Details

sample295.0ms

Algorithm

intervals

Results

17.0ms	331×	body	80	nan
14.0ms	256×	body	80	valid
2.0ms	53×	body	80	overflowed

simplify55.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

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:

3.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(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)))
16.0ms	(sqrt (atan2 b b))

simplify39.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	148	325
1	425	298
2	1346	292
3	5001	290

prune126.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
0.0b	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
16×	`pow-exp`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-exp`
7×	`pow1` `pow-to-exp` `add-cube-cbrt`
6×	`sqrt-prod`
5×	`pow-unpow` `pow-pow`
4×	`add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow1/2`
1×	`pow2` `sub-neg` `unpow-prod-down` `sqrt-unprod` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

7.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
5.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series99.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
59.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify70.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	167	525
1	444	445
2	2052	428
3	5001	426

prune173.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (* (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)) (pow (pow (sqrt (atan2 b b)) 1/2) (- b a))))
0.0b	(* (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)) (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

144×	`unpow-prod-down`
76×	`add-sqr-sqrt`
40×	`pow-exp`
36×	`unswap-sqr`
34×	`add-exp-log`
32×	`sqrt-prod` `sqr-pow`
25×	`prod-exp`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`pow-to-exp` `swap-sqr`
16×	`associate-r` `associate-l`
12×	`unpow-prod-up`
6×	`pow1` `sub-neg` `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 → 162

Calls

4 calls:

10.0ms	(sin (* (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)) (pow (pow (sqrt (atan2 b b)) 1/2) (- b a))))
39.0ms	(* (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)) (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series153.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(sin (* (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)) (pow (pow (sqrt (atan2 b b)) 1/2) (- b a))))
40.0ms	(* (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)) (pow (pow (sqrt (atan2 b b)) 1/2) (- b a)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify65.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	359	1970
1	1391	1835
2	5002	1770

prune324.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes32.0ms

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	10	10

end0.0ms

sample1.4s

Algorithm

intervals

Results

455.0ms	9890×	body	80	nan
444.0ms	7993×	body	80	valid
78.0ms	1801×	body	80	overflowed
61.0ms	24×	body	10240	exit
6.0ms	2×	body	5120	valid
2.0ms	3×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid