Details

analyze787.0ms

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

sample201.0ms

Algorithm

intervals

Results

75.0ms	89×	body	1280	valid
73.0ms	35×	body	2560	valid
18.0ms	46×	body	640	valid
6.0ms	26×	body	320	valid
5.0ms	11×	body	640	invalid
3.0ms	49×	body	80	valid
3.0ms	3×	body	1280	invalid
2.0ms	1×	body	2560	invalid
2.0ms	6×	body	320	invalid
2.0ms	11×	body	160	valid
1.0ms	16×	body	80	invalid
1.0ms	22×	body	80	nan
0.0ms	1×	body	160	invalid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5281	15

prune10.0ms

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: 47.2b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
0.0b	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
1.2b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.5b	(pow (+ 1.0 (/ i n)) n)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
26×	`associate-r`
22×	`times-frac`
19×	`add-exp-log` `add-cube-cbrt`
18×	`add-cbrt-cube`
12×	`pow1` `difference-of-squares`
8×	`unpow-prod-down`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
5×	`sqr-pow`
4×	`pow-prod-down` `distribute-lft-out--`
3×	`pow-unpow` `associate-*r/`
2×	`cbrt-undiv` `div-exp` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

16.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
15.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0ms	(pow (+ 1.0 (/ i n)) n)

series181.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
64.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
36.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms	(pow (+ 1.0 (/ i n)) n)

simplify62.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4987	2281
1	4987	2281

prune247.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	7	112

Merged error: 10.8b

Counts

112 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
0.1b	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
10.8b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
11.4b	(* (* i i) (* 0.5 (log 1.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
30×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
23×	`pow1`
19×	`times-frac`
15×	`associate-r` `prod-exp` `cbrt-unprod`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in` `pow-prod-down`
7×	`associate-l`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/r` `-commutative` `associate-/l`
2×	`associate-+r-` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+`

Counts

4 → 117

Calls

4 calls:

14.0ms	(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
14.0ms	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
12.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
8.0ms	(* (* i i) (* 0.5 (log 1.0)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
27.0ms	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
15.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
14.0ms	(* (* i i) (* 0.5 (log 1.0)))

simplify40.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5088	2897

prune296.0ms

Filtered

84 candidates to 129 candidates (-53.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	122	7	129
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	122	14	136

Merged error: 10.8b

Counts

136 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
0.6b	(cbrt n)
10.8b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
1.0ms	(cbrt n)
9.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series82.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt n)
22.0ms	(cbrt n)
24.0ms	(cbrt n)
15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify45.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4950	1005
1	4950	1005

prune205.0ms

Filtered

57 candidates to 74 candidates (-29.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	73	15	88

Merged error: 10.8b

Counts

88 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

6.8b	(cbrt (* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))))
10.8b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.8b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.8b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

12.0ms	(cbrt (* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))))
10.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
9.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series627.0ms

Counts

4 → 12

Calls

4 calls:

583.0ms	(cbrt (* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))))
14.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
15.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify64.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4944	2897
1	4944	2897

prune683.0ms

Filtered

94 candidates to 109 candidates (-16.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	2	11	13
Picked	1	0	1
Done	0	1	1
Total	109	15	124

Merged error: 10.8b

Counts

124 → 15

regimes574.0ms

Accuracy

65% (7.2b remaining)

Error of 16.7b against oracle of 9.5b and baseline of 30.1b

bsearch245.0ms

Steps

Iters	Range		Point
10	5.460460098490599e+172	4.353290260259419e+191	5.460223498175969e+181
9	1.4909904148743054e-21	2.4513381972445114e-16	2.3385135141275714e-16
9	-6.007577350450598e-10	-6.525337881431085e-15	-5.932755958531832e-10

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	517	319
1	517	319

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.3s	2740×	body	1280	valid
2.0s	955×	body	2560	valid
591.0ms	1529×	body	640	valid
162.0ms	731×	body	320	valid
110.0ms	1687×	body	80	valid
101.0ms	211×	body	640	invalid
78.0ms	96×	body	1280	invalid
52.0ms	175×	body	320	invalid
49.0ms	349×	body	160	valid
42.0ms	479×	body	80	invalid
33.0ms	9×	body	5120	valid
30.0ms	16×	body	2560	invalid
16.0ms	87×	body	160	invalid
14.0ms	318×	body	80	nan

Details

analyze787.0ms

sample201.0ms

simplify34.0ms

prune10.0ms

localize10.0ms

rewrite53.0ms

series181.0ms

simplify62.0ms

prune247.0ms

localize16.0ms

rewrite54.0ms

series82.0ms

simplify40.0ms

prune296.0ms

localize18.0ms

rewrite14.0ms

series82.0ms

simplify45.0ms

prune205.0ms

localize20.0ms

rewrite43.0ms

series627.0ms

simplify64.0ms

prune683.0ms

regimes574.0ms

bsearch245.0ms

simplify8.0ms

end0.0ms

sample5.8s

Profiling