Details

sample18.0ms

Algorithm

intervals

Results

10.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 37.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
34.9b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite14.0ms

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:

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

series160.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (* x x) (* y y))
35.0ms	(+ (+ (* x x) (* y y)) (* z z))
99.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify83.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 3 (79.0ms)

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

prune95.0ms

Filtered

48 candidates to 37 candidates (77.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 18.3b

Counts

49 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

30.4b	(cbrt (+ (* x x) (* y y)))
30.4b	(cbrt (+ (* x x) (* y y)))
30.4b	(cbrt (+ (* x x) (* y y)))
34.9b	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

rewrite29.0ms

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:

3.0ms	(cbrt (+ (* x x) (* y y)))
4.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
17.0ms	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ (* x x) (* y y)))
90.0ms	(cbrt (+ (* x x) (* y y)))
91.0ms	(cbrt (+ (* x x) (* y y)))
102.0ms	(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

simplify67.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	201	739
1	622	690
2	2121	690
3	5003	689

prune177.0ms

Filtered

66 candidates to 57 candidates (86.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	65	6	71

Merged error: 18.3b

Counts

71 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

30.4b	(cbrt (+ (* x x) (* y y)))
30.4b	(cbrt (+ (* x x) (* y y)))
36.1b	(cbrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))
36.1b	(cbrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ (* x x) (* y y)))
3.0ms	(cbrt (+ (* x x) (* y y)))
17.0ms	(cbrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))
18.0ms	(cbrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ (* x x) (* y y)))
90.0ms	(cbrt (+ (* x x) (* y y)))
105.0ms	(cbrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))
109.0ms	(cbrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

simplify86.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	226	1100
1	801	1008
2	2856	972
3	5001	972

prune289.0ms

Filtered

64 candidates to 62 candidates (96.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	64	6	70

Merged error: 18.3b

Counts

70 → 6

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

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)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	3	3
Total	6	6

Merged error: 18.3b

Counts

6 → 6

regimes321.0ms

Accuracy

64% (6.9b remaining)

Error of 25.2b against oracle of 18.3b and baseline of 37.6b

bsearch53.0ms

Steps

Iters	Range		Point
10	1.0552035162483894e+111	5.722192015150889e+120	4.1598843652442944e+111
5	-3.222127529430611e+149	-1.364030571909353e+149	-1.7013657575679381e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	7
1	21	7

end0.0ms

sample481.0ms

Algorithm

intervals

Results

317.0ms

8000×

body

valid

Details

sample18.0ms

simplify6.0ms

prune2.0ms

localize8.0ms

rewrite14.0ms

series160.0ms

simplify83.0ms

prune95.0ms

localize12.0ms

rewrite29.0ms

series373.0ms

simplify67.0ms

prune177.0ms

localize17.0ms

rewrite43.0ms

series394.0ms

simplify86.0ms

prune289.0ms

localize1.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes321.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample481.0ms

Profiling