Details

analyze42.0ms

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

sample35.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6024	53

prune14.0ms

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: 52.5b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.8b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
46.0b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

12.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
12.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
24.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
25.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
308.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
58.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify70.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5029	10113

prune549.0ms

Filtered

153 candidates to 212 candidates (-38.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	8	212
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	206	8	214

Merged error: 34.8b

Counts

214 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

30.8b	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
30.8b	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
35.3b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
35.3b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
24×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`pow1`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
6×	`sqrt-div` `associate-/l*`
4×	`sqrt-pow1` `flip3-+` `associate-/r/` `flip-+` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-times` `frac-2neg` `pow1/2` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `clear-num` `sqrt-prod` `div-inv`

Counts

4 → 98

Calls

4 calls:

22.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
22.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
9.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
10.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

series137.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
41.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
26.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
28.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4852	2844
1	4852	2844

prune403.0ms

Filtered

90 candidates to 110 candidates (-22.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	109	9	118

Merged error: 34.8b

Counts

118 → 9

localize39.0ms

Local error

Found 4 expressions with local error:

23.3b	(/ (/ (+ (* alpha beta) (* i (+ alpha (+ beta i)))) (sqrt (+ alpha (+ beta (* i 2.0))))) (sqrt (+ alpha (+ beta (* i 2.0)))))
30.8b	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (/ (+ (* alpha beta) (* i (+ alpha (+ beta i)))) (sqrt (+ alpha (+ beta (* i 2.0))))) (sqrt (+ alpha (+ beta (* i 2.0)))))))
30.8b	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
35.3b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

369×	`times-frac`
293×	`*-un-lft-identity`
210×	`sqrt-prod`
181×	`add-sqr-sqrt` `add-cube-cbrt`
56×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
11×	`add-exp-log` `flip3-+` `associate-/r*` `add-cbrt-cube` `flip-+`
10×	`pow1` `div-inv`
4×	`cbrt-undiv` `sqrt-pow1` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`frac-times` `frac-2neg` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num`

Counts

4 → 303

Calls

4 calls:

24.0ms	(/ (/ (+ (* alpha beta) (* i (+ alpha (+ beta i)))) (sqrt (+ alpha (+ beta (* i 2.0))))) (sqrt (+ alpha (+ beta (* i 2.0)))))
40.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (/ (+ (* alpha beta) (* i (+ alpha (+ beta i)))) (sqrt (+ alpha (+ beta (* i 2.0))))) (sqrt (+ alpha (+ beta (* i 2.0)))))))
23.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
11.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (/ (+ (* alpha beta) (* i (+ alpha (+ beta i)))) (sqrt (+ alpha (+ beta (* i 2.0))))) (sqrt (+ alpha (+ beta (* i 2.0)))))
71.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (/ (+ (* alpha beta) (* i (+ alpha (+ beta i)))) (sqrt (+ alpha (+ beta (* i 2.0))))) (sqrt (+ alpha (+ beta (* i 2.0)))))))
46.0ms	(sqrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
27.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

simplify119.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5064	12850

prune1.2s

Filtered

148 candidates to 315 candidates (-112.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	315	0	315
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	315	9	324

Merged error: 34.8b

Counts

324 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

31.8b	(cbrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
35.3b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
35.3b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
35.3b	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

55×	`*-un-lft-identity`
36×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`associate-/r*` `distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `cbrt-div` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`

Counts

4 → 117

Calls

4 calls:

22.0ms	(cbrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
10.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
12.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
10.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(cbrt (* (/ i (/ (+ alpha (+ beta (* i 2.0))) (+ i (+ alpha beta)))) (/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))))
26.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
29.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))
27.0ms	(/ (+ (* alpha beta) (* i (+ i (+ alpha beta)))) (+ alpha (+ beta (* i 2.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5388	3370

prune558.0ms

Filtered

105 candidates to 129 candidates (-22.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	129	9	138

Merged error: 34.8b

Counts

138 → 9

regimes264.0ms

Accuracy

37.4% (2.4b remaining)

Error of 36.3b against oracle of 33.9b and baseline of 37.7b

bsearch23.0ms

Steps

Iters	Range		Point
7	1.9915711490592043e+207	2.5051444746191463e+209	2.0265518640508438e+207

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	129	100
1	129	100

end0.0ms

sample998.0ms

Algorithm

intervals

Results

642.0ms	8000×	body	80	valid
172.0ms	8000×	pre	80	true

Details

analyze42.0ms

sample35.0ms

simplify30.0ms

prune14.0ms

localize14.0ms

rewrite95.0ms

series403.0ms

simplify70.0ms

prune549.0ms

localize28.0ms

rewrite66.0ms

series137.0ms

simplify72.0ms

prune403.0ms

localize39.0ms

rewrite116.0ms

series182.0ms

simplify119.0ms

prune1.2s

localize33.0ms

rewrite58.0ms

series411.0ms

simplify59.0ms

prune558.0ms

regimes264.0ms

bsearch23.0ms

simplify2.0ms

end0.0ms

sample998.0ms

Profiling