Details

sample104.0ms

Algorithm

intervals

Results

28.0ms	109×	body	320	valid
25.0ms	142×	body	160	valid
22.0ms	253×	body	80	nan
0.0ms	5×	body	80	valid

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	19	37
1	43	37
2	119	36
3	283	36
4	528	36
5	771	36
6	934	36
7	1133	36
8	2417	36
done	5000	36

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 37.5b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
8.4b	(cbrt (* (- (sqrt (- (* g g) (* h h))) g) (/ 1.0 (* 2.0 a))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-div`
8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `flip--`
4×	`add-exp-log` `frac-times` `sqrt-div` `add-cbrt-cube` `add-log-exp`
3×	`associate-r/` `associate-l/`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

16.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
12.0ms	(cbrt (* (- (sqrt (- (* g g) (* h h))) g) (/ 1.0 (* 2.0 a))))
4.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
57.0ms	(cbrt (* (- (sqrt (- (* g g) (* h h))) g) (/ 1.0 (* 2.0 a))))
8.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

simplify619.0ms

Counts

72 → 72

Iterations

Useful iterations: done (617.0ms)

Iter	Nodes	Cost
0	205	1451
1	455	1269
2	1508	1168
done	5000	1149

prune281.0ms

Filtered

66 candidates to 72 candidates (-9.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	55	17	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	17	73

Merged error: 32.6b

Counts

73 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
13.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
5.0ms	(sqrt (- (* g g) (* h h)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
74.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	136	1115
1	297	991
2	1028	887
3	4849	865
done	5000	865

prune247.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	70	18	88

Merged error: 32.5b

Counts

88 → 18

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*l/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
13.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
5.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
73.0ms	(cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))
7.0ms	(sqrt (- (* g g) (* h h)))
8.0ms	(sqrt (- (* g g) (* h h)))

simplify2.2s

Counts

71 → 71

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	136	1115
1	297	991
2	1028	887
3	4849	865
done	5000	865

prune239.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	0	17	17
Picked	1	0	1
Done	0	0	0
Total	71	18	89

Merged error: 32.5b

Counts

89 → 18

localize21.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (* g g) (* h h))
8.4b	(cbrt (* (- (sqrt (- (* g g) (* h h))) g) (/ 1.0 (* 2.0 a))))
31.0b	(sqrt (- (* g g) (* h h)))
31.0b	(sqrt (- (* g g) (* h h)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `sqrt-prod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`cbrt-div` `flip3--` `flip--`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/`
1×	`cbrt-prod` `sub-neg` `pow1/3` `diff-log` `associate-*r/`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (* g g) (* h h))
12.0ms	(cbrt (* (- (sqrt (- (* g g) (* h h))) g) (/ 1.0 (* 2.0 a))))
5.0ms	(sqrt (- (* g g) (* h h)))
4.0ms	(sqrt (- (* g g) (* h h)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(- (* g g) (* h h))
58.0ms	(cbrt (* (- (sqrt (- (* g g) (* h h))) g) (/ 1.0 (* 2.0 a))))
8.0ms	(sqrt (- (* g g) (* h h)))
7.0ms	(sqrt (- (* g g) (* h h)))

simplify1.5s

Counts

71 → 71

Iterations

Useful iterations: 3 (576.0ms)

Iter	Nodes	Cost
0	163	1146
1	352	1008
2	1081	917
3	4242	900
done	5000	900

prune155.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	15	17
Picked	1	0	1
Done	0	0	0
Total	72	17	89

Merged error: 32.5b

Counts

89 → 17

regimes775.0ms

Accuracy

67.3% (1.1b remaining)

Error of 31.7b against oracle of 30.7b and baseline of 34.0b

bsearch51.0ms

Steps

Iters	Range		Point
4	-6.728240533841265e-160	-3.494541859308342e-160	-3.5793765345256297e-160

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	38	77
1	46	75
done	46	75

end0.0ms

sample3.1s

Algorithm

intervals

Results

981.0ms	3679×	body	320	valid
745.0ms	4191×	body	160	valid
698.0ms	7817×	body	80	nan
11.0ms	130×	body	80	valid

Details

sample104.0ms

simplify5.5s

prune10.0ms

localize19.0ms

rewrite39.0ms

series148.0ms

simplify619.0ms

prune281.0ms

localize21.0ms

rewrite31.0ms

series95.0ms

simplify2.2s

prune247.0ms

localize20.0ms

rewrite27.0ms

series94.0ms

simplify2.2s

prune239.0ms

localize21.0ms

rewrite27.0ms

series79.0ms

simplify1.5s

prune155.0ms

regimes775.0ms

bsearch51.0ms

simplify4.0ms

end0.0ms

sample3.1s

Profiling