Details

analyze815.0ms

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

sample189.0ms

Algorithm

intervals

Results

78.0ms	95×	body	1280	valid
60.0ms	30×	body	2560	valid
16.0ms	41×	body	640	valid
6.0ms	27×	body	320	valid
5.0ms	5×	body	1280	invalid
3.0ms	7×	body	640	invalid
3.0ms	47×	body	80	valid
3.0ms	16×	body	160	valid
3.0ms	8×	body	320	invalid
1.0ms	14×	body	80	invalid
1.0ms	4×	body	160	invalid
1.0ms	12×	body	80	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

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: 47.2b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
0.0b	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.7b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.6b	(pow (+ 1.0 (/ i n)) n)

rewrite52.0ms

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:

15.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
17.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
10.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)

series179.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
56.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
33.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms	(pow (+ 1.0 (/ i n)) n)

simplify66.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4987	2281
1	4987	2281

prune258.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Merged error: 9.8b

Counts

112 → 8

localize18.0ms

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)))
10.1b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
10.6b	(* (* i i) (* 0.5 (log 1.0)))

rewrite52.0ms

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:

24.0ms	(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
30.0ms	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
14.0ms	(/ (+ (* 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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5088	2897

prune325.0ms

Filtered

84 candidates to 129 candidates (-53.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	117	12	129
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	118	19	137

Merged error: 9.7b

Counts

137 → 19

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))
0.0b	(* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
0.1b	(* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)))
10.1b	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite46.0ms

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`
14×	`associate-r`
11×	`pow1`
9×	`add-log-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l`
4×	`pow-prod-down`
3×	`cbrt-undiv` `associate-r/` `div-exp` `associate-/r` `sum-log` `associate-/l*`
2×	`flip3-+` `*-commutative` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `frac-2neg` `clear-num`

Counts

4 → 95

Calls

4 calls:

8.0ms	(+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))
11.0ms	(* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
13.0ms	(* 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)

series78.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))
15.0ms	(* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
26.0ms	(* n (* 100.0 (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)))
26.0ms	(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5022	2576

prune327.0ms

Filtered

80 candidates to 107 candidates (-33.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	16	18
Picked	0	1	1
Done	0	0	0
Total	107	19	126

Merged error: 9.7b

Counts

126 → 19

localize20.0ms

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)))))) (/ 1 i)))
0.1b	(* 100.0 (* n (* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i))))
10.2b	(* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i))
10.6b	(* (* i i) (* 0.5 (log 1.0)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
44×	`add-cbrt-cube`
36×	`prod-exp`
32×	`pow1`
25×	`add-sqr-sqrt`
24×	`cbrt-unprod`
21×	`associate-*r/`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt` `pow-prod-down`
16×	`associate-r`
12×	`distribute-rgt-in` `log-prod` `distribute-lft-in`
11×	`times-frac`
10×	`associate-l`
6×	`frac-times` `flip3-+` `div-exp` `associate-*l/` `flip-+`
4×	`*-commutative` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `un-div-inv` `unswap-sqr`
1×	`div-inv`

Counts

4 → 133

Calls

4 calls:

15.0ms	(* n (* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i)))
18.0ms	(* 100.0 (* n (* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i))))
15.0ms	(* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i))
8.0ms	(* (* i i) (* 0.5 (log 1.0)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* n (* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i)))
26.0ms	(* 100.0 (* n (* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i))))
18.0ms	(* (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ 1 i))
13.0ms	(* (* i i) (* 0.5 (log 1.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5007	2998

prune238.0ms

Filtered

84 candidates to 145 candidates (-72.6%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	4	13	17
Picked	0	1	1
Done	0	1	1
Total	145	19	164

Merged error: 9.7b

Counts

164 → 19

regimes354.0ms

Accuracy

69.2% (6.1b remaining)

Error of 15.3b against oracle of 9.2b and baseline of 29.0b

bsearch132.0ms

Steps

Iters	Range	Point
6	3.625646590916209e-05	0.00019035649969593936	0.00017000305165270794
1	-5.0356569090425854e-204	-4.8119507054610565e-204	-4.9797303581472035e-204
6	-5.3176609444338126e-11	-7.738779818716208e-12	-5.254825670150266e-11

Iters

Range

Point

3.625646590916209e-05

0.00019035649969593936

0.00017000305165270794

-5.0356569090425854e-204

-4.8119507054610565e-204

-4.9797303581472035e-204

-5.3176609444338126e-11

-7.738779818716208e-12

-5.254825670150266e-11

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	575	336
1	575	336

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2824×	body	1280	valid
2.1s	967×	body	2560	valid
603.0ms	1521×	body	640	valid
170.0ms	737×	body	320	valid
118.0ms	242×	body	640	invalid
108.0ms	1602×	body	80	valid
103.0ms	127×	body	1280	invalid
61.0ms	194×	body	320	invalid
52.0ms	343×	body	160	valid
41.0ms	436×	body	80	invalid
23.0ms	6×	body	5120	valid
17.0ms	91×	body	160	invalid
16.0ms	9×	body	2560	invalid
14.0ms	309×	body	80	nan

Details

analyze815.0ms

sample189.0ms

simplify35.0ms

prune9.0ms

localize13.0ms

rewrite52.0ms

series179.0ms

simplify66.0ms

prune258.0ms

localize18.0ms

rewrite52.0ms

series82.0ms

simplify41.0ms

prune325.0ms

localize16.0ms

rewrite46.0ms

series78.0ms

simplify52.0ms

prune327.0ms

localize20.0ms

rewrite62.0ms

series81.0ms

simplify59.0ms

prune238.0ms

regimes354.0ms

bsearch132.0ms

simplify8.0ms

end0.0ms

sample6.0s

Profiling