Details

analyze512.0ms

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

sample155.0ms

Algorithm

intervals

Results

74.0ms	56×	body	2560	valid
49.0ms	94×	body	1280	valid
15.0ms	59×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	1×	body	5120	valid
2.0ms	14×	body	160	valid
0.0ms	7×	body	80	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	7
1	9	7

prune2.0ms

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: 30.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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))
3.0ms	(- 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))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5247	606

prune134.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	38	19	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	19	58

Merged error: 0.1b

Counts

58 → 19

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)))
2.0b	(- 1.0 (cos x))

rewrite22.0ms

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 → 97

Calls

4 calls:

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

series26.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify58.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4951	1088
1	4951	1088

prune148.0ms

Filtered

60 candidates to 109 candidates (-81.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	6	12	18
Picked	1	0	1
Done	0	0	0
Total	110	18	128

Merged error: 0.1b

Counts

128 → 18

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(pow E (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.0b	(- 1.0 (cos x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`log-prod`
25×	`unpow-prod-up`
15×	`unpow-prod-down`
12×	`add-exp-log` `associate-/l*`
7×	`pow1` `distribute-lft-out--` `difference-of-squares`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
5×	`sqr-pow`
4×	`pow-unpow` `flip3--` `div-exp` `pow-exp` `flip--` `pow-sub`
3×	`associate-/r*`
2×	`pow-to-exp` `e-exp-1` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 123

Calls

4 calls:

8.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
5.0ms	(pow E (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series80.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
28.0ms	(pow E (log (- 1.0 (cos x))))
15.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

simplify39.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5223	1635

prune221.0ms

Filtered

94 candidates to 135 candidates (-43.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	2	15	17
Picked	0	1	1
Done	0	0	0
Total	132	21	153

Merged error: 0.1b

Counts

153 → 21

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)))
1.5b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
2.0b	(- 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 → 111

Calls

4 calls:

7.0ms	(/ (- 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))))
3.0ms	(- 1.0 (cos x))

series29.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify72.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4949	1214
1	4949	1214

prune143.0ms

Filtered

87 candidates to 123 candidates (-41.4%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	5	14	19
Picked	1	0	1
Done	0	1	1
Total	124	20	144

Merged error: 0.1b

Counts

144 → 20

regimes257.0ms

Accuracy

98.2% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 30.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	54
1	38	54

end0.0ms

analyze509.0ms

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

sample4.5s

Algorithm

intervals

Results

2.2s	1565×	body	2560	valid
1.4s	2747×	body	1280	valid
507.0ms	1905×	body	640	valid
169.0ms	968×	body	320	valid
58.0ms	469×	body	160	valid
26.0ms	341×	body	80	valid
19.0ms	5×	body	5120	valid

Details

analyze512.0ms

sample155.0ms

simplify2.0ms

prune2.0ms

localize8.0ms

rewrite10.0ms

series12.0ms

simplify36.0ms

prune134.0ms

localize11.0ms

rewrite22.0ms

series26.0ms

simplify58.0ms

prune148.0ms

localize13.0ms

rewrite23.0ms

series80.0ms

simplify39.0ms

prune221.0ms

localize11.0ms

rewrite27.0ms

series29.0ms

simplify72.0ms

prune143.0ms

regimes257.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

analyze509.0ms

sample4.5s

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