Details

sample126.0ms

Algorithm

intervals

Results

49.0ms	50×	body	2560	valid
20.0ms	40×	body	1280	valid
18.0ms	52×	body	640	valid
11.0ms	66×	body	80	valid
8.0ms	34×	body	320	valid
2.0ms	14×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize17.0ms

Local error

Found 2 expressions with local error:

1.1b	(- 1.0 (cos x))
14.2b	(/ (- 1.0 (cos x)) (* x x))

rewrite86.0ms

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:

11.0ms	(- 1.0 (cos x))
72.0ms	(/ (- 1.0 (cos x)) (* x x))

series145.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- 1.0 (cos x))
100.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

48 → 48

Iterations

Useful iterations: 2 (294.0ms)

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

prune302.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
1.1b	(- 1.0 (cos x))

rewrite103.0ms

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:

40.0ms	(/ (/ (- 1.0 (cos x)) x) x)
38.0ms	(/ (- 1.0 (cos x)) x)
12.0ms	(- 1.0 (cos x))

series198.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (/ (- 1.0 (cos x)) x) x)
88.0ms	(/ (- 1.0 (cos x)) x)
35.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

156 → 156

Iterations

Useful iterations: done (1.6s)

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

prune799.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
1.1b	(- 1.0 (cos x))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 114

Calls

3 calls:

60.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
35.0ms	(/ (- 1.0 (cos x)) x)
12.0ms	(- 1.0 (cos x))

series205.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
79.0ms	(/ (- 1.0 (cos x)) x)
37.0ms	(- 1.0 (cos x))

simplify3.4s

Counts

123 → 123

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	189	1536
1	546	1395
2	3228	1245
done	5000	1237

prune671.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

49.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
14.0ms	(exp (log (- 1.0 (cos x))))
10.0ms	(log (- 1.0 (cos x)))
13.0ms	(- 1.0 (cos x))

series277.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
32.0ms	(exp (log (- 1.0 (cos x))))
135.0ms	(log (- 1.0 (cos x)))
35.0ms	(- 1.0 (cos x))

simplify755.0ms

Counts

110 → 110

Iterations

Useful iterations: done (746.0ms)

Iter	Nodes	Cost
0	169	1343
1	309	1102
2	930	1032
done	5001	1031

prune506.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes162.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.5b

bsearch127.0ms

Steps

Iters	Range		Point
10	2.8868360106527892e-08	453261925.93168354	0.029848537881546774
9	-4.26929226401081	-3.26160511802404e-08	-0.030963531967900033

simplify12.0ms

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	31	45
1	38	43
2	40	41
done	40	41

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.7s	1562×	body	2560	valid
1.4s	1238×	body	1280	valid
683.0ms	1516×	body	640	valid
235.0ms	932×	body	320	valid
195.0ms	2301×	body	80	valid
74.0ms	451×	body	160	valid