Details

sample312.0ms

Algorithm

intervals

Results

22.0ms	38×	body	10240	exit
14.0ms	255×	body	80	valid
14.0ms	263×	body	80	nan
0.0ms	1×	body	160	valid

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: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(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:

18.0ms	(pow (sqrt (atan2 b b)) (- b a))
72.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
16.0ms	(sqrt (atan2 b b))

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1346	292
3	5001	290

prune130.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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))
0.2b	(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))

series98.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
56.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
13.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify71.0ms

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

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a)))
0.2b	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
5×	`add-exp-log`
4×	`pow1` `unpow-prod-up` `pow-exp`
3×	`add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `distribute-lft-in` `sqr-pow`
1×	`rem-sqrt-square` `pow-unpow` `pow-pow` `sqrt-pow1` `pow1/2` `sqrt-pow2` `unpow1/2`

Counts

3 → 49

Calls

3 calls:

4.0ms	(pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a)))
10.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
1.0ms	(sqrt (atan2 b b))

series127.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a)))
77.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
13.0ms	(sqrt (atan2 b b))

simplify100.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	233	473
1	586	410
2	3133	393
3	5001	375

prune132.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (pow (* (sqrt (atan2 b b)) (sqrt (atan2 b b))) (* 1/2 (- b a))))
1.0b	(* (sqrt (atan2 b b)) (sqrt (atan2 b b)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

5.0ms	(sin (pow (* (sqrt (atan2 b b)) (sqrt (atan2 b b))) (* 1/2 (- b a))))
6.0ms	(* (sqrt (atan2 b b)) (sqrt (atan2 b b)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series82.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (pow (* (sqrt (atan2 b b)) (sqrt (atan2 b b))) (* 1/2 (- b a))))
1.0ms	(* (sqrt (atan2 b b)) (sqrt (atan2 b b)))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify184.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	142	398
1	574	344
2	3930	329
3	5001	321

prune176.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

regimes69.0ms

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	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

711.0ms	1692×	body	10240	exit
451.0ms	9614×	body	80	nan
444.0ms	7993×	body	80	valid
1.0ms	2×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid