Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	274×	body	80	valid
6.0ms	238×	body	80	nan

simplify21.0ms

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

prune7.0ms

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)

rewrite2.0ms

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)

series66.0ms

Counts

1 → 3

Calls

1 calls:

65.0ms

(fma (sqrt z) y x)

simplify65.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 4 (62.0ms)

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

prune45.0ms

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

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

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))

series74.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+ x (* y (sqrt z)))
40.0ms	(* y (sqrt z))

simplify121.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (117.0ms)

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

prune116.0ms

Filtered

46 candidates to 35 candidates (76.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	45	6	51

Merged error: 0.0b

Counts

51 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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:

4.0ms	(sqrt (sqrt z))
3.0ms	(sqrt (sqrt z))
11.0ms	(* y (sqrt (sqrt z)))
21.0ms	(* (* y (sqrt (sqrt z))) (sqrt (sqrt z)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (sqrt z))
134.0ms	(sqrt (sqrt z))
77.0ms	(* y (sqrt (sqrt z)))
43.0ms	(* (* 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

prune239.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	107	7	114

Merged error: 0.0b

Counts

114 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (* y (pow z 1/4)) (sqrt (sqrt z))))
0.1b	(sqrt (sqrt z))
0.2b	(* y (pow z 1/4))
0.3b	(* (* y (pow z 1/4)) (sqrt (sqrt z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`add-exp-log` `sqrt-prod`
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` `unpow-prod-down` `sqrt-pow1` `associate-l` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `unswap-sqr`
2×	`pow-to-exp` `rem-sqrt-square` `pow1/2` `pow-exp` `*-commutative` `sqr-pow`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `flip-+`

Counts

4 → 91

Calls

4 calls:

3.0ms	(+ x (* (* y (pow z 1/4)) (sqrt (sqrt z))))
2.0ms	(sqrt (sqrt z))
5.0ms	(* y (pow z 1/4))
8.0ms	(* (* y (pow z 1/4)) (sqrt (sqrt z)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(+ x (* (* y (pow z 1/4)) (sqrt (sqrt z))))
133.0ms	(sqrt (sqrt z))
56.0ms	(* y (pow z 1/4))
80.0ms	(* (* y (pow z 1/4)) (sqrt (sqrt z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	498	604
1	2233	543
2	5001	537

prune241.0ms

Filtered

103 candidates to 73 candidates (70.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	104	6	110

Merged error: 0.0b

Counts

110 → 6

regimes111.0ms

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	10	4
1	10	4

end0.0ms

sample787.0ms

Algorithm

intervals

Results

242.0ms	8543×	body	80	valid
216.0ms	8276×	body	80	nan