Details

sample72.0ms

Algorithm

intervals

Results

21.0ms	118×	body	320	valid
16.0ms	133×	body	160	valid
13.0ms	229×	body	80	nan
0.0ms	5×	body	80	valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	21
1	122	21
2	299	21
3	591	21
4	931	21
5	1162	21
6	1388	21
7	2798	21
8	5002	21

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.3b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-sqr-sqrt`
124×	`associate-l`
112×	`cbrt-div`
110×	`*-un-lft-identity`
108×	`cbrt-prod`
78×	`add-cube-cbrt`
76×	`times-frac`
72×	`frac-times` `associate-/r*`
67×	`sqrt-prod`
52×	`difference-of-squares`
48×	`associate-r`
40×	`unswap-sqr`
36×	`associate-*l/`
34×	`*-commutative`
24×	`swap-sqr`
21×	`flip3--` `flip--`
19×	`flip3-+` `flip-+`
18×	`associate-/l*`
12×	`distribute-lft-out--`
6×	`pow1` `frac-2neg` `clear-num`
4×	`add-exp-log` `sqrt-div` `associate-*r/` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv` `distribute-lft-out`

Counts

4 → 326

Calls

4 calls:

59.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
19.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series812.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
359.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
53.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify107.0ms

Algorithm

egg-herbie

Counts

338 → 338

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2001	5376
1	5001	5334

prune1.2s

Filtered

338 candidates to 233 candidates (31.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	314	24	338
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	315	24	339

Merged error: 30.5b

Counts

339 → 24

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
8.0b	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

215×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
75×	`difference-of-squares`
70×	`associate-l`
66×	`sqrt-prod`
56×	`cbrt-div`
53×	`cbrt-prod`
42×	`add-cube-cbrt`
40×	`unswap-sqr`
38×	`times-frac`
37×	`*-commutative`
36×	`frac-times` `swap-sqr` `associate-/r*`
23×	`associate-r`
19×	`flip3-+` `flip-+`
18×	`associate-*l/`
15×	`distribute-lft-out--`
9×	`associate-/l*`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `distribute-lft-out`
1×	`sub-neg` `distribute-rgt-neg-in` `pow1/3` `diff-log` `div-inv`

Counts

4 → 249

Calls

4 calls:

17.0ms	(- (* g g) (* h h))
56.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
22.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* g g) (* h h))
351.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
49.0ms	(sqrt (- (* g g) (* h h)))
56.0ms	(sqrt (- (* g g) (* h h)))

simplify67.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1438	3102
1	5001	3072

prune904.0ms

Filtered

261 candidates to 152 candidates (41.8%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	249	12	261
Fresh	10	13	23
Picked	1	0	1
Done	0	0	0
Total	260	25	285

Merged error: 29.8b

Counts

285 → 25

localize25.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

208×	`add-sqr-sqrt`
100×	`difference-of-squares`
66×	`sqrt-prod`
54×	`*-un-lft-identity`
48×	`swap-sqr`
40×	`*-commutative` `unswap-sqr`
20×	`distribute-lft-out--`
16×	`associate-l`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 174

Calls

4 calls:

18.0ms	(- (* g g) (* h h))
17.0ms	(- (* g g) (* h h))
21.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* g g) (* h h))
33.0ms	(- (* g g) (* h h))
55.0ms	(sqrt (- (* g g) (* h h)))
55.0ms	(sqrt (- (* g g) (* h h)))

simplify83.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	180	872
1	567	844
2	2176	844
3	5001	844

prune510.0ms

Filtered

186 candidates to 68 candidates (63.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	182	4	186
Fresh	4	20	24
Picked	1	0	1
Done	0	0	0
Total	187	24	211

Merged error: 29.8b

Counts

211 → 24

localize19.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* g g) (* h h))
3.8b	(- (* g g) (* h h))
29.0b	(sqrt (- (* g g) (* h h)))
29.0b	(sqrt (- (* g g) (* h h)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

208×	`add-sqr-sqrt`
100×	`difference-of-squares`
66×	`sqrt-prod`
54×	`*-un-lft-identity`
48×	`swap-sqr`
40×	`*-commutative` `unswap-sqr`
20×	`distribute-lft-out--`
16×	`associate-l`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 174

Calls

4 calls:

16.0ms	(- (* g g) (* h h))
20.0ms	(- (* g g) (* h h))
18.0ms	(sqrt (- (* g g) (* h h)))
18.0ms	(sqrt (- (* g g) (* h h)))

series169.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* g g) (* h h))
37.0ms	(- (* g g) (* h h))
47.0ms	(sqrt (- (* g g) (* h h)))
53.0ms	(sqrt (- (* g g) (* h h)))

simplify82.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	180	872
1	567	844
2	2176	844
3	5001	844

prune325.0ms

Filtered

186 candidates to 68 candidates (63.4%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	1	22	23
Picked	1	0	1
Done	0	0	0
Total	186	24	210

Merged error: 29.8b

Counts

210 → 24

regimes939.0ms

Accuracy

0% (1.4b remaining)

Error of 32.2b against oracle of 30.8b and baseline of 32.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	23
1	28	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

620.0ms	3724×	body	320	valid
453.0ms	4130×	body	160	valid
444.0ms	8079×	body	80	nan
8.0ms	146×	body	80	valid