Details

sample205.0ms

Algorithm

intervals

Results

83.0ms	39×	body	2560	valid
69.0ms	82×	body	1280	valid
19.0ms	55×	body	640	valid
7.0ms	93×	body	80	valid
5.0ms	20×	body	320	valid
3.0ms	73×	body	80	nan
3.0ms	20×	body	160	valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	59	7
2	141	7
3	346	7
4	1171	7
5	5001	7

prune2.0ms

Filtered

1 candidates to 0 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 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b	(pow (+ 1.0 (/ i n)) n)
9.7b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite94.0ms

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 → 281

Calls

4 calls:

36.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
13.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms	(pow (+ 1.0 (/ i n)) n)
17.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts

4 → 12

Calls

4 calls:

367.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
242.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
204.0ms	(pow (+ 1.0 (/ i n)) n)
373.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	3285
1	5002	3166

prune680.0ms

Filtered

293 candidates to 223 candidates (76.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	283	10	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	284	10	294

Merged error: 21.4b

Counts

294 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (pow i 2))
0.1b	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.6b	(* (pow i 2) (log 1.0))
19.1b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
111×	`add-sqr-sqrt`
90×	`add-cube-cbrt` `*-un-lft-identity`
56×	`associate-r`
28×	`add-exp-log`
22×	`add-cbrt-cube`
14×	`associate-l`
13×	`associate-/r*`
11×	`unswap-sqr`
9×	`prod-exp` `div-inv`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `log-prod` `div-exp`
5×	`cbrt-unprod`
4×	`unpow2` `add-log-exp` `sqr-pow`
3×	`distribute-rgt-in` `distribute-lft-in` `-commutative` `associate-/l`
2×	`pow-to-exp` `pow-exp` `associate-/r/` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-prod-down` `clear-num` `log-pow` `flip--`

Counts

4 → 200

Calls

4 calls:

7.0ms	(* 0.5 (pow i 2))
18.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms	(* (pow i 2) (log 1.0))
13.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series554.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 0.5 (pow i 2))
206.0ms	(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
130.0ms	(* (pow i 2) (log 1.0))
194.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify147.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	907	3537
1	4856	3275
2	5001	3275

prune669.0ms

Filtered

212 candidates to 157 candidates (74.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	199	13	212
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	200	22	222

Merged error: 10.9b

Counts

222 → 22

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.1b	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0b	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b	(* (pow i 2) (log 1.0))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`associate-l`
22×	`add-cbrt-cube`
19×	`times-frac`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
6×	`log-prod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`associate-*l/` `div-inv` `associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `div-sub` `associate-*r/` `pow-exp` `clear-num` `log-pow` `flip--`

Counts

4 → 117

Calls

4 calls:

11.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
12.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
16.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms	(* (pow i 2) (log 1.0))

series690.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
232.0ms	(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
130.0ms	(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
139.0ms	(* (pow i 2) (log 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	529	1979
1	2435	1684
2	5001	1679

prune383.0ms

Filtered

129 candidates to 87 candidates (67.4%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	2	19	21
Picked	0	1	1
Done	0	0	0
Total	130	21	151

Merged error: 10.9b

Counts

151 → 21

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
2.9b	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
11.6b	(* (pow i 2) (log 1.0))
12.5b	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
22×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
12×	`pow1`
10×	`prod-exp`
8×	`associate-r` `cbrt-unprod`
6×	`log-prod` `associate-*l/`
5×	`unswap-sqr`
4×	`unpow-prod-down` `associate-*r/` `pow-prod-down` `add-log-exp`
3×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `distribute-lft-in` `times-frac` `div-exp` `associate-/r` `-commutative` `flip--`
2×	`associate-/l/` `unpow2` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `log-pow` `div-inv` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

12.0ms	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
11.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
6.0ms	(* (pow i 2) (log 1.0))
14.0ms	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)

series635.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
137.0ms	(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
137.0ms	(* (pow i 2) (log 1.0))
207.0ms	(/ (* 100.0 (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)

simplify84.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	509	1627
1	2779	1331
2	5001	1331

prune251.0ms

Filtered

111 candidates to 71 candidates (64.0%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	4	15	19
Picked	0	1	1
Done	0	1	1
Total	112	20	132

Merged error: 10.9b

Counts

132 → 20

regimes351.0ms

Accuracy

69.2% (5.6b remaining)

Error of 16.1b against oracle of 10.5b and baseline of 28.8b

bsearch273.0ms

Steps

Iters	Range		Point
7	0.00022027325057658872	0.008784522488119305	0.005619708242321016
10	-18784469646.78796	-0.08793709934347878	-0.21878848523850206

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	50
1	69	50
2	69	50

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	2886×	body	1280	valid
2.1s	1003×	body	2560	valid
724.0ms	1746×	body	640	valid
229.0ms	908×	body	320	valid
182.0ms	2475×	body	80	valid
110.0ms	2304×	body	80	nan
68.0ms	436×	body	160	valid
11.0ms	3×	body	5120	valid

Details

sample205.0ms

simplify42.0ms

prune2.0ms

localize9.0ms

rewrite94.0ms

series1.2s

simplify63.0ms

prune680.0ms

localize17.0ms

rewrite63.0ms

series554.0ms

simplify147.0ms

prune669.0ms

localize17.0ms

rewrite49.0ms

series690.0ms

simplify78.0ms

prune383.0ms

localize18.0ms

rewrite46.0ms

series635.0ms

simplify84.0ms

prune251.0ms

regimes351.0ms

bsearch273.0ms

simplify3.0ms

end0.0ms

sample6.2s

Profiling