Details

sample223.0ms

Algorithm

intervals

Results

102.0ms	57×	body	2560	valid
73.0ms	83×	body	1280	valid
21.0ms	55×	body	640	valid
9.0ms	36×	body	320	valid
3.0ms	18×	body	160	valid
1.0ms	7×	body	80	valid

simplify12.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

15.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series126.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- 1.0 (cos x)) (sin x))
59.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1211
1	309
0	134

prune398.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

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))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `log-div` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `fma-neg`
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 → 118

Calls

4 calls:

17.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
11.0ms	(exp (log (- 1.0 (cos x))))
11.0ms	(log (- 1.0 (cos x)))
11.0ms	(- 1.0 (cos x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
33.0ms	(exp (log (- 1.0 (cos x))))
85.0ms	(log (- 1.0 (cos x)))
32.0ms	(- 1.0 (cos x))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1284
1	373
0	200

prune709.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

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))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
112×	`add-sqr-sqrt` `*-un-lft-identity`
78×	`add-cube-cbrt`
26×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
9×	`prod-diff`
8×	`div-exp`
6×	`flip3--` `div-inv` `flip--` `associate-/l*`
5×	`add-log-exp`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`sub-neg` `diff-log` `pow-flip` `inv-pow`

Counts

3 → 177

Calls

3 calls:

18.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
19.0ms	(/ (sin x) (- 1.0 (cos x)))
6.0ms	(- 1.0 (cos x))

series129.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
56.0ms	(/ (sin x) (- 1.0 (cos x)))
26.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	3505
1	656
0	269

prune788.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

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))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

705×	`times-frac`
403×	`add-sqr-sqrt` `*-un-lft-identity`
309×	`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`
9×	`prod-diff`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`clear-num` `frac-2neg` `fma-neg`
2×	`pow-flip` `inv-pow`
1×	`sub-neg` `diff-log` `associate-/l/`

Counts

4 → 445

Calls

4 calls:

5.0ms	(/ 1 (sin x))
9.0ms	(/ 1 (- 1.0 (cos x)))
37.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
11.0ms	(- 1.0 (cos x))

series154.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (sin x))
34.0ms	(/ 1 (- 1.0 (cos x)))
63.0ms	(/ (/ 1 (sin x)) (/ 1 (- 1.0 (cos x))))
31.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

457 → 457

Iterations

Iter	Nodes
done	5000
1	2073
0	608

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes217.0ms

Accuracy

99.1% (0.3b remaining)

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

bsearch99.0ms

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	32
1	32
0	24

end0.0ms

sample8.5s

Algorithm

intervals

Results

3.5s	1626×	body	2560	valid
3.1s	2727×	body	1280	valid
1.1s	1880×	body	640	valid
365.0ms	935×	body	320	valid
158.0ms	494×	body	160	valid
89.0ms	336×	body	80	valid
8.0ms	2×	body	5120	valid