Details

sample204.0ms

Algorithm

intervals

Results

98.0ms	49×	body	2560	valid
56.0ms	85×	body	1280	valid
19.0ms	60×	body	640	valid
7.0ms	27×	body	320	valid
5.0ms	1×	body	5120	valid
3.0ms	21×	body	160	valid
1.0ms	13×	body	80	valid

simplify14.0ms

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: 28.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.3b	(- 1.0 (cos x))

rewrite31.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

20.0ms	(/ (- 1.0 (cos x)) (sin x))
8.0ms	(- 1.0 (cos x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- 1.0 (cos x)) (sin x))
43.0ms	(- 1.0 (cos x))

simplify1.8s

Counts

74 → 74

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	134	964
1	295	831
2	743	731
3	2333	692
done	5000	683

prune211.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

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)))
2.3b	(- 1.0 (cos x))

rewrite95.0ms

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` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 118

Calls

4 calls:

43.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
14.0ms	(exp (log (- 1.0 (cos x))))
14.0ms	(log (- 1.0 (cos x)))
15.0ms	(- 1.0 (cos x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
41.0ms	(exp (log (- 1.0 (cos x))))
95.0ms	(log (- 1.0 (cos x)))
33.0ms	(- 1.0 (cos x))

simplify2.6s

Counts

130 → 130

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	200	1750
1	351	1386
2	804	1245
3	2433	1206
done	5001	1178

prune415.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.3b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.3b	(- 1.0 (cos x))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `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 → 132

Calls

4 calls:

23.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
30.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
8.0ms	(- 1.0 (cos x))

series208.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- 1.0 (cos x)) (sin x))
59.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
57.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
20.0ms	(- 1.0 (cos x))

simplify1.9s

Counts

144 → 144

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	195	1743
1	370	1509
2	856	1372
3	2563	1333
done	5000	1322

prune537.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.3b	(- 1.0 (cos x))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
13×	`times-frac` `associate-r` `exp-sum`
10×	`add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
8×	`pow1` `log-div` `associate-l`
6×	`exp-diff` `add-log-exp` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `exp-prod` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg`
2×	`frac-times` `div-exp` `associate-*l/` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv` `rem-exp-log`

Counts

4 → 117

Calls

4 calls:

66.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
7.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
8.0ms	(- 1.0 (cos x))

series206.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (exp (log (- 1.0 (cos x)))) (/ 1 (sin x)))
20.0ms	(exp (log (- 1.0 (cos x))))
117.0ms	(log (- 1.0 (cos x)))
32.0ms	(- 1.0 (cos x))

simplify3.1s

Counts

129 → 129

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	210	1688
1	427	1276
2	1060	1099
3	3705	1060
done	5000	1044

prune365.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.2b

regimes262.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.4b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	51
1	28	43
done	28	43

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.3s	1584×	body	2560	valid
1.9s	2834×	body	1280	valid
736.0ms	1868×	body	640	valid
238.0ms	893×	body	320	valid
79.0ms	468×	body	160	valid
52.0ms	7×	body	5120	valid
35.0ms	346×	body	80	valid