Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	269×	body	80	valid
4.0ms	236×	body	80	nan

simplify20.0ms

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 (0.0%)

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 1 expressions with local error:

0.2b	(* y (sqrt x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`associate-r`
4×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
3×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
2×	`unswap-sqr`
1×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`

Counts

1 → 24

Calls

1 calls:

5.0ms

(* y (sqrt x))

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

(* y (sqrt x))

simplify91.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	153	119
1	621	106
2	3130	100
3	5001	100

prune47.0ms

Filtered

27 candidates to 18 candidates (33.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	21	6	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	7	28

Merged error: 0.0b

Counts

28 → 7

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)))
0.4b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite29.0ms

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)))
15.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series380.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt (sqrt x))
129.0ms	(sqrt (sqrt x))
78.0ms	(* y (sqrt (sqrt x)))
44.0ms	(* (* 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	375	849
1	1547	698
2	5001	662

prune211.0ms

Filtered

139 candidates to 81 candidates (41.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	139	7	146

Merged error: 0b

Counts

146 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 x) -1/4)
0.1b	(sqrt (sqrt x))
0.2b	(* y (pow (/ 1 x) -1/4))
0.4b	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
54×	`unpow-prod-down`
43×	`associate-r` `unswap-sqr`
41×	`add-exp-log` `*-un-lft-identity`
37×	`times-frac` `sqrt-prod`
36×	`add-cube-cbrt` `associate-l`
19×	`prod-exp`
15×	`pow1`
12×	`pow-exp`
11×	`add-cbrt-cube`
8×	`sqr-pow`
6×	`div-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `pow-pow` `1-exp` `*-commutative` `div-inv`
2×	`rem-sqrt-square` `pow1/2`
1×	`pow-flip` `inv-pow`

Counts

4 → 176

Calls

4 calls:

4.0ms	(pow (/ 1 x) -1/4)
2.0ms	(sqrt (sqrt x))
11.0ms	(* y (pow (/ 1 x) -1/4))
23.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(pow (/ 1 x) -1/4)
141.0ms	(sqrt (sqrt x))
67.0ms	(* y (pow (/ 1 x) -1/4))
88.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	663	1289
1	2805	1198
2	5001	1187

prune342.0ms

Filtered

188 candidates to 117 candidates (37.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	189	6	195

Merged error: 0b

Counts

195 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt x) (cbrt x))
0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)

rewrite11.0ms

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:

6.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series703.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cbrt x) (cbrt x))
169.0ms	(cbrt x)
167.0ms	(cbrt x)
169.0ms	(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	3251	261
3	5002	258

prune293.0ms

Filtered

96 candidates to 72 candidates (25.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	96	6	102

Merged error: 0b

Counts

102 → 6

regimes83.0ms

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

sample592.0ms

Algorithm

intervals

Results

178.0ms	8521×	body	80	valid
158.0ms	8318×	body	80	nan
0.0ms	1×	body	320	valid