Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	274×	body	80	valid
7.0ms	282×	body	80	nan

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	5
1	51	4
2	86	4
3	126	4
4	151	4
5	169	4
6	185	4
7	187	4
8	187	4

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.1b

Counts

2 → 2

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (sqrt z) y x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (sqrt z) y x)

series62.0ms

Counts

1 → 3

Calls

1 calls:

62.0ms

(fma (sqrt z) y x)

simplify59.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 4 (57.0ms)

Iter	Nodes	Cost
0	70	58
1	176	50
2	528	50
3	1813	46
4	5001	43

prune51.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	10	3	13
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	11	4	15

Merged error: 0.0b

Counts

15 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* y (sqrt z)))
0.2b	(* y (sqrt z))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`fma-def` `associate-l`
2×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 40

Calls

2 calls:

3.0ms	(+ x (* y (sqrt z)))
5.0ms	(* y (sqrt z))

series73.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ x (* y (sqrt z)))
39.0ms	(* y (sqrt z))

simplify115.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	231	204
1	879	180
2	4188	173
3	5001	170

prune108.0ms

Filtered

46 candidates to 35 candidates (76.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	40	6	46
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Merged error: 0.0b

Counts

50 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt z))
0.1b	(sqrt (sqrt z))
0.3b	(* y (sqrt (sqrt z)))
0.3b	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

2.0ms	(sqrt (sqrt z))
2.0ms	(sqrt (sqrt z))
6.0ms	(* y (sqrt (sqrt z)))
9.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(sqrt (sqrt z))
133.0ms	(sqrt (sqrt z))
83.0ms	(* y (sqrt (sqrt z)))
44.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	351	549
1	1510	488
2	5001	461

prune239.0ms

Filtered

108 candidates to 67 candidates (62.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	108	7	115

Merged error: 0b

Counts

115 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
33×	`associate-r`
30×	`add-sqr-sqrt`
23×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
19×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`sqrt-pow1`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `pow1/2` `*-commutative`

Counts

4 → 117

Calls

4 calls:

3.0ms	(sqrt (sqrt (sqrt z)))
8.0ms	(* y (sqrt (sqrt (sqrt z))))
12.0ms	(* (* y (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z))))
19.0ms	(* (* (* y (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z)))) (sqrt (sqrt z)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (sqrt (sqrt z)))
89.0ms	(* y (sqrt (sqrt (sqrt z))))
79.0ms	(* (* y (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z))))
39.0ms	(* (* (* y (sqrt (sqrt (sqrt z)))) (sqrt (sqrt (sqrt z)))) (sqrt (sqrt z)))

simplify63.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	484	966
1	2320	799
2	5001	724

prune294.0ms

Filtered

129 candidates to 73 candidates (56.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	3	1	4
Picked	0	1	1
Done	0	2	2
Total	130	6	136

Merged error: 0b

Counts

136 → 6

regimes215.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	13	5

end0.0ms

sample915.0ms

Algorithm

intervals

Results

265.0ms	8568×	body	80	valid
253.0ms	8679×	body	80	nan