Details

sample140.0ms

Algorithm

intervals

Results

72.0ms	54×	body	2560	valid
39.0ms	84×	body	1280	valid
15.0ms	69×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	7×	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: 28.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite13.0ms

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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series57.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- 1.0 (cos x)) (sin x))
19.0ms	(- 1.0 (cos x))

simplify80.0ms

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

prune163.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite25.0ms

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:

10.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
6.0ms	(exp (log (- 1.0 (cos x))))
2.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series145.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
74.0ms	(log (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))

simplify85.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (73.0ms)

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

prune241.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite14.0ms

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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series52.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 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

prune131.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.2b	(- 1.0 (cos x))

rewrite41.0ms

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:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
15.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series134.0ms

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))

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

prune278.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 0.1b

regimes193.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.1b

bsearch78.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.023267676544555443
9	-5.7596417613087905	-6.7357437175194845e-09	-0.019541465084207187

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	37	17
2	37	17

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.0s	1566×	body	2560	valid
1.2s	2771×	body	1280	valid
422.0ms	1917×	body	640	valid
145.0ms	941×	body	320	valid
53.0ms	444×	body	160	valid
22.0ms	357×	body	80	valid
13.0ms	4×	body	5120	valid