Details

analyze800.0ms

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

sample188.0ms

Algorithm

intervals

Results

77.0ms	92×	body	1280	valid
61.0ms	30×	body	2560	valid
17.0ms	42×	body	640	valid
5.0ms	24×	body	320	valid
5.0ms	5×	body	320	invalid
4.0ms	61×	body	80	valid
3.0ms	4×	body	1280	invalid
3.0ms	6×	body	640	invalid
2.0ms	22×	body	80	invalid
1.0ms	7×	body	160	valid
1.0ms	3×	body	160	invalid
1.0ms	12×	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: 45.9b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
0.1b	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
0.5b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b	(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:

14.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
18.0ms	(* 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:

62.0ms	(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
55.0ms	(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
37.0ms	(- (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 (49.0ms)

Iter	Nodes	Cost
0	4987	2281
1	4987	2281

prune233.0ms

Filtered

82 candidates to 110 candidates (-34.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	6	112

Merged error: 8.1b

Counts

112 → 6

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)))
13.6b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
14.3b	(* (* i i) (* 0.5 (log 1.0)))

rewrite49.0ms

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:

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

series78.0ms

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)))))) i))
25.0ms	(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
16.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
13.0ms	(* (* i i) (* 0.5 (log 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5088	2897

prune269.0ms

Filtered

84 candidates to 129 candidates (-53.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	7	129
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 8.1b

Counts

135 → 12

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `*-un-lft-identity`
6×	`associate-r/` `associate-l*`
5×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in` `associate-r`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `*-commutative` `flip-+` `add-log-exp`
1×	`distribute-lft-out` `unswap-sqr`

Counts

2 → 47

Calls

2 calls:

11.0ms	(* n (+ 1.0 (+ (* i 0.5) (- (* (/ (log 1.0) i) n) (* i (* 0.5 (log 1.0)))))))
12.0ms	(* 100.0 (* n (+ 1.0 (+ (* i 0.5) (- (* (/ (log 1.0) i) n) (* i (* 0.5 (log 1.0))))))))

series33.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(* n (+ 1.0 (+ (* i 0.5) (- (* (/ (log 1.0) i) n) (* i (* 0.5 (log 1.0)))))))
17.0ms	(* 100.0 (* n (+ 1.0 (+ (* i 0.5) (- (* (/ (log 1.0) i) n) (* i (* 0.5 (log 1.0))))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5540	1095

prune130.0ms

Filtered

36 candidates to 53 candidates (-47.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	48	5	53
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	53	12	65

Merged error: 8.1b

Counts

65 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (* (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))) (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))) (/ (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))) i))
14.4b	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
14.4b	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
14.4b	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
22×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times`
15×	`flip3-+` `flip-+`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 100

Calls

4 calls:

28.0ms	(* (* (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))) (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))) (/ (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))) i))
6.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
6.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
6.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))

series178.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (* (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))) (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))) (/ (cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0))))))) i))
53.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
55.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))
53.0ms	(cbrt (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))))

simplify77.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4977	5180
1	4977	5180

prune680.0ms

Filtered

95 candidates to 112 candidates (-17.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	111	13	124

Merged error: 8.1b

Counts

124 → 13

regimes314.0ms

Accuracy

66.5% (6.4b remaining)

Error of 15.3b against oracle of 8.9b and baseline of 28.0b

bsearch384.0ms

Steps

Iters	Range		Point
8	1.1077057863947448e+273	3.512856707582331e+277	1.5515047937283527e+274
9	5.021362463463957e+190	1.505753257532481e+196	1.4891434779341286e+196
12	177.9839318729715	4.274336514364149e+48	180.39130391037708
7	-5.11715253290391e-05	-2.9931197223106747e-06	-4.872324559716277e-05

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	506	318
1	506	318

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	2897×	body	1280	valid
2.2s	1027×	body	2560	valid
588.0ms	1468×	body	640	valid
160.0ms	674×	body	320	valid
119.0ms	240×	body	640	invalid
113.0ms	1599×	body	80	valid
99.0ms	123×	body	1280	invalid
58.0ms	183×	body	320	invalid
50.0ms	331×	body	160	valid
41.0ms	441×	body	80	invalid
29.0ms	15×	body	2560	invalid
18.0ms	97×	body	160	invalid
15.0ms	333×	body	80	nan
13.0ms	4×	body	5120	valid

Details

analyze800.0ms

sample188.0ms

simplify34.0ms

prune9.0ms

localize10.0ms

rewrite52.0ms

series179.0ms

simplify62.0ms

prune233.0ms

localize16.0ms

rewrite49.0ms

series78.0ms

simplify37.0ms

prune269.0ms

localize14.0ms

rewrite24.0ms

series33.0ms

simplify41.0ms

prune130.0ms

localize18.0ms

rewrite49.0ms

series178.0ms

simplify77.0ms

prune680.0ms

regimes314.0ms

bsearch384.0ms

simplify8.0ms

end0.0ms

sample6.2s

Profiling