ms	(* 9/40 (* x x))
126.0ms	(- (- (* 9/40 (* x x)) 1/2) (* 27/2800 (pow x 4)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (* 9/40 (* x x)) 1/2)
46.0ms	(* 27/2800 (pow x 4))
41.0ms	(* 9/40 (* x x))
73.0ms	(- (- (* 9/40 (* x x)) 1/2) (* 27/2800 (pow x 4)))

simplify1.0s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1742
1	348
0	127

prune336.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes86.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch101.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.02964489669427243
8	-0.9341403346610884	-0.003292329160956242	-0.029656023299900573

simplify3.0ms

Iterations

Iter	Nodes
done	27
1	27
0	22

end0.0ms

sample13.9s

Algorithm

intervals

Results

6.5s	1636×	body	2560	valid
4.3s	2687×	body	1280	valid
1.5s	1902×	body	640	valid
696.0ms	923×	body	320	valid
656.0ms	504×	body	160	valid
57.0ms	348×	body	80	valid