Details

sample128.0ms

Algorithm

intervals

Results

61.0ms	51×	body	2560	valid
36.0ms	85×	body	1280	valid
14.0ms	62×	body	640	valid
5.0ms	35×	body	320	valid
2.0ms	17×	body	160	valid
0.0ms	6×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	4
1	14	4
2	16	4
3	16	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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:

24.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(- 1.0 (cos x))

series48.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (- 1.0 (cos x)) (sin x))
17.0ms	(- 1.0 (cos x))

simplify78.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	233	396
1	673	373
2	2654	373
3	5001	373

prune156.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 1.0 (cos x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `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 → 112

Calls

4 calls:

18.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
25.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
6.0ms	(- 1.0 (cos x))

series126.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- 1.0 (cos x)) (sin x))
38.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
16.0ms	(- 1.0 (cos x))

simplify87.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	303	818
1	799	768
2	2970	766
3	5001	766

prune304.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`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 → 98

Calls

4 calls:

21.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
7.0ms	(exp (log (- 1.0 (cos x))))
5.0ms	(log (- 1.0 (cos x)))
9.0ms	(- 1.0 (cos x))

series138.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
16.0ms	(exp (log (- 1.0 (cos x))))
68.0ms	(log (- 1.0 (cos x)))
17.0ms	(- 1.0 (cos x))

simplify80.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	289	829
1	791	761
2	2667	734
3	5001	708

prune250.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

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))

rewrite53.0ms

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:

19.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
16.0ms	(/ (sin x) (- 1.0 (cos x)))
7.0ms	(- 1.0 (cos x))

series86.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
32.0ms	(/ (sin x) (- 1.0 (cos x)))
17.0ms	(- 1.0 (cos x))

simplify60.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	510	1595
1	2396	1452
2	5002	1339

prune237.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

regimes159.0ms

Accuracy

98.3% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	28
1	39	28

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1593×	body	2560	valid
1.2s	2803×	body	1280	valid
422.0ms	1876×	body	640	valid
136.0ms	915×	body	320	valid
51.0ms	482×	body	160	valid
20.0ms	327×	body	80	valid
13.0ms	4×	body	5120	valid