Details

sample130.0ms

Algorithm

intervals

Results

68.0ms	66×	body	5120	exit
22.0ms	384×	body	80	nan
20.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify51.0ms

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	321	5
5	1627	5
6	5001	5

prune3.0ms

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

localize8.0ms

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))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`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 → 63

Calls

3 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
5.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series90.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
61.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2703	425
3	5001	408

prune132.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 0.2b

Counts

73 → 4

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))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 171

Calls

4 calls:

25.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
4.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series144.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
88.0ms	(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))

simplify68.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	451	2193
1	1880	1915
2	5002	1883

prune349.0ms

Filtered

183 candidates to 96 candidates (52.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	182	5	187

Merged error: 0.2b

Counts

187 → 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))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

66×	`unpow-prod-down`
28×	`cbrt-prod` `add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
22×	`unpow-prod-up`
21×	`sqrt-prod`
18×	`prod-diff`
6×	`add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `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 → 104

Calls

4 calls:

8.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
10.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
9.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
2.0ms	(sqrt (atan2 b b))

series193.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
55.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
88.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
10.0ms	(sqrt (atan2 b b))

simplify49.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	458	1372
1	1311	1178
2	5002	1163

prune266.0ms

Filtered

116 candidates to 66 candidates (56.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	3	3
Picked	1	0	1
Done	1	0	1
Total	116	5	121

Merged error: 0.2b

Counts

121 → 5

localize15.0ms

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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

33×	`unpow-prod-down`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-pow`
1×	`sub-neg` `pow-pow`

Counts

4 → 81

Calls

4 calls:

8.0ms	(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))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series158.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 4)
87.0ms	(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))

simplify42.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	405	887
1	1228	769
2	5001	766

prune254.0ms

Filtered

93 candidates to 58 candidates (62.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Merged error: 0.2b

Counts

98 → 5

regimes82.0ms

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

sample3.4s

Algorithm

intervals

Results

1.8s	1831×	body	5120	exit
622.0ms	7989×	body	80	valid
562.0ms	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