Details

sample217.0ms

Algorithm

intervals

Results

67.0ms	115×	body	1280	valid
39.0ms	31×	body	1280	nan
26.0ms	59×	body	640	valid
17.0ms	25×	body	640	nan
16.0ms	112×	body	80	overflowed
10.0ms	103×	body	80	valid
10.0ms	192×	body	80	nan
7.0ms	25×	body	320	valid
3.0ms	7×	body	320	nan
2.0ms	11×	body	160	nan
1.0ms	8×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

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: 33.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
7.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series473.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(pow x (/ 1.0 n))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune205.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 21.6b

Counts

89 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt n)
0.5b	(cbrt n)
0.6b	(* (cbrt n) (cbrt n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
22×	`cbrt-prod`
17×	`unpow-prod-down`
16×	`*-un-lft-identity`
15×	`difference-of-squares`
14×	`add-cube-cbrt`
11×	`pow1` `sqr-pow`
8×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`add-cbrt-cube` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
6.0ms	(* (cbrt n) (cbrt n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt n)
175.0ms	(cbrt n)
199.0ms	(* (cbrt n) (cbrt n))
437.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	386	953
1	1274	904
2	5001	877

prune290.0ms

Filtered

102 candidates to 81 candidates (79.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	102	4	106

Merged error: 21.5b

Counts

106 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt n) (cbrt n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
51×	`unpow-prod-down`
45×	`difference-of-squares`
33×	`sqr-pow`
18×	`*-un-lft-identity`
16×	`cbrt-prod`
12×	`add-cube-cbrt`
11×	`pow1`
10×	`add-log-exp`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

9.0ms	(* (cbrt n) (cbrt n))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

series1.5s

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt n) (cbrt n))
449.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
445.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
446.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

simplify55.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	2293
1	1158	2194
2	5002	2159

prune594.0ms

Filtered

136 candidates to 111 candidates (81.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	136	4	140

Merged error: 21.5b

Counts

140 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (log x) 1.0) (* x (pow n 2)))
4.0b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.1b	(* x (pow n 2))
9.9b	(/ (/ 0.5 n) (pow x 2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

7.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
68.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
5.0ms	(* x (pow n 2))
8.0ms	(/ (/ 0.5 n) (pow x 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
70.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
29.0ms	(* x (pow n 2))
25.0ms	(/ (/ 0.5 n) (pow x 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1113	2111
1	5001	1860

prune520.0ms

Filtered

232 candidates to 140 candidates (60.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	228	4	232
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	229	7	236

Merged error: 21.3b

Counts

236 → 7

regimes160.0ms

Accuracy

81.2% (2.0b remaining)

Error of 23.9b against oracle of 21.9b and baseline of 32.8b

bsearch219.0ms

Steps

Iters	Range		Point
11	1.8195789593932265e-08	444534403533.2454	2742253.531371596
8	-19310315965.464554	-4308662.012678887	-45586875.445913486

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	69
1	59	69

end0.0ms

sample7.3s

Algorithm

intervals

Results

2.1s	3894×	body	1280	valid
1.4s	1051×	body	1280	nan
819.0ms	1796×	body	640	valid
657.0ms	921×	body	640	nan
622.0ms	4042×	body	80	overflowed
328.0ms	3096×	body	80	valid
314.0ms	6228×	body	80	nan
258.0ms	825×	body	320	valid
177.0ms	408×	body	320	nan
94.0ms	475×	body	160	valid
49.0ms	214×	body	160	nan

Details

sample217.0ms

simplify35.0ms

prune2.0ms

localize9.0ms

rewrite25.0ms

series473.0ms

simplify44.0ms

prune205.0ms

localize17.0ms

rewrite23.0ms

series986.0ms

simplify47.0ms

prune290.0ms

localize24.0ms

rewrite48.0ms

series1.5s

simplify55.0ms

prune594.0ms

localize19.0ms

rewrite101.0ms

series211.0ms

simplify49.0ms

prune520.0ms

regimes160.0ms

bsearch219.0ms

simplify2.0ms

end0.0ms

sample7.3s

Profiling