Details

sample392.0ms

Algorithm

intervals

Results

70.0ms	66×	body	5120	exit
25.0ms	384×	body	80	nan
21.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	315	5
5	1609	5
6	5001	5

prune17.0ms

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: 0.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series107.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (sqrt (atan2 b b)) (- b a))
70.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms	(sqrt (atan2 b b))

simplify48.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1346	292
3	5001	290

prune117.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 0.2b

Counts

58 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.3b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

16.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
3.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series151.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
90.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify52.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	280	1645
1	1169	1507
2	5001	1483

prune254.0ms

Filtered

148 candidates to 71 candidates (48.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Merged error: 0.2b

Counts

151 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
0.1b	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
0.3b	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
1.0b	(sqrt (atan2 b b))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

48×	`unpow-prod-down`
21×	`sqrt-prod`
19×	`cbrt-prod`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
5×	`pow1`
4×	`unpow-prod-up` `pow-exp` `add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`pow-unpow`
2×	`pow-to-exp` `sub-neg`
1×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 78

Calls

4 calls:

7.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
6.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
7.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
2.0ms	(sqrt (atan2 b b))

series199.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
62.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
89.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
10.0ms	(sqrt (atan2 b b))

simplify191.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	298	904
1	820	821
2	4299	792
3	5001	792

prune218.0ms

Filtered

90 candidates to 54 candidates (60.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	90	5	95

Merged error: 0.2b

Counts

95 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4)
0.3b	(sin (cbrt (* (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4) (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 2))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

24×	`unpow-prod-down`
15×	`sqrt-prod`
13×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`unpow-prod-up` `pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-pow`
1×	`sub-neg` `pow-pow`

Counts

4 → 64

Calls

4 calls:

6.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4)
4.0ms	(sin (cbrt (* (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4) (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 2))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series156.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4)
89.0ms	(sin (cbrt (* (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4) (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 2))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify127.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	260	631
1	786	569
2	3462	553
3	5001	553

prune209.0ms

Filtered

76 candidates to 48 candidates (63.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Merged error: 0.2b

Counts

81 → 5

regimes86.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	1831×	body	5120	exit
635.0ms	7989×	body	80	valid
579.0ms	9930×	body	80	nan
3.0ms	1×	body	5120	valid
2.0ms	3×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid