Details

sample21.0ms

Algorithm

intervals

Results

5.0ms	273×	body	80	valid
4.0ms	242×	body	80	nan

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	13	4
1	25	3
2	44	3
3	69	3
4	102	3
5	171	3
6	192	3
7	225	3
8	316	3
9	351	3
10	351	3

prune4.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (- 1.0 x) (* y (sqrt x)))
0.2b	(* y (sqrt x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`prod-diff`
7×	`add-log-exp`
6×	`associate-r`
5×	`fma-def` `associate-l`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `distribute-lft-out`
3×	`distribute-lft-out--`
2×	`expm1-log1p-u` `sum-log` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

2 → 59

Calls

2 calls:

16.0ms	(+ (- 1.0 x) (* y (sqrt x)))
5.0ms	(* y (sqrt x))

series77.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (- 1.0 x) (* y (sqrt x)))
41.0ms	(* y (sqrt x))

simplify47.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	355
1	1115	264
2	5002	256

prune143.0ms

Filtered

65 candidates to 48 candidates (73.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Merged error: 0.0b

Counts

66 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

74×	`sqrt-prod`
69×	`add-sqr-sqrt`
27×	`associate-r` `unswap-sqr`
26×	`associate-l`
20×	`add-cube-cbrt` `*-un-lft-identity`
15×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`

Counts

4 → 127

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
19.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (sqrt x))
138.0ms	(sqrt (sqrt x))
81.0ms	(* y (sqrt (sqrt x)))
41.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	377	853
1	1559	698
2	5002	662

prune265.0ms

Filtered

139 candidates to 82 candidates (59.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Merged error: 0b

Counts

145 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
8×	`add-cbrt-cube`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 84

Calls

4 calls:

9.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series739.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* (cbrt x) (cbrt x))
185.0ms	(cbrt x)
180.0ms	(cbrt x)
180.0ms	(cbrt x)

simplify91.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	128	331
1	526	287
2	3275	261
3	5001	258

prune363.0ms

Filtered

96 candidates to 72 candidates (75.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	96	7	103

Merged error: 0b

Counts

103 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt (sqrt x))))
0.3b	(* (* (* y (sqrt (sqrt (sqrt x)))) (sqrt (sqrt (sqrt x)))) (sqrt (sqrt x)))
0.3b	(* (* y (sqrt (sqrt (sqrt x)))) (sqrt (sqrt (sqrt x))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

460×	`sqrt-prod`
407×	`add-sqr-sqrt`
255×	`unswap-sqr`
118×	`associate-l`
69×	`associate-r`
35×	`add-cube-cbrt` `*-un-lft-identity`
22×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`*-commutative`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow1/2`

Counts

4 → 277

Calls

4 calls:

2.0ms	(sqrt (sqrt x))
8.0ms	(* y (sqrt (sqrt (sqrt x))))
38.0ms	(* (* (* y (sqrt (sqrt (sqrt x)))) (sqrt (sqrt (sqrt x)))) (sqrt (sqrt x)))
19.0ms	(* (* y (sqrt (sqrt (sqrt x)))) (sqrt (sqrt (sqrt x))))

series379.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (sqrt x))
89.0ms	(* y (sqrt (sqrt (sqrt x))))
46.0ms	(* (* (* y (sqrt (sqrt (sqrt x)))) (sqrt (sqrt (sqrt x)))) (sqrt (sqrt x)))
83.0ms	(* (* y (sqrt (sqrt (sqrt x)))) (sqrt (sqrt (sqrt x))))

simplify133.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	582	3957
1	2669	2353
2	5002	2275

prune460.0ms

Filtered

289 candidates to 119 candidates (41.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	289	7	296

Merged error: 0b

Counts

296 → 7

regimes88.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample594.0ms

Algorithm

intervals

Results

179.0ms	8506×	body	80	valid
155.0ms	8646×	body	80	nan
0.0ms	2×	body	1280	valid
0.0ms	1×	body	640	valid