Details

analyze462.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

sample21.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 42.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

3.0ms	(+ (* x x) (* y y))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series25.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(+ (* x x) (* y y))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify58.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	173	212
1	707	203
2	1993	203
3	5001	202

prune57.0ms

Filtered

26 candidates to 32 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	6	33

Merged error: 22.6b

Counts

33 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.5b	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`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`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
18.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
19.0ms	(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
18.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	288	1477
1	1262	1381
2	5001	1338

prune102.0ms

Filtered

76 candidates to 146 candidates (-92.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Merged error: 22.6b

Counts

152 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
6.1b	(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

6.0ms	(+ (* x x) (* y y))
8.0ms	(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series53.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
19.0ms	(exp (log (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
29.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify61.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	220	425
1	776	411
2	2094	396
3	5001	388

prune83.0ms

Filtered

39 candidates to 57 candidates (-46.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	54	9	63

Merged error: 22.6b

Counts

63 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

6.3b	(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
39.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
5.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (exp (* (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))) (cbrt (log (sqrt (+ (+ (* x x) (* y y)) (* z z))))))
19.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
21.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))
20.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify62.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	198	1225
1	574	1128
2	2010	1113
3	5002	1109

prune100.0ms

Filtered

61 candidates to 82 candidates (-34.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	82	9	91

Merged error: 22.6b

Counts

91 → 9

regimes888.0ms

Accuracy

63.4% (7.0b remaining)

Error of 25.5b against oracle of 18.4b and baseline of 37.7b

bsearch445.0ms

Steps

Iters	Range		Point
7	6.349027110634636e+112	1.6109970442087614e+115	1.5188168019060442e+115
10	-1.0777439710251489e+102	-1.0773346131038458e+84	-1.0613899974916552e+102

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	7
1	21	7

end0.0ms

analyze530.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12
66.9%	33%	0.1%	13
71.7%	28.2%	0.1%	14

sample679.0ms

Algorithm

intervals

Results

456.0ms

8000×

body

valid

Details

analyze462.0ms

sample21.0ms

simplify6.0ms

prune3.0ms

localize7.0ms

rewrite9.0ms

series25.0ms

simplify58.0ms

prune57.0ms

localize10.0ms

rewrite39.0ms

series91.0ms

simplify53.0ms

prune102.0ms

localize12.0ms

rewrite21.0ms

series53.0ms

simplify61.0ms

prune83.0ms

localize23.0ms

rewrite21.0ms

series170.0ms

simplify62.0ms

prune100.0ms

regimes888.0ms

bsearch445.0ms

simplify1.0ms

end0.0ms

analyze530.0ms

sample679.0ms

Profiling