Details

sample212.0ms

Algorithm

intervals

Results

92.0ms	47×	body	2560	valid
66.0ms	83×	body	1280	valid
23.0ms	55×	body	640	valid
12.0ms	41×	body	320	valid
3.0ms	11×	body	160	valid
2.0ms	19×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize41.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.3b	(- 1.0 (cos x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 1.0 (cos x))

simplify3.2s

Counts

58 → 58

Iterations

Useful iterations: 3 (985.0ms)

Iter	Nodes	Cost
0	106	665
1	240	645
2	805	611
3	4711	609
done	5002	609

prune268.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
0.2b	(/ (sin x) (- 1.0 (cos x)))
1.3b	(- 1.0 (cos x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
105×	`add-sqr-sqrt` `*-un-lft-identity`
71×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `inv-pow`

Counts

3 → 159

Calls

3 calls:

27.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
24.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series183.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
71.0ms	(/ (sin x) (- 1.0 (cos x)))
40.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

168 → 168

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	239	2702
1	583	2361
2	2654	2196
done	5001	2092

prune378.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.0b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.3b	(- 1.0 (cos x))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
27.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
30.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
13.0ms	(- 1.0 (cos x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (- 1.0 (cos x)) (sin x))
75.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
59.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
25.0ms	(- 1.0 (cos x))

simplify724.0ms

Counts

124 → 124

Iterations

Useful iterations: done (721.0ms)

Iter	Nodes	Cost
0	163	1406
1	318	1293
2	952	1222
done	5000	1218

prune454.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
0.3b	(log (- 1.0 (cos x)))
1.0b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.3b	(- 1.0 (cos x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

56×	`exp-prod`
52×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
38×	`log-prod`
36×	`add-cube-cbrt`
30×	`exp-sum` `log-pow`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube`
2×	`log-div` `flip3--` `rem-log-exp` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `rem-exp-log`

Counts

4 → 106

Calls

4 calls:

32.0ms	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
5.0ms	(log (- 1.0 (cos x)))
67.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
7.0ms	(- 1.0 (cos x))

series258.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
114.0ms	(log (- 1.0 (cos x)))
46.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
22.0ms	(- 1.0 (cos x))

simplify3.0s

Counts

118 → 118

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	191	1425
1	312	1128
2	744	1043
3	3133	1041
done	5000	1015

prune483.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.1b

regimes256.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.5b

bsearch127.0ms

Steps

Iters	Range		Point
9	5.2366538615162886e-09	1.4124627081995123	0.02393964535351435
8	-0.03117879455470207	-1.716801800522696e-06	-0.022947908688991478

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	41
1	36	41
done	36	41

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.6s	1607×	body	2560	valid
3.4s	2739×	body	1280	valid
1.0s	1869×	body	640	valid
340.0ms	936×	body	320	valid
164.0ms	472×	body	160	valid
43.0ms	374×	body	80	valid
9.0ms	3×	body	5120	valid