Details

sample146.0ms

Algorithm

intervals

Results

76.0ms	57×	body	2560	valid
36.0ms	83×	body	1280	valid
17.0ms	73×	body	640	valid
8.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite15.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series57.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: 3 (626.0ms)

Iter	Nodes	Cost
0	134	964
1	291	831
2	804	731
3	4419	719
done	5000	719

prune180.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* 1/2 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

series117.0ms

Counts

1 → 3

Calls

1 calls:

116.0ms

(fma 1/240 (pow x 5) (* 1/2 x))

simplify3.4s

Counts

13 → 13

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	18	140
1	28	137
2	62	121
3	198	121
4	822	121
5	4898	121
done	5000	121

prune56.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (- 1.0 (cos x)))
0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
1.2b	(- 1.0 (cos x))

rewrite28.0ms

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:

7.0ms	(/ (sin x) (- 1.0 (cos x)))
9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

series89.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (sin x) (- 1.0 (cos x)))
34.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
21.0ms	(- 1.0 (cos x))

simplify803.0ms

Counts

186 → 186

Iterations

Useful iterations: 2 (222.0ms)

Iter	Nodes	Cost
0	269	3021
1	572	2564
2	1630	2279
done	5001	2279

prune258.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

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)))
0.9b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.2b	(- 1.0 (cos x))

rewrite42.0ms

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:

9.0ms	(/ (- 1.0 (cos x)) (sin x))
11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
14.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series130.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (- 1.0 (cos x)) (sin x))
40.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
36.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify2.3s

Counts

144 → 144

Iterations

Useful iterations: 3 (681.0ms)

Iter	Nodes	Cost
0	195	1743
1	367	1509
2	924	1372
3	4739	1360
done	5000	1360

prune303.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes134.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 31.6b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	53
1	29	53
done	29	53

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.2s	1656×	body	2560	valid
1.2s	2763×	body	1280	valid
447.0ms	1843×	body	640	valid
152.0ms	921×	body	320	valid
57.0ms	448×	body	160	valid
25.0ms	365×	body	80	valid
16.0ms	4×	body	5120	valid