Details

sample198.0ms

Algorithm

intervals

Results

70.0ms	89×	body	1280	valid
62.0ms	29×	body	2560	valid
24.0ms	61×	body	640	valid
8.0ms	34×	body	320	valid
8.0ms	90×	body	80	valid
4.0ms	91×	body	80	nan
2.0ms	11×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5270	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: 45.5b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.4b	(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b	(pow (+ 1.0 (/ i n)) n)
9.4b	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite81.0ms

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:

33.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms	(- (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))

series367.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms	(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms	(pow (+ 1.0 (/ i n)) n)
63.0ms	(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify103.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4964	5855
1	4964	5855

prune585.0ms

Filtered

226 candidates to 293 candidates (-29.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	9	293
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	286	9	295

Merged error: 18.8b

Counts

295 → 9

localize19.0ms

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)))
10.1b	(* (* 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))

rewrite56.0ms

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:

9.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0))))))
19.0ms	(* 100.0 (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n)))
7.0ms	(* (* i i) (* 0.5 (log 1.0)))
13.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

series70.0ms

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)))
23.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) (/ i n))

simplify61.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5618	5673

prune517.0ms

Filtered

147 candidates to 200 candidates (-36.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	189	11	200
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	190	19	209

Merged error: 8.8b

Counts

209 → 19

localize15.0ms

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)))))
0.0b	(* (* 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))
9.6b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt` `*-un-lft-identity`
14×	`pow1` `add-cube-cbrt`
9×	`times-frac` `add-log-exp`
8×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down`
5×	`associate-r`
4×	`associate-l`
3×	`associate-r/` `associate-/r` `sum-log` `associate-/l*`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `div-exp` `*-commutative` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `flip3--` `distribute-rgt-out--` `frac-2neg` `associate-*l/` `clear-num` `flip--` `div-inv` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

7.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
7.0ms	(* (* i i) (- 0.5 (* (log 1.0) 0.5)))
12.0ms	(* 100.0 (* (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) n))
9.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

series62.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5)))))
15.0ms	(* (* 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)

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5011	2283

prune249.0ms

Filtered

70 candidates to 101 candidates (-44.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	98	3	101
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	100	20	120

Merged error: 8.8b

Counts

120 → 20

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 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) (/ 1 n)))
0.2b	(/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n))
9.6b	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
419×	`add-sqr-sqrt`
396×	`*-un-lft-identity`
393×	`add-cube-cbrt`
178×	`associate-r`
65×	`add-exp-log`
57×	`div-inv`
41×	`add-cbrt-cube`
33×	`div-exp`
17×	`cbrt-undiv`
16×	`associate-/r` `associate-/l`
12×	`prod-exp`
11×	`pow1`
8×	`cbrt-unprod` `unswap-sqr`
4×	`rec-exp` `1-exp` `associate-l` `pow-prod-down` `add-log-exp`
3×	`associate-*r/` `associate-/l/`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/` `*-commutative`
1×	`flip3--` `distribute-rgt-out--` `flip3-+` `flip--` `flip-+`

Counts

4 → 482

Calls

4 calls:

7.0ms	(* (* i i) (- 0.5 (* (log 1.0) 0.5)))
46.0ms	(* 100.0 (/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n)))
15.0ms	(/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n))
9.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

series74.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* 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) (/ 1 n)))
19.0ms	(/ (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i) (/ 1 n))
16.0ms	(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (* (* i i) (- 0.5 (* (log 1.0) 0.5))))) i)

simplify173.0ms

Algorithm

egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4974	17474
1	4974	17474

prune1.8s

Filtered

327 candidates to 494 candidates (-51.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	492	2	494
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	495	19	514

Merged error: 8.8b

Counts

514 → 19

regimes282.0ms

Accuracy

68.8% (6.5b remaining)

Error of 15.3b against oracle of 8.8b and baseline of 29.5b

bsearch97.0ms

Steps

Iters	Range		Point
3	0.3184006052855057	0.41648793310771814	0.33679197925217047
7	-3.757234823736941e-17	-7.873507946935529e-19	-3.697189764724927e-17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	77
1	55	77

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.5s	2921×	body	1280	valid
2.1s	997×	body	2560	valid
725.0ms	1803×	body	640	valid
226.0ms	920×	body	320	valid
168.0ms	2374×	body	80	valid
99.0ms	2351×	body	80	nan
73.0ms	464×	body	160	valid
23.0ms	6×	body	5120	valid

Details

sample198.0ms

simplify67.0ms

prune9.0ms

localize9.0ms

rewrite81.0ms

series367.0ms

simplify103.0ms

prune585.0ms

localize19.0ms

rewrite56.0ms

series70.0ms

simplify61.0ms

prune517.0ms

localize15.0ms

rewrite37.0ms

series62.0ms

simplify46.0ms

prune249.0ms

localize16.0ms

rewrite112.0ms

series74.0ms

simplify173.0ms

prune1.8s

regimes282.0ms

bsearch97.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling