Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	42×	body	2560	valid
17.0ms	43×	body	1280	valid
13.0ms	51×	body	640	valid
8.0ms	37×	body	320	valid
4.0ms	66×	body	80	valid
2.0ms	17×	body	160	valid

simplify14.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize7.0ms

Local error

Found 2 expressions with local error:

1.9b	(- 1.0 (cos x))
14.1b	(/ (- 1.0 (cos x)) (* x x))

rewrite72.0ms

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:

14.0ms	(- 1.0 (cos x))
55.0ms	(/ (- 1.0 (cos x)) (* x x))

series133.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- 1.0 (cos x))
90.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify2.2s

Counts

48 → 48

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	88	507
1	212	489
2	548	441
3	1500	441
done	5000	441

prune206.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

8.0ms	(cbrt (- 1.0 (cos x)))
12.0ms	(- 1.0 (cos x))
12.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))
26.0ms	(- 1.0 (cos x))
48.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

69 → 69

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	76	627
1	152	608
2	337	554
3	803	534
4	2936	527
done	5000	527

prune272.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))
1.9b	(- 1.0 (cos x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))
6.0ms	(- 1.0 (cos x))

series115.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- 1.0 (cos x))
25.0ms	(- 1.0 (cos x))
24.0ms	(- 1.0 (cos x))
32.0ms	(- 1.0 (cos x))

simplify2.4s

Counts

68 → 68

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	44	552
1	90	536
2	188	504
3	389	504
4	1008	504
5	2816	504
done	5001	504

prune398.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))
14.1b	(/ (exp (log (- 1.0 (cos x)))) (* x x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`log-prod`
15×	`exp-sum`
11×	`add-cube-cbrt`
9×	`add-cbrt-cube`
8×	`add-exp-log` `times-frac` `associate-/l*`
6×	`pow1` `log-div` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
2×	`cbrt-undiv` `div-exp` `log-pow` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))
38.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (log (- 1.0 (cos x))))
110.0ms	(log (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))
49.0ms	(/ (exp (log (- 1.0 (cos x)))) (* x x))

simplify1.9s

Counts

94 → 94

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	138	1077
1	261	909
2	654	829
3	1738	829
done	5000	819

prune201.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes72.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 31.1b

bsearch100.0ms

Steps

Iters	Range		Point
10	8.937283511995443e-05	28405617999702.24	0.02432033747417449
9	-7465.585501010854	-0.008005822963963436	-0.032962631270408896

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	68
1	47	68
done	47	68

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.8s	1656×	body	2560	valid
479.0ms	1222×	body	1280	valid
458.0ms	1503×	body	640	valid
163.0ms	2251×	body	80	valid
158.0ms	935×	body	320	valid
51.0ms	433×	body	160	valid