Details

sample183.0ms

Algorithm

intervals

Results

72.0ms	88×	body	1280	valid
66.0ms	45×	body	2560	valid
20.0ms	54×	body	640	valid
8.0ms	34×	body	320	valid
4.0ms	21×	body	160	valid
2.0ms	14×	body	80	valid

simplify21.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.4b	(- 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:

29.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(- 1.0 (cos x))

series98.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(- 1.0 (cos x))

simplify1.1s

Counts: 58 → 58

prune199.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)))
2.4b	(- 1.0 (cos x))

rewrite58.0ms

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:

25.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
17.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series124.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
52.0ms	(/ (sin x) (- 1.0 (cos x)))
20.0ms	(- 1.0 (cos x))

simplify1.1s

Counts: 168 → 168

prune578.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- 1.0 (cos x)))
0.2b	(/ (log (exp (- 1.0 (cos x)))) (sin x))
2.4b	(- 1.0 (cos x))
2.5b	(log (exp (- 1.0 (cos x))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

29.0ms	(exp (- 1.0 (cos x)))
66.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
13.0ms	(- 1.0 (cos x))
36.0ms	(log (exp (- 1.0 (cos x))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(exp (- 1.0 (cos x)))
67.0ms	(/ (log (exp (- 1.0 (cos x)))) (sin x))
36.0ms	(- 1.0 (cos x))
40.0ms	(log (exp (- 1.0 (cos x))))

simplify1.3s

Counts: 115 → 115

prune418.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sin x))
0.2b	(/ (cos x) (sin x))
2.5b	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

6.0ms	(/ 1.0 (sin x))
11.0ms	(/ (cos x) (sin x))
36.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ 1.0 (sin x))
42.0ms	(/ (cos x) (sin x))
114.0ms	(- (/ 1.0 (sin x)) (/ (cos x) (sin x)))

simplify1.2s

Counts: 86 → 86

prune314.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.1b

regimes212.0ms

Accuracy

97.9% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 30.3b

bsearch1.0ms

simplify941.0ms

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.1s	1534×	body	2560	valid
2.7s	2826×	body	1280	valid
885.0ms	1863×	body	640	valid
576.0ms	458×	body	160	valid
503.0ms	956×	body	320	valid
50.0ms	359×	body	80	valid
17.0ms	4×	body	5120	valid