Details

sample129.0ms

Algorithm

intervals

Results

63.0ms	45×	body	2560	valid
36.0ms	90×	body	1280	valid
15.0ms	63×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	17×	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: 27.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite12.0ms

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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

series59.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
25.0ms	(- 1.0 (cos x))

simplify81.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (7.0ms)

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

prune151.0ms

Pruning

14 alts after pruning (14 fresh and 0 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)))
1.1b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite27.0ms

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:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
6.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series133.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
41.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
38.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify89.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (21.0ms)

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

prune300.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
0.4b	(log (- 1.0 (cos x)))
1.1b	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
1.5b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

56×	`exp-prod`
52×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
38×	`log-prod`
36×	`add-cube-cbrt`
30×	`exp-sum` `log-pow`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`add-cbrt-cube`
2×	`log-div` `flip3--` `rem-log-exp` `flip--` `div-inv`
1×	`sub-neg` `diff-log` `rem-exp-log`

Counts

4 → 106

Calls

4 calls:

8.0ms	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
3.0ms	(log (- 1.0 (cos x)))
9.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
4.0ms	(- 1.0 (cos x))

series170.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))
73.0ms	(log (- 1.0 (cos x)))
39.0ms	(log (exp (/ (exp (log (- 1.0 (cos x)))) (sin x))))
18.0ms	(- 1.0 (cos x))

simplify65.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	302	832
1	715	753
2	2109	730
3	5001	702

prune354.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.3b	(log (sqrt (exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))))
1.3b	(log (sqrt (exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))))
1.5b	(- 1.0 (cos x))
1.5b	(- 1.0 (cos x))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

62×	`log-pow`
58×	`sqrt-pow1`
56×	`exp-prod`
54×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
42×	`log-prod`
38×	`add-cube-cbrt`
30×	`exp-sum`
8×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
6×	`add-exp-log` `sqrt-prod`
4×	`add-cbrt-cube`
2×	`sub-neg` `flip3--` `pow1/2` `diff-log` `rem-log-exp` `flip--` `div-inv`

Counts

4 → 118

Calls

4 calls:

10.0ms	(log (sqrt (exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))))
10.0ms	(log (sqrt (exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))))
4.0ms	(- 1.0 (cos x))
4.0ms	(- 1.0 (cos x))

series324.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(log (sqrt (exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))))
144.0ms	(log (sqrt (exp (/ (exp (log (- 1.0 (cos x)))) (sin x)))))
18.0ms	(- 1.0 (cos x))
22.0ms	(- 1.0 (cos x))

simplify65.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	269	1004
1	600	918
2	1705	898
3	5001	874

prune490.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes168.0ms

Accuracy

97.6% (0.7b remaining)

Error of 0.9b against oracle of 0.2b and baseline of 30.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	31
1	48	31

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1664×	body	2560	valid
1.2s	2668×	body	1280	valid
426.0ms	1899×	body	640	valid
136.0ms	924×	body	320	valid
55.0ms	467×	body	160	valid
30.0ms	377×	body	80	valid
3.0ms	1×	body	5120	valid