Details

sample74.0ms

Algorithm

intervals

Results

29.0ms	57×	body	2560	valid
13.0ms	36×	body	320	valid
10.0ms	34×	body	1280	valid
8.0ms	41×	body	640	valid
3.0ms	70×	body	80	valid
2.0ms	18×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize14.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
16.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
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×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 42

Calls

2 calls:

6.0ms	(- 1.0 (cos x))
31.0ms	(/ (- 1.0 (cos x)) (* x x))

series122.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(- 1.0 (cos x))
90.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.0s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
2	1129
1	232
0	88

prune270.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- 1.0 (cos x)) x) x)
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite62.0ms

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

Counts

3 → 147

Calls

3 calls:

31.0ms	(/ (/ (- 1.0 (cos x)) x) x)
17.0ms	(/ (- 1.0 (cos x)) x)
5.0ms	(- 1.0 (cos x))

series146.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (/ (- 1.0 (cos x)) x) x)
58.0ms	(/ (- 1.0 (cos x)) x)
21.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

156 → 156

Iterations

Iter	Nodes
done	5001
2	2463
1	549
0	229

prune856.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) x)
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

32.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
9.0ms	(exp (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (exp (log (- 1.0 (cos x)))) x)
34.0ms	(exp (log (- 1.0 (cos x))))
122.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify810.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	930
1	309
0	169

prune650.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x)))) x)
0.3b	(* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x))))
2.0b	(- 1.0 (cos x))
2.0b	(- 1.0 (cos x))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
30×	`sqrt-prod`
24×	`sqrt-div`
19×	`pow1`
14×	`flip3--` `add-cube-cbrt` `flip--`
12×	`swap-sqr`
11×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `distribute-lft-out--` `add-log-exp` `associate-/l/`
6×	`difference-of-squares`
5×	`pow-prod-up`
4×	`associate-l/` `associate-r/` `unswap-sqr`
3×	`associate-/r*` `times-frac` `pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `prod-exp` `cbrt-unprod`
1×	`pow2` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `-commutative` `div-inv` `associate-/l`

Counts

4 → 122

Calls

4 calls:

31.0ms	(/ (* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x)))) x)
65.0ms	(* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x))))
10.0ms	(- 1.0 (cos x))
14.0ms	(- 1.0 (cos x))

series142.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x)))) x)
22.0ms	(* (sqrt (- 1.0 (cos x))) (sqrt (- 1.0 (cos x))))
33.0ms	(- 1.0 (cos x))
30.0ms	(- 1.0 (cos x))

simplify1.4s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	1955
1	347
0	158

prune547.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes130.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch113.0ms

Steps

Iters	Range		Point
10	2.777137017098532e-16	1126.7541422477805	0.030783396840863963
9	-0.042530208599811804	-3.2052418334402957e-07	-0.03162480067046474

simplify4.0ms

Iterations

Iter	Nodes
done	29
1	29
0	22

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	1629×	body	2560	valid
875.0ms	1487×	body	640	valid
571.0ms	1270×	body	1280	valid
250.0ms	934×	body	320	valid
115.0ms	2187×	body	80	valid
97.0ms	493×	body	160	valid