Details

sample223.0ms

Algorithm

intervals

Results

91.0ms	97×	body	1280	valid
76.0ms	40×	body	2560	valid
25.0ms	55×	body	640	valid
12.0ms	37×	body	320	valid
4.0ms	19×	body	160	valid
1.0ms	8×	body	80	valid

simplify5.0ms

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: 29.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.7b	(- 1.0 (cos x))

rewrite40.0ms

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))
10.0ms	(- 1.0 (cos x))

series120.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- 1.0 (cos x)) (sin x))
52.0ms	(- 1.0 (cos x))

simplify459.0ms

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	805
1	240
0	106

prune354.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite70.0ms

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:

37.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
11.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
9.0ms	(- 1.0 (cos x))

series226.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
35.0ms	(exp (log (- 1.0 (cos x))))
97.0ms	(log (- 1.0 (cos x)))
28.0ms	(- 1.0 (cos x))

simplify2.0s

Counts

110 → 110

Iterations

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

prune541.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `div-inv`

Counts

4 → 124

Calls

4 calls:

30.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
6.0ms	(pow E (log (- 1.0 (cos x))))
4.0ms	(log (- 1.0 (cos x)))
5.0ms	(- 1.0 (cos x))

series770.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
294.0ms	(pow E (log (- 1.0 (cos x))))
141.0ms	(log (- 1.0 (cos x)))
31.0ms	(- 1.0 (cos x))

simplify924.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1722
1	456
0	214

prune867.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.7b	(- 1.0 (cos x))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `div-inv`

Counts

4 → 124

Calls

4 calls:

34.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
12.0ms	(pow E (log (- 1.0 (cos x))))
8.0ms	(log (- 1.0 (cos x)))
10.0ms	(- 1.0 (cos x))

series825.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
345.0ms	(pow E (log (- 1.0 (cos x))))
123.0ms	(log (- 1.0 (cos x)))
39.0ms	(- 1.0 (cos x))

simplify959.0ms

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1722
1	456
0	214

prune693.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes471.0ms

Accuracy

97.4% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 30.2b

bsearch3.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	54
1	54
0	41

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.3s	1565×	body	2560	valid
3.2s	2769×	body	1280	valid
872.0ms	1842×	body	640	valid
316.0ms	967×	body	320	valid
91.0ms	473×	body	160	valid
41.0ms	379×	body	80	valid
36.0ms	5×	body	5120	valid