Details

analyze779.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

sample245.0ms

Algorithm

intervals

Results

103.0ms	100×	body	1280	valid
59.0ms	24×	body	2560	valid
23.0ms	42×	body	640	valid
12.0ms	2×	body	5120	valid
8.0ms	15×	body	640	invalid
8.0ms	24×	body	320	valid
6.0ms	10×	body	320	invalid
5.0ms	53×	body	80	valid
3.0ms	25×	body	80	invalid
2.0ms	11×	body	160	valid
1.0ms	7×	body	160	invalid
1.0ms	1×	body	1280	invalid
1.0ms	14×	body	80	nan

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5281	15

prune9.0ms

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: 47.4b

Counts

2 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.3b	(pow (+ 1.0 (/ i n)) n)
10.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

320×	`times-frac`
289×	`add-sqr-sqrt`
198×	`*-un-lft-identity`
140×	`add-cube-cbrt`
96×	`associate-r`
84×	`difference-of-squares`
32×	`unpow-prod-down`
29×	`sqr-pow`
28×	`distribute-lft-out--`
19×	`add-exp-log`
18×	`add-cbrt-cube`
17×	`div-inv`
13×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-unpow` `associate-l` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `distribute-lft-out`

Counts

4 → 280

Calls

4 calls:

32.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
12.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms	(pow (+ 1.0 (/ i n)) n)
15.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series259.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
38.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
44.0ms	(pow (+ 1.0 (/ i n)) n)
68.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify98.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4988	5853
1	4988	5853

prune569.0ms

Filtered

226 candidates to 292 candidates (-29.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	284	8	292
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	286	8	294

Merged error: 17.5b

Counts

294 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
0.1b	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
12.8b	(* (* i i) (* 0.5 (log 1.0)))
17.2b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
95×	`add-sqr-sqrt`
86×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
13×	`associate-/r*` `add-log-exp`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down` `div-inv`
6×	`cbrt-undiv` `div-exp`
5×	`sum-log`
4×	`associate-+r-` `associate-l`
3×	`associate-/l*` `unswap-sqr`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `frac-2neg` `diff-log` `div-sub` `associate-*r/` `clear-num`

Counts

4 → 188

Calls

4 calls:

10.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
21.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
8.0ms	(* (* i i) (* 0.5 (log 1.0)))
14.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
21.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
14.0ms	(* (* i i) (* 0.5 (log 1.0)))
19.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

simplify60.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5701	5673

prune585.0ms

Filtered

147 candidates to 200 candidates (-36.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	189	11	200
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	190	18	208

Merged error: 7.1b

Counts

208 → 18

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
0.0b	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
0.1b	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
12.2b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `add-cbrt-cube`
19×	`times-frac`
16×	`associate-l`
11×	`pow1`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
4×	`associate-r` `pow-prod-down`
3×	`cbrt-undiv` `div-exp` `associate-/r` `sum-log` `associate-/l`
2×	`flip3-+` `associate-l/` `-commutative` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 95

Calls

4 calls:

10.0ms	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
7.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
11.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
10.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

series68.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n)
13.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
21.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
15.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

simplify33.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5313	2584

prune277.0ms

Filtered

81 candidates to 107 candidates (-32.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	4	13	17
Picked	0	1	1
Done	0	0	0
Total	107	18	125

Merged error: 7.1b

Counts

125 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (* (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))) (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))) (/ i (cbrt (+ (* n (log 1.0)) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))))))
13.0b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
13.0b	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
13.0b	(cbrt (+ (* n (log 1.0)) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`cbrt-prod`
24×	`associate-/r*`
22×	`cbrt-div`
16×	`add-exp-log`
11×	`flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
5×	`associate-/r/`
4×	`pow1` `frac-times` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`associate-r/` `associate-l/` `prod-exp` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 115

Calls

4 calls:

25.0ms	(/ (* (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))) (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))) (/ i (cbrt (+ (* n (log 1.0)) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
6.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
4.0ms	(cbrt (+ (* n (log 1.0)) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (* (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))) (cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))) (/ i (cbrt (+ (* n (log 1.0)) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))))))
61.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
59.0ms	(cbrt (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))))
235.0ms	(cbrt (+ (* n (log 1.0)) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))))

simplify85.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4959	6086
1	4959	6086

prune838.0ms

Filtered

114 candidates to 127 candidates (-11.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	15	16
Picked	1	0	1
Done	0	1	1
Total	127	18	145

Merged error: 7.1b

Counts

145 → 18

regimes288.0ms

Accuracy

69.3% (6.2b remaining)

Error of 15.0b against oracle of 8.8b and baseline of 29.0b

bsearch116.0ms

Steps

Iters	Range		Point
11	7.612601920526394e-16	1065007711201.1888	0.001881761355889925
3	-9.48713484558147e-11	-6.912584096032108e-11	-9.326225423734636e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	65
1	108	65

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	2862×	body	1280	valid
1.9s	922×	body	2560	valid
591.0ms	1516×	body	640	valid
172.0ms	775×	body	320	valid
115.0ms	231×	body	640	invalid
105.0ms	1584×	body	80	valid
77.0ms	101×	body	1280	invalid
63.0ms	207×	body	320	invalid
46.0ms	329×	body	160	valid
44.0ms	12×	body	5120	valid
38.0ms	438×	body	80	invalid
20.0ms	98×	body	160	invalid
16.0ms	9×	body	2560	invalid
15.0ms	349×	body	80	nan

Details

analyze779.0ms

sample245.0ms

simplify34.0ms

prune9.0ms

localize8.0ms

rewrite82.0ms

series259.0ms

simplify98.0ms

prune569.0ms

localize16.0ms

rewrite63.0ms

series66.0ms

simplify60.0ms

prune585.0ms

localize14.0ms

rewrite41.0ms

series68.0ms

simplify33.0ms

prune277.0ms

localize24.0ms

rewrite44.0ms

series373.0ms

simplify85.0ms

prune838.0ms

regimes288.0ms

bsearch116.0ms

simplify2.0ms

end0.0ms

sample5.9s

Profiling