Details

analyze495.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample316.0ms

Algorithm

intervals

Results

60.0ms	48×	body	2560	valid
39.0ms	80×	body	1280	valid
18.0ms	76×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	12×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	229	7
1	229	7

prune3.0ms

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: 29.8b

Counts

2 → 1

localize57.0ms

Local error

Found 2 expressions with local error:

14.2b	(/ (- 1.0 (cos x)) (sin x))
15.4b	(- 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 → 51

Calls

2 calls:

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
4.0ms	(- 1.0 (cos x))

simplify37.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5058	605

prune128.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	42	15	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	15	58

Merged error: 0.2b

Counts

58 → 15

localize58.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (sin x) (- 1.0 (cos x))))
14.2b	(/ (sin x) (- 1.0 (cos x)))
15.4b	(- 1.0 (cos x))

rewrite25.0ms

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 → 158

Calls

3 calls:

9.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
6.0ms	(/ (sin x) (- 1.0 (cos x)))
4.0ms	(- 1.0 (cos x))

series18.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(/ 1 (/ (sin x) (- 1.0 (cos x))))
7.0ms	(/ (sin x) (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify58.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5093	2252

prune193.0ms

Filtered

97 candidates to 167 candidates (-72.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	159	8	167
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	168	14	182

Merged error: 0.2b

Counts

182 → 14

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos x) 3)
0.4b	(+ 1.0 (cos x))
14.2b	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x))))) (sin x))
15.2b	(- (pow 1.0 3) (pow (cos x) 3))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

543×	`times-frac`
517×	`add-sqr-sqrt`
337×	`*-un-lft-identity`
208×	`difference-of-squares`
205×	`add-cube-cbrt`
159×	`unpow-prod-down` `cube-prod`
105×	`sqr-pow`
81×	`associate-/l*`
65×	`distribute-lft-out--`
13×	`difference-cubes`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/r*`
2×	`div-sub`
1×	`+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `pow-exp` `clear-num` `sum-log` `flip--` `associate-/l/` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 411

Calls

4 calls:

2.0ms	(pow (cos x) 3)
4.0ms	(+ 1.0 (cos x))
32.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x))))) (sin x))
11.0ms	(- (pow 1.0 3) (pow (cos x) 3))

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos x) 3)
2.0ms	(+ 1.0 (cos x))
31.0ms	(/ (/ (- (pow 1.0 3) (pow (cos x) 3)) (+ (* 1.0 1.0) (* (cos x) (+ 1.0 (cos x))))) (sin x))
7.0ms	(- (pow 1.0 3) (pow (cos x) 3))

simplify151.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4989	15160
1	4989	15160

prune862.0ms

Filtered

211 candidates to 423 candidates (-100.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	417	6	423
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	420	17	437

Merged error: 0.2b

Counts

437 → 17

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (/ (- 1.0 (cos x)) (sin x)))
14.2b	(/ (- 1.0 (cos x)) (sin x))
15.4b	(- 1.0 (cos x))
29.0b	(log (exp (/ (- 1.0 (cos x)) (sin 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 → 111

Calls

4 calls:

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
7.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5525	1215

prune153.0ms

Filtered

89 candidates to 123 candidates (-38.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	123	17	140

Merged error: 0.2b

Counts

140 → 17

regimes259.0ms

Accuracy

98.4% (0.5b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 30.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	69
1	63	69

end0.0ms

sample11.8s

Algorithm

intervals

Results

2.2s	1563×	body	2560	valid
1.5s	2722×	body	1280	valid
480.0ms	1937×	body	640	valid
164.0ms	946×	body	320	valid
62.0ms	495×	body	160	valid
27.0ms	330×	body	80	valid
27.0ms	7×	body	5120	valid

Details

analyze495.0ms

sample316.0ms

simplify10.0ms

prune3.0ms

localize57.0ms

rewrite11.0ms

series12.0ms

simplify37.0ms

prune128.0ms

localize58.0ms

rewrite25.0ms

series18.0ms

simplify58.0ms

prune193.0ms

localize66.0ms

rewrite84.0ms

series44.0ms

simplify151.0ms

prune862.0ms

localize93.0ms

rewrite27.0ms

series29.0ms

simplify52.0ms

prune153.0ms

regimes259.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample11.8s

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