Details

sample306.0ms

Algorithm

intervals

Results

163.0ms	57×	body	2560	valid
79.0ms	83×	body	1280	valid
29.0ms	55×	body	640	valid
13.0ms	36×	body	320	valid
5.0ms	18×	body	160	valid
1.0ms	7×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.0b	(- 1.0 (cos x))

rewrite35.0ms

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

Counts

2 → 52

Calls

2 calls:

27.0ms	(/ (- 1.0 (cos x)) (sin x))
5.0ms	(- 1.0 (cos x))

series96.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- 1.0 (cos x)) (sin x))
49.0ms	(- 1.0 (cos x))

simplify879.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune347.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite58.0ms

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:

30.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
11.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series192.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
30.0ms	(exp (log (- 1.0 (cos x))))
91.0ms	(log (- 1.0 (cos x)))
27.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
3	4209
2	830
1	302
0	168

prune531.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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

rewrite52.0ms

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--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 159

Calls

3 calls:

21.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
13.0ms	(/ (sin x) (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series154.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
73.0ms	(/ (sin x) (- 1.0 (cos x)))
36.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

168 → 168

Iterations

Iter	Nodes
done	5004
2	2765
1	583
0	239

prune669.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin x))
0.1b	(/ 1 (- 1.0 (cos x)))
0.2b	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
2.0b	(- 1.0 (cos x))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

705×	`times-frac`
396×	`add-sqr-sqrt` `*-un-lft-identity`
302×	`add-cube-cbrt`
52×	`add-exp-log`
47×	`distribute-lft-out--` `difference-of-squares`
39×	`div-inv`
36×	`div-exp`
31×	`associate-/r/`
29×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-/l*`
16×	`flip3--` `flip--`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `associate-/l/`

Counts

4 → 425

Calls

4 calls:

15.0ms	(/ 1 (sin x))
14.0ms	(/ 1 (- 1.0 (cos x)))
26.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
9.0ms	(- 1.0 (cos x))

series162.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (sin x))
51.0ms	(/ 1 (- 1.0 (cos x)))
62.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
23.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

437 → 437

Iterations

Iter	Nodes
done	5000
1	1919
0	576

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes279.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 31.0b

bsearch176.0ms

Steps

Iters	Range		Point
10	2.777137017098532e-16	1126.7541422477805	0.020402141047047902
9	-0.042530208599811804	-3.2052418334402957e-07	-0.022089907824363444

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	25

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.9s	1626×	body	2560	valid
2.8s	2727×	body	1280	valid
1.1s	1880×	body	640	valid
494.0ms	935×	body	320	valid
110.0ms	494×	body	160	valid
38.0ms	336×	body	80	valid
10.0ms	2×	body	5120	valid