Details

analyze516.0ms

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

sample141.0ms

Algorithm

intervals

Results

67.0ms	51×	body	2560	valid
45.0ms	92×	body	1280	valid
12.0ms	47×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	22×	body	80	valid
1.0ms	8×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	7
1	9	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: 30.9b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.9b	(- 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))

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	5247	606

prune119.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	43	14	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	14	58

Merged error: 0.2b

Counts

58 → 14

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
0.0b	(* 1/240 (pow x 5))
0.2b	(* 1/24 (pow x 3))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
13×	`add-exp-log`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`cube-prod` `sqr-pow`
3×	`pow1` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `flip-+`

Counts

3 → 69

Calls

3 calls:

7.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
5.0ms	(* 1/240 (pow x 5))
6.0ms	(* 1/24 (pow x 3))

series16.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* 1/24 (pow x 3)) (+ (* 1/240 (pow x 5)) (* x 1/2)))
6.0ms	(* 1/240 (pow x 5))
4.0ms	(* 1/24 (pow x 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4917	697
1	4917	697

prune138.0ms

Filtered

49 candidates to 78 candidates (-59.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	78	14	92

Merged error: 0.2b

Counts

92 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.3b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.9b	(- 1.0 (cos x))

rewrite21.0ms

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:

7.0ms	(/ (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))

series28.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
14.0ms	(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

62 candidates to 109 candidates (-75.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	101	8	109
Fresh	5	7	12
Picked	1	0	1
Done	0	1	1
Total	107	16	123

Merged error: 0.2b

Counts

123 → 16

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)
1.9b	(- 1.0 (cos x))

rewrite15.0ms

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(log (- 1.0 (cos x)))
12.0ms	(cbrt (pow (log (- 1.0 (cos x))) 3))
20.0ms	(pow (log (- 1.0 (cos x))) 3)
3.0ms	(- 1.0 (cos x))

simplify54.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5015	832

prune112.0ms

Filtered

49 candidates to 89 candidates (-81.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	13	14
Picked	1	0	1
Done	0	1	1
Total	89	16	105

Merged error: 0.2b

Counts

105 → 16

regimes225.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 32.5b

bsearch51.0ms

Steps

Iters	Range		Point
9	0.013525992122201645	2825143.787960234	0.01943327581439173
8	-0.14791979388410675	-2.3423084468719934e-05	-0.024063447430569557

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms

analyze515.0ms

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	1569×	body	2560	valid
1.4s	2816×	body	1280	valid
493.0ms	1896×	body	640	valid
165.0ms	919×	body	320	valid
55.0ms	445×	body	160	valid
26.0ms	350×	body	80	valid
19.0ms	5×	body	5120	valid

Details

analyze516.0ms

sample141.0ms

simplify2.0ms

prune3.0ms

localize12.0ms

rewrite11.0ms

series12.0ms

simplify37.0ms

prune119.0ms

localize10.0ms

rewrite20.0ms

series16.0ms

simplify47.0ms

prune138.0ms

localize10.0ms

rewrite21.0ms

series28.0ms

simplify58.0ms

prune148.0ms

localize13.0ms

rewrite15.0ms

series48.0ms

simplify54.0ms

prune112.0ms

regimes225.0ms

bsearch51.0ms

simplify1.0ms

end0.0ms

analyze515.0ms

sample4.5s

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