Details

sample714.0ms

Algorithm

intervals

Results

322.0ms	58×	body	2560	valid
128.0ms	32×	body	320	valid
107.0ms	75×	body	1280	valid
46.0ms	65×	body	640	valid
5.0ms	15×	body	160	valid
2.0ms	11×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite117.0ms

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:

47.0ms	(/ (- x (sin x)) (- x (tan x)))
15.0ms	(- x (tan x))
47.0ms	(- x (sin x))

series245.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify1.2s

Counts

89 → 89

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	157	1237
1	371	1200
2	1358	1149
done	5001	1147

prune339.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
14.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite69.0ms

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:

18.0ms	(* 27/2800 (pow x 4))
17.0ms	(* 9/40 (pow x 2))
30.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series184.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 27/2800 (pow x 4))
46.0ms	(* 9/40 (pow x 2))
90.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify931.0ms

Counts

75 → 75

Iterations

Useful iterations: done (928.0ms)

Iter	Nodes	Cost
0	121	788
1	291	703
2	1116	645
done	5000	643

prune279.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.6b	(- x (tan x))
1.6b	(- x (tan x))

rewrite188.0ms

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

Counts

4 → 94

Calls

4 calls:

18.0ms	(/ (sin x) (- x (tan x)))
137.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
11.0ms	(- x (tan x))
12.0ms	(- x (tan x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ (sin x) (- x (tan x)))
254.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
108.0ms	(- x (tan x))
98.0ms	(- x (tan x))

simplify791.0ms

Counts

106 → 106

Iterations

Useful iterations: done (786.0ms)

Iter	Nodes	Cost
0	177	1565
1	388	1511
2	1424	1450
done	5000	1449

prune375.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow x 3))
1.6b	(- x (tan x))
19.8b	(/ (- (+ (* 1/5040 (pow x 7)) (* 1/6 (pow x 3))) (* 1/120 (pow x 5))) (- x (tan x)))
21.5b	(- (+ (* 1/5040 (pow x 7)) (* 1/6 (pow x 3))) (* 1/120 (pow x 5)))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`times-frac`
12×	`associate-r`
11×	`add-exp-log` `add-log-exp`
8×	`add-cbrt-cube`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `unpow-prod-down` `flip3--` `cube-prod` `flip--` `unswap-sqr`
3×	`diff-log` `associate-l` `prod-exp` `associate-/l*`
2×	`sub-neg` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `cube-mult` `pow-to-exp` `frac-2neg` `unpow3` `div-sub` `div-exp` `pow-exp` `associate--l+` `clear-num` `sum-log` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 99

Calls

4 calls:

28.0ms	(* 1/6 (pow x 3))
8.0ms	(- x (tan x))
100.0ms	(/ (- (+ (* 1/5040 (pow x 7)) (* 1/6 (pow x 3))) (* 1/120 (pow x 5))) (- x (tan x)))
57.0ms	(- (+ (* 1/5040 (pow x 7)) (* 1/6 (pow x 3))) (* 1/120 (pow x 5)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/6 (pow x 3))
88.0ms	(- x (tan x))
139.0ms	(/ (- (+ (* 1/5040 (pow x 7)) (* 1/6 (pow x 3))) (* 1/120 (pow x 5))) (- x (tan x)))
119.0ms	(- (+ (* 1/5040 (pow x 7)) (* 1/6 (pow x 3))) (* 1/120 (pow x 5)))

simplify1.2s

Counts

111 → 111

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	197	2351
1	517	2270
2	2033	2117
done	5001	2091

prune459.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.3b

bsearch160.0ms

Steps

Iters	Range		Point
8	0.0004268116563047139	15.006088268796836	0.029128717039290496
8	-101.50163225226844	-0.031678663534995	-0.03379760502135155

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	24	49
1	30	36
done	30	36

end0.0ms

sample13.8s

Algorithm

intervals

Results

6.7s	1549×	body	2560	valid
4.5s	2796×	body	1280	valid
1.6s	1891×	body	640	valid
496.0ms	934×	body	320	valid
145.0ms	461×	body	160	valid
63.0ms	369×	body	80	valid