Details

sample389.0ms

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

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	321	5
5	1627	5
6	5001	5

prune4.0ms

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))

rewrite19.0ms

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)))
4.0ms	(sqrt (atan2 b b))

series106.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
69.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms	(sqrt (atan2 b b))

simplify78.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (71.0ms)

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

prune136.0ms

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))

rewrite43.0ms

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:

27.0ms	(* (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))
2.0ms	(sqrt (atan2 b b))

series145.0ms

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))))
9.0ms	(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

localize13.0ms

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))

rewrite33.0ms

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:

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

series195.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
61.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
83.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
13.0ms	(sqrt (atan2 b b))

simplify53.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (36.0ms)

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

prune264.0ms

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 (sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))) 3)
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))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`unpow-prod-down`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`prod-diff`
7×	`add-exp-log`
6×	`pow1` `pow-unpow`
5×	`pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `cube-prod` `sqr-pow`
2×	`pow-pow`
1×	`cube-mult` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3` `rem-cube-cbrt`

Counts

4 → 91

Calls

4 calls:

12.0ms	(pow (sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))) 3)
8.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
11.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
2.0ms	(sqrt (atan2 b b))

series289.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(pow (sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))) 3)
60.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
87.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
10.0ms	(sqrt (atan2 b b))

simplify57.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	508	1085
1	1805	954
2	5002	939

prune261.0ms

Filtered

103 candidates to 61 candidates (59.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Merged error: 0.2b

Counts

108 → 5

regimes119.0ms

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	16	12

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	1831×	body	5120	exit
639.0ms	7989×	body	80	valid
583.0ms	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