Details

sample298.0ms

Algorithm

intervals

Results

145.0ms	50×	body	2560	valid
76.0ms	80×	body	1280	valid
37.0ms	68×	body	640	valid
13.0ms	36×	body	320	valid
3.0ms	13×	body	160	valid
1.0ms	9×	body	80	valid

simplify19.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize25.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.1b	(- 1.0 (cos x))

rewrite108.0ms

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:

87.0ms	(/ (- 1.0 (cos x)) (sin x))
16.0ms	(- 1.0 (cos x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (- 1.0 (cos x)) (sin x))
35.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	134	964
1	309	834
2	1215	733
done	5001	692

prune441.0ms

Pruning

12 alts after pruning (12 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))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.1b	(- 1.0 (cos x))

rewrite98.0ms

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:

46.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
14.0ms	(exp (log (- 1.0 (cos x))))
14.0ms	(log (- 1.0 (cos x)))
16.0ms	(- 1.0 (cos x))

series304.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
42.0ms	(exp (log (- 1.0 (cos x))))
144.0ms	(log (- 1.0 (cos x)))
47.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

130 → 130

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	200	1750
1	374	1389
2	1294	1247
done	5001	1206

prune790.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

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)))
1.1b	(- 1.0 (cos x))

rewrite102.0ms

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:

42.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
15.0ms	(exp (log (- 1.0 (cos x))))
13.0ms	(log (- 1.0 (cos x)))
17.0ms	(- 1.0 (cos x))

series294.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
37.0ms	(exp (log (- 1.0 (cos x))))
153.0ms	(log (- 1.0 (cos x)))
35.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

130 → 130

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	200	1750
1	374	1389
2	1294	1247
done	5001	1206

prune837.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
1.1b	(- 1.0 (cos x))

rewrite102.0ms

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

Counts

3 → 177

Calls

3 calls:

33.0ms	(/ (sin x) (- 1.0 (cos x)))
33.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
22.0ms	(- 1.0 (cos x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ (sin x) (- 1.0 (cos x)))
62.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
40.0ms	(- 1.0 (cos x))

simplify2.2s

Counts

186 → 186

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	269	3021
1	654	2567
2	3118	2363
done	5000	2347

prune684.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 0.2b

regimes446.0ms

Accuracy

98.5% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.0b

bsearch3.0ms

simplify13.0ms

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	38	70
1	46	70
2	48	66
done	48	66

end0.0ms

sample10.7s

Algorithm

intervals

Results

4.8s	1561×	body	2560	valid
3.1s	2783×	body	1280	valid
1.2s	1938×	body	640	valid
979.0ms	933×	body	320	valid
113.0ms	449×	body	160	valid
62.0ms	335×	body	80	valid
5.0ms	1×	body	5120	valid