Details

analyze502.0ms

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

sample146.0ms

Algorithm

intervals

Results

72.0ms	48×	body	2560	valid
42.0ms	84×	body	1280	valid
16.0ms	61×	body	640	valid
6.0ms	35×	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: 29.9b

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 → 51

Calls

2 calls:

6.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series11.0ms

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	5058	605

prune135.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	40	17	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	17	58

Merged error: 0.1b

Counts

58 → 17

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
2.3b	(- 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)))
4.0ms	(- 1.0 (cos x))

series26.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (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))

simplify65.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4878	1087
1	4878	1087

prune148.0ms

Filtered

61 candidates to 109 candidates (-78.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	6	10	16
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Merged error: 0.1b

Counts

126 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
0.3b	(log (- 1.0 (cos x)))
0.4b	(pow E (log (- 1.0 (cos x))))
2.3b	(- 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))
3.0ms	(log (- 1.0 (cos x)))
5.0ms	(pow E (log (- 1.0 (cos x))))
4.0ms	(- 1.0 (cos x))

series78.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (pow E (log (- 1.0 (cos x)))) (sin x))
12.0ms	(log (- 1.0 (cos x)))
30.0ms	(pow E (log (- 1.0 (cos x))))
3.0ms	(- 1.0 (cos x))

simplify67.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5149	1616

prune218.0ms

Filtered

91 candidates to 135 candidates (-48.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	132	18	150

Merged error: 0.0b

Counts

150 → 18

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (- 1.0 (cos x)))
0.3b	(cbrt (pow (log (- 1.0 (cos x))) 3))
0.4b	(pow (log (- 1.0 (cos x))) 3)
2.3b	(- 1.0 (cos x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`cbrt-prod`
11×	`add-cube-cbrt`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod`
6×	`add-exp-log` `add-log-exp`
5×	`log-prod` `log-pow` `add-cbrt-cube`
3×	`pow-unpow`
2×	`cube-mult` `log-div` `flip3--` `unpow3` `flip--` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 77

Calls

4 calls:

3.0ms	(log (- 1.0 (cos x)))
2.0ms	(cbrt (pow (log (- 1.0 (cos x))) 3))
3.0ms	(pow (log (- 1.0 (cos x))) 3)
4.0ms	(- 1.0 (cos x))

series50.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(log (- 1.0 (cos x)))
12.0ms	(cbrt (pow (log (- 1.0 (cos x))) 3))
22.0ms	(pow (log (- 1.0 (cos x))) 3)
3.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5101	832

prune115.0ms

Filtered

49 candidates to 89 candidates (-81.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Merged error: 0.0b

Counts

107 → 15

regimes183.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 29.6b

bsearch43.0ms

Steps

Iters	Range		Point
11	0.0024895362443886435	4.6108752015700794e+17	0.02260847323572308
9	-956.5805619630278	-0.00022011233497199002	-0.022162484295299056

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	54
1	54	54

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.3s	1578×	body	2560	valid
1.3s	2729×	body	1280	valid
492.0ms	1902×	body	640	valid
165.0ms	940×	body	320	valid
60.0ms	486×	body	160	valid
26.0ms	359×	body	80	valid
22.0ms	6×	body	5120	valid

Details

analyze502.0ms

sample146.0ms

simplify10.0ms

prune3.0ms

localize7.0ms

rewrite11.0ms

series11.0ms

simplify36.0ms

prune135.0ms

localize10.0ms

rewrite22.0ms

series26.0ms

simplify65.0ms

prune148.0ms

localize13.0ms

rewrite23.0ms

series78.0ms

simplify67.0ms

prune218.0ms

localize13.0ms

rewrite13.0ms

series50.0ms

simplify43.0ms

prune115.0ms

regimes183.0ms

bsearch43.0ms

simplify1.0ms

end0.0ms

sample4.5s

Profiling