Details

sample92.0ms

Algorithm

intervals

Results

44.0ms	66×	body	2560	valid
14.0ms	54×	body	640	valid
10.0ms	28×	body	1280	valid
5.0ms	34×	body	320	valid
4.0ms	59×	body	80	valid
2.0ms	15×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	28	8
done	28	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize15.0ms

Local error

Found 2 expressions with local error:

2.6b	(- 1.0 (cos x))
18.4b	(/ (- 1.0 (cos x)) (* x x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

12.0ms	(- 1.0 (cos x))
70.0ms	(/ (- 1.0 (cos x)) (* x x))

series82.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- 1.0 (cos x))
55.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify701.0ms

Counts

48 → 48

Iterations

Useful iterations: 2 (161.0ms)

Iter	Nodes	Cost
0	88	507
1	232	489
2	1094	441
done	5001	441

prune129.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
12.2b	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite99.0ms

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--` `associate--l+` `sum-log` `flip--`

Counts

3 → 66

Calls

3 calls:

12.0ms	(* 1/24 (pow x 2))
12.0ms	(* 1/720 (pow x 4))
74.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* 1/24 (pow x 2))
58.0ms	(* 1/720 (pow x 4))
49.0ms	(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify995.0ms

Counts

75 → 75

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	121	780
1	286	703
2	1105	645
done	5000	635

prune276.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/24 (pow x 2))
0.3b	(* 1/720 (pow x 4))
0.8b	(log (exp (* 1/720 (pow x 4))))
12.2b	(- (+ (log (exp (* 1/720 (pow x 4)))) 1/2) (* 1/24 (pow x 2)))

rewrite123.0ms

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` `associate--l+` `sum-log` `flip--`

Counts

4 → 80

Calls

4 calls:

19.0ms	(* 1/24 (pow x 2))
21.0ms	(* 1/720 (pow x 4))
3.0ms	(log (exp (* 1/720 (pow x 4))))
77.0ms	(- (+ (log (exp (* 1/720 (pow x 4)))) 1/2) (* 1/24 (pow x 2)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/24 (pow x 2))
60.0ms	(* 1/720 (pow x 4))
59.0ms	(log (exp (* 1/720 (pow x 4))))
63.0ms	(- (+ (log (exp (* 1/720 (pow x 4)))) 1/2) (* 1/24 (pow x 2)))

simplify1.1s

Counts

92 → 92

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	140	973
1	314	823
2	1241	757
done	5001	747

prune352.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.6b	(- 1.0 (cos x))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
24×	`associate-/l*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log`

Counts

3 → 147

Calls

3 calls:

29.0ms	(/ (/ (- 1.0 (cos x)) x) x)
16.0ms	(/ (- 1.0 (cos x)) x)
6.0ms	(- 1.0 (cos x))

series128.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (/ (- 1.0 (cos x)) x) x)
53.0ms	(/ (- 1.0 (cos x)) x)
25.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

156 → 156

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	229	2262
1	549	2156
2	2484	2048
done	5000	2028

prune415.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes72.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.6b

bsearch130.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.033975437319783745
10	-911936.9907706906	-4.3470241882695893e-07	-0.030405916147053742

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	34	43
done	34	43

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	1658×	body	2560	valid
574.0ms	1259×	body	1280	valid
429.0ms	1430×	body	640	valid
162.0ms	943×	body	320	valid
122.0ms	2222×	body	80	valid
58.0ms	488×	body	160	valid