Details

sample58.0ms

Algorithm

intervals

Results

16.0ms	47×	body	10240	exit
14.0ms	256×	body	80	valid
13.0ms	295×	body	80	nan

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	315	5
5	1609	5
6	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

4.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series34.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sqrt (atan2 b b))

simplify37.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	120	239
1	357	224
2	1225	224
3	5001	222

prune97.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
26.0ms	(* (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))

series86.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
36.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
9.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify55.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	292	1754
1	1319	1646
2	5002	1602

prune343.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series316.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- b a))
150.0ms	(cbrt (- b a))
9.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify111.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 4 (106.0ms)

Iter	Nodes	Cost
0	161	308
1	327	296
2	871	290
3	2911	276
4	5001	272

prune264.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series40.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify115.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	182	348
1	637	321
2	3255	301
3	5002	281

prune113.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes33.0ms

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	14	19
1	14	19

end0.0ms

sample2.1s

Algorithm

intervals

Results

745.0ms	1767×	body	10240	exit
476.0ms	9759×	body	80	nan
462.0ms	7992×	body	80	valid
4.0ms	3×	body	2560	valid
3.0ms	1×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid