Details

sample49.0ms

Algorithm

intervals

Results

13.0ms	274×	body	80	valid
11.0ms	260×	body	80	nan

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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)

simplify58.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 4 (55.0ms)

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

prune40.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	10	3	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Merged error: 0.1b

Counts

15 → 5

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:

35.0ms	(+ x (* y (sqrt z)))
38.0ms	(* y (sqrt z))

simplify119.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (115.0ms)

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

prune104.0ms

Filtered

46 candidates to 35 candidates (76.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	38	8	46
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	42	9	51

Merged error: 0.0b

Counts

51 → 9

localize13.0ms

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)))

rewrite22.0ms

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)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (sqrt z))
133.0ms	(sqrt (sqrt z))
78.0ms	(* y (sqrt (sqrt z)))
38.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

simplify45.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

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

prune226.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	109	8	117

Merged error: 0b

Counts

117 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (* y (sqrt (sqrt z))) (pow z 1/4)))
0.1b	(sqrt (sqrt z))
0.3b	(* y (sqrt (sqrt z)))
0.3b	(* (* y (sqrt (sqrt z))) (pow z 1/4))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`sqrt-prod`
21×	`add-sqr-sqrt`
19×	`add-exp-log`
16×	`associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-cbrt-cube`
10×	`prod-exp`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `cbrt-unprod` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-def` `unswap-sqr`
2×	`pow-to-exp` `rem-sqrt-square` `pow1/2` `pow-exp` `*-commutative`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `flip-+` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

3.0ms	(+ x (* (* y (sqrt (sqrt z))) (pow z 1/4)))
2.0ms	(sqrt (sqrt z))
6.0ms	(* y (sqrt (sqrt z)))
8.0ms	(* (* y (sqrt (sqrt z))) (pow z 1/4))

series341.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ x (* (* y (sqrt (sqrt z))) (pow z 1/4)))
133.0ms	(sqrt (sqrt z))
78.0ms	(* y (sqrt (sqrt z)))
79.0ms	(* (* y (sqrt (sqrt z))) (pow z 1/4))

simplify65.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	537	644
1	2387	585
2	5001	579

prune226.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Merged error: 0b

Counts

111 → 8

regimes134.0ms

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	10	4
1	10	4

end0.0ms

sample826.0ms

Algorithm

intervals

Results

238.0ms	8492×	body	80	valid
222.0ms	8538×	body	80	nan