Details

sample58.0ms

Algorithm

intervals

Results

31.0ms	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))

rewrite4.0ms

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×	`expm1-log1p-u` `flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

4.0ms

(log (+ 1.0 x))

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(log (+ 1.0 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	131	99
1	363	89
2	1292	86
3	5002	81

prune51.0ms

Filtered

20 candidates to 15 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	15	5	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	16	5	21

Merged error: 0.1b

Counts

21 → 5

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite33.0ms

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` `expm1-log1p-u` `frac-2neg` `pow-prod-down` `*-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 132

Calls

1 calls:

26.0ms

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

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

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

simplify61.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	574	705
1	2550	587
2	5001	586

prune311.0ms

Filtered

135 candidates to 84 candidates (62.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Merged error: 0.1b

Counts

140 → 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)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-def`

Counts

4 → 82

Calls

4 calls:

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

series240.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ 1.0 x))
31.0ms	(sqrt (+ 1.0 x))
85.0ms	(log (sqrt (+ 1.0 x)))
85.0ms	(log (sqrt (+ 1.0 x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	187	508
1	531	462
2	2062	442
3	5002	428

prune206.0ms

Filtered

94 candidates to 70 candidates (74.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	94	5	99

Merged error: 0.1b

Counts

99 → 5

localize10.0ms

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))))

rewrite25.0ms

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×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`rem-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 100

Calls

4 calls:

8.0ms	(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))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (sqrt (+ 1.0 x)))
83.0ms	(log (sqrt (+ 1.0 x)))
128.0ms	(log (sqrt (sqrt (+ 1.0 x))))
123.0ms	(log (sqrt (sqrt (+ 1.0 x))))

simplify147.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	370	784
1	1190	730
2	4805	706
3	5001	706

prune328.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	113	4	117

Merged error: 0.1b

Counts

117 → 4

regimes58.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	23
1	29	23

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.0s	2306×	body	1280	valid
340.0ms	1644×	body	640	valid
93.0ms	848×	body	320	valid
63.0ms	2731×	body	80	valid
36.0ms	2595×	body	80	nan
30.0ms	471×	body	160	valid