Details

analyze39.0ms

Algorithm

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

sample37.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4776	53
1	4776	53

prune12.0ms

Filtered

1 candidates to 1 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: 49.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
0.0b	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
40.5b	(* (* i (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))))
46.2b	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

90×	`frac-times`
60×	`flip3-+` `flip-+`
52×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
49×	`associate-*r/`
38×	`associate-r`
30×	`flip3--` `flip--`
28×	`associate-*l/`
25×	`prod-exp` `cbrt-unprod`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`pow1`
15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`associate--l+`
11×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp` `associate-l`
7×	`pow-prod-down`
6×	`sub-neg` `times-frac`
4×	`add-log-exp`
3×	`-commutative` `associate-/l`
2×	`div-inv` `associate-/l/` `distribute-lft-out`
1×	`frac-2neg` `clear-num` `associate-/r*` `difference-of-squares` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

37.0ms	(* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
28.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
67.0ms	(* (* i (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))))
51.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))
60.0ms	(* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))
312.0ms	(* (* i (+ i (+ alpha beta))) (/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)))))
111.0ms	(/ (+ (* i (+ i (+ alpha beta))) (* alpha beta)) (* (+ alpha (+ beta (* i 2.0))) (* (+ alpha (+ beta (* i 2.0))) (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))))

simplify70.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4986	9875
1	4986	9875

prune544.0ms

Filtered

145 candidates to 219 candidates (-51.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	214	7	221

Merged error: 39.7b

Counts

221 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b	(exp (- (log (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)) (* 2 (log (+ alpha (+ beta (* i 2.0))))))))
35.5b	(log (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
40.5b	(* (* i (+ i (+ alpha beta))) (exp (- (log (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)) (* 2 (log (+ alpha (+ beta (* i 2.0)))))))))
43.0b	(log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `log-prod` `*-un-lft-identity`
12×	`pow1` `exp-sum`
10×	`add-cube-cbrt`
9×	`add-exp-log` `associate-r` `add-cbrt-cube`
8×	`log-div`
7×	`add-log-exp`
6×	`exp-prod` `associate--l+`
5×	`associate-*r/`
4×	`associate-+l-` `exp-diff` `associate--r-`
3×	`flip3--` `flip3-+` `pow-prod-down` `prod-exp` `log-pow` `flip--` `cbrt-unprod` `flip-+` `rem-exp-log`
2×	`frac-times` `sub-neg` `diff-log` `rem-log-exp` `associate-*l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate-l` `sum-log` `*-commutative`

Counts

4 → 81

Calls

4 calls:

13.0ms	(exp (- (log (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)) (* 2 (log (+ alpha (+ beta (* i 2.0))))))))
7.0ms	(log (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
23.0ms	(* (* i (+ i (+ alpha beta))) (exp (- (log (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)) (* 2 (log (+ alpha (+ beta (* i 2.0)))))))))
11.0ms	(log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

series776.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(exp (- (log (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)) (* 2 (log (+ alpha (+ beta (* i 2.0))))))))
18.0ms	(log (+ (* i (+ i (+ alpha beta))) (* alpha beta)))
409.0ms	(* (* i (+ i (+ alpha beta))) (exp (- (log (+ (* i (+ i (+ alpha beta))) (* alpha beta))) (+ (log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0)) (* 2 (log (+ alpha (+ beta (* i 2.0)))))))))
56.0ms	(log (- (* (+ alpha (+ beta (* i 2.0))) (+ alpha (+ beta (* i 2.0)))) 1.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5347	2539

prune276.0ms

Filtered

82 candidates to 93 candidates (-13.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	87	13	100

Merged error: 14.4b

Counts

100 → 13

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b	(* i (/ (/ 1 i) (* 4.0 (* 2.0 2.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
30×	`add-cbrt-cube`
25×	`prod-exp`
22×	`times-frac`
18×	`div-exp`
17×	`associate-r`
13×	`cbrt-unprod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-undiv`
3×	`pow1` `rec-exp` `1-exp` `associate-l`
2×	`div-inv`
1×	`associate-r/` `pow-prod-down` `-commutative` `add-log-exp` `unswap-sqr`

Counts

1 → 51

Calls

1 calls:

13.0ms

(* i (/ (/ 1 i) (* 4.0 (* 2.0 2.0))))

series1.0ms

Counts

1 → 3

Calls

1 calls:

1.0ms

(* i (/ (/ 1 i) (* 4.0 (* 2.0 2.0))))

simplify52.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5022	419

prune93.0ms

Filtered

28 candidates to 54 candidates (-92.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	54	13	67

Merged error: 14.3b

Counts

67 → 13

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	12	12
Picked	1	1
Done	0	0
Total	13	13

Merged error: 14.3b

Counts

13 → 13

regimes397.0ms

Accuracy

43.6% (4.4b remaining)

Error of 15.7b against oracle of 11.3b and baseline of 19.1b

bsearch199.0ms

Steps

Iters	Range		Point
6	5.383944394113721e+82	3.9029149920398764e+83	2.6665270239172677e+83

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	57
1	44	57

end0.0ms

analyze40.0ms

Algorithm

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

sample1.0s

Algorithm

intervals

Results

658.0ms	8000×	body	80	valid
177.0ms	8000×	pre	80	true

Details

analyze39.0ms

sample37.0ms

simplify31.0ms

prune12.0ms

localize24.0ms

rewrite207.0ms

series576.0ms

simplify70.0ms

prune544.0ms

localize29.0ms

rewrite57.0ms

series776.0ms

simplify92.0ms

prune276.0ms

localize7.0ms

rewrite17.0ms

series1.0ms

simplify52.0ms

prune93.0ms

localize0.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune0.0ms

regimes397.0ms

bsearch199.0ms

simplify1.0ms

end0.0ms

analyze40.0ms

sample1.0s

Profiling