Details

sample131.0ms

Algorithm

intervals

Results

62.0ms	46×	body	2560	valid
38.0ms	84×	body	1280	valid
16.0ms	68×	body	640	valid
6.0ms	37×	body	320	valid
1.0ms	11×	body	160	valid
1.0ms	10×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 30.8b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (- 1.0 (cos x)) (sin x))
2.3b	(- 1.0 (cos x))

rewrite11.0ms

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:

40.0ms	(/ (- 1.0 (cos x)) (sin x))
18.0ms	(- 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	2640	373
3	5002	373

prune147.0ms

Filtered

58 candidates to 42 candidates (72.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	45	13	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	13	59

Merged error: 0.1b

Counts

59 → 13

localize11.0ms

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)))
2.3b	(- 1.0 (cos x))

rewrite23.0ms

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:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
5.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series152.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
18.0ms	(exp (log (- 1.0 (cos x))))
75.0ms	(log (- 1.0 (cos x)))
23.0ms	(- 1.0 (cos x))

simplify84.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 3 (75.0ms)

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

prune210.0ms

Filtered

110 candidates to 66 candidates (60.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	108	15	123

Merged error: 0.1b

Counts

123 → 15

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)))
1.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.3b	(- 1.0 (cos x))

rewrite31.0ms

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)))
11.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
4.0ms	(- 1.0 (cos x))

series136.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0 (cos x)) (sin x))
47.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
35.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

simplify91.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (22.0ms)

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

prune283.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	122	17	139

Merged error: 0.1b

Counts

139 → 17

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (cos x) 1.0)
0.4b	(pow (cos x) 3)
1.7b	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))))
2.1b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac`
417×	`add-sqr-sqrt`
279×	`*-un-lft-identity`
248×	`log-pow`
247×	`exp-prod`
177×	`add-cube-cbrt`
160×	`difference-of-squares`
123×	`unpow-prod-down` `cube-prod`
81×	`sqr-pow`
50×	`distribute-lft-out--`
10×	`difference-cubes`
8×	`add-log-exp`
6×	`pow1` `associate-/r/`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+` `div-inv`
3×	`pow-unpow` `log-prod`
2×	`div-sub`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `unpow3` `rem-log-exp` `pow-exp` `sum-log` `flip--` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 329

Calls

4 calls:

4.0ms	(+ (cos x) 1.0)
3.0ms	(pow (cos x) 3)
64.0ms	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))))
12.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series265.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (cos x) 1.0)
28.0ms	(pow (cos x) 3)
172.0ms	(log (exp (/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* (cos x) (+ (cos x) 1.0)) (* 1.0 1.0))) (sin x))))
55.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify134.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1189	4560
1	4287	4463
2	5001	4371

prune799.0ms

Filtered

341 candidates to 192 candidates (56.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	336	5	341
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	341	17	358

Merged error: 0.1b

Counts

358 → 17

regimes175.0ms

Accuracy

98.7% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample4.2s

Algorithm

intervals

Results

2.1s	1541×	body	2560	valid
1.3s	2765×	body	1280	valid
470.0ms	1879×	body	640	valid
156.0ms	937×	body	320	valid
58.0ms	499×	body	160	valid
26.0ms	375×	body	80	valid
13.0ms	4×	body	5120	valid

Details

sample131.0ms

simplify6.0ms

prune2.0ms

localize7.0ms

rewrite11.0ms

series59.0ms

simplify80.0ms

prune147.0ms

localize11.0ms

rewrite23.0ms

series152.0ms

simplify84.0ms

prune210.0ms

localize10.0ms

rewrite31.0ms

series136.0ms

simplify91.0ms

prune283.0ms

localize23.0ms

rewrite113.0ms

series265.0ms

simplify134.0ms

prune799.0ms

regimes175.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample4.2s

Profiling