Details

sample67.0ms

Algorithm

intervals

Results

26.0ms	56×	body	10240	exit
14.0ms	254×	body	80	valid
11.0ms	292×	body	80	nan
1.0ms	2×	body	320	valid

simplify53.0ms

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: 0.5b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.5b	(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)))
2.0ms	(sqrt (atan2 b b))

series92.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
62.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify77.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (70.0ms)

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

prune138.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.4b

Counts

73 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.5b	(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))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`pow1` `unpow-prod-down` `prod-diff`
6×	`sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

7.0ms	(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))

series137.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
89.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify119.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	308	751
1	889	651
2	4114	639
3	5002	636

prune228.0ms

Filtered

95 candidates to 60 candidates (63.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 0.4b

Counts

98 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.5b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

4.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
7.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
81.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify107.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	337	829
1	838	695
2	3652	687
3	5002	661

prune252.0ms

Filtered

89 candidates to 57 candidates (64.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Merged error: 0.4b

Counts

94 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (cbrt (pow (log (pow (sqrt (sqrt (atan2 b b))) (- b a))) 3)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.5b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

3.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (cbrt (pow (log (pow (sqrt (sqrt (atan2 b b))) (- b a))) 3)))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
6.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (cbrt (pow (log (pow (sqrt (sqrt (atan2 b b))) (- b a))) 3)))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
82.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify106.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	343	840
1	850	715
2	3680	707
3	5002	681

prune267.0ms

Filtered

89 candidates to 57 candidates (64.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	89	6	95

Merged error: 0.4b

Counts

95 → 6

regimes68.0ms

Accuracy

0% (0.0b 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	15	16
1	15	16

end0.0ms

sample2.0s

Algorithm

intervals

Results

840.0ms	1874×	body	10240	exit
459.0ms	7983×	body	80	valid
362.0ms	9665×	body	80	nan
18.0ms	6×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	2560	valid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	160	valid