Details

sample334.0ms

Algorithm

intervals

Results

26.0ms	52×	body	10240	exit
20.0ms	302×	body	80	nan
18.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify58.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite26.0ms

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:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series103.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(pow (sqrt (atan2 b b)) (- b a))
61.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms	(sqrt (atan2 b b))

simplify68.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	255	515
1	727	433
2	2663	425
3	5001	408

prune150.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (/ (- b a) 2))
0.2b	(sin (pow (atan2 b b) (/ (- b a) 2)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow-unpow`
18×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `unpow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 45

Calls

2 calls:

4.0ms	(pow (atan2 b b) (/ (- b a) 2))
3.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

series81.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(pow (atan2 b b) (/ (- b a) 2))
61.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

simplify75.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	238	341
1	772	323
2	3169	307
3	5001	304

prune131.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- b a)) (cbrt (- b a)))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

20.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))

series565.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
143.0ms	(cbrt (- b a))
147.0ms	(cbrt (- b a))
149.0ms	(cbrt (- b a))

simplify159.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (150.0ms)

Iter	Nodes	Cost
0	270	790
1	950	753
2	4633	700
3	5001	694

prune407.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
3.0b	(expm1 (log1p (cbrt (- b a))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 62

Calls

4 calls:

2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))
2.0ms	(cbrt (- b a))
0.0ms	(expm1 (log1p (cbrt (- b a))))

series624.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (- b a))
142.0ms	(cbrt (- b a))
145.0ms	(cbrt (- b a))
193.0ms	(expm1 (log1p (cbrt (- b a))))

simplify111.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 4 (105.0ms)

Iter	Nodes	Cost
0	162	411
1	344	391
2	945	379
3	3167	351
4	5001	341

prune308.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes37.0ms

Accuracy

0% (0.1b 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	17	15
1	17	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

989.0ms	1864×	body	10240	exit
595.0ms	9960×	body	80	nan
560.0ms	7992×	body	80	valid
9.0ms	3×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid