Details

sample16.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	6
1	20	6
2	22	6
3	22	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.0b	(+ (* x x) (* y y))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`add-sqr-sqrt`
4×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sum-log`
3×	`add-exp-log` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`+-commutative` `sqrt-div`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

3 → 39

Calls

3 calls:

11.0ms	(+ (+ (* x x) (* y y)) (* z z))
2.0ms	(+ (* x x) (* y y))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (+ (* x x) (* y y)) (* z z))
29.0ms	(+ (* x x) (* y y))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify88.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	209	340
1	959	320
2	3316	316
3	5001	315

prune126.0ms

Filtered

48 candidates to 37 candidates (77.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.5b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
18×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

2.0ms	(+ (* x x) (* y y))
68.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x x) (* y y))
99.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
100.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	294	1310
1	1288	1219
2	5002	1188

prune262.0ms

Filtered

136 candidates to 71 candidates (52.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 19.4b

localize23.0ms

Local error

Found 4 expressions with local error:

36.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
38.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
38.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
38.2b	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

13.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
7.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
7.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
7.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
108.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
107.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))
109.0ms	(cbrt (+ (+ (* x x) (* y y)) (* z z)))

simplify69.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	154	667
1	541	623
2	2150	602
3	5002	601

prune314.0ms

Filtered

66 candidates to 60 candidates (90.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 19.4b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 19.4b

regimes365.0ms

Accuracy

63.2% (7.2b remaining)

Error of 25.4b against oracle of 18.3b and baseline of 37.7b

bsearch60.0ms

Steps

Iters	Range		Point
6	2.508969909788503e+84	1.0523857078141318e+85	7.080985686669876e+84
11	-9.916277796985818e+165	-4.657848749767963e+130	-7.973789795621918e+148

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	7
1	21	7

end0.0ms

sample382.0ms

Algorithm

intervals

Results

229.0ms

8000×

body

valid