Details

sample59.0ms

Algorithm

intervals

Results

33.0ms	69×	body	1280	valid
13.0ms	58×	body	640	valid
3.0ms	27×	body	320	valid
2.0ms	91×	body	80	valid
1.0ms	66×	body	80	nan
1.0ms	11×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	2
1	5	2

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 38.5b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

3.3b	(log (+ 1.0 x))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

1 → 15

Calls

1 calls:

3.0ms

(log (+ 1.0 x))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(log (+ 1.0 x))

simplify43.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	122	95
1	327	86
2	1161	81
3	5002	78

prune42.0ms

Filtered

18 candidates to 13 candidates (72.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	13	5	18
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	5	19

Merged error: 0.1b

Counts

19 → 5

localize10.0ms

Local error

Found 1 expressions with local error:

0.2b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
73×	`add-sqr-sqrt`
68×	`associate-r`
62×	`unpow-prod-down`
40×	`*-un-lft-identity`
39×	`add-cube-cbrt`
26×	`unpow2` `sqr-pow`
24×	`add-exp-log`
19×	`associate-*r/`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp` `associate-/l*`
8×	`associate-/r*`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`clear-num` `un-div-inv` `cbrt-unprod`
1×	`cbrt-undiv` `frac-2neg` `pow-prod-down` `*-commutative` `div-inv` `add-log-exp`

Counts

1 → 130

Calls

1 calls:

27.0ms

(* 1/2 (/ (pow x 2) (pow 1.0 2)))

series53.0ms

Counts

1 → 3

Calls

1 calls:

53.0ms

(* 1/2 (/ (pow x 2) (pow 1.0 2)))

simplify66.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	570	695
1	2544	577
2	5001	576

prune278.0ms

Filtered

133 candidates to 82 candidates (61.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Merged error: 0.1b

Counts

138 → 5

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.0b	(sqrt (+ 1.0 x))
3.3b	(log (sqrt (+ 1.0 x)))
3.3b	(log (sqrt (+ 1.0 x)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
4.0ms	(log (sqrt (+ 1.0 x)))
4.0ms	(log (sqrt (+ 1.0 x)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ 1.0 x))
32.0ms	(sqrt (+ 1.0 x))
78.0ms	(log (sqrt (+ 1.0 x)))
79.0ms	(log (sqrt (+ 1.0 x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	176	480
1	494	436
2	1896	418
3	5001	406

prune177.0ms

Filtered

84 candidates to 60 candidates (71.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	84	5	89

Merged error: 0.1b

Counts

89 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ 1.0 x)))
3.3b	(log (sqrt (+ 1.0 x)))
3.3b	(log (sqrt (sqrt (+ 1.0 x))))
3.3b	(log (sqrt (sqrt (+ 1.0 x))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

38×	`sqrt-prod`
27×	`log-prod`
22×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
14×	`pow1` `add-cube-cbrt` `sqrt-div`
13×	`sqrt-pow1` `log-pow`
7×	`add-exp-log` `pow1/2`
6×	`log-div`
4×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`rem-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 92

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ 1.0 x)))
4.0ms	(log (sqrt (+ 1.0 x)))
5.0ms	(log (sqrt (sqrt (+ 1.0 x))))
5.0ms	(log (sqrt (sqrt (+ 1.0 x))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(sqrt (sqrt (+ 1.0 x)))
79.0ms	(log (sqrt (+ 1.0 x)))
118.0ms	(log (sqrt (sqrt (+ 1.0 x))))
125.0ms	(log (sqrt (sqrt (+ 1.0 x))))

simplify151.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	350	755
1	1097	708
2	4395	676
3	5001	651

prune257.0ms

Filtered

104 candidates to 73 candidates (70.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	105	4	109

Merged error: 0.1b

Counts

109 → 4

regimes57.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	2306×	body	1280	valid
346.0ms	1644×	body	640	valid
91.0ms	848×	body	320	valid
63.0ms	2731×	body	80	valid
36.0ms	2595×	body	80	nan
30.0ms	471×	body	160	valid