Details

sample135.0ms

Algorithm

intervals

Results

31.0ms	195×	body	80	valid
29.0ms	256×	pre	80	true
24.0ms	23×	body	2560	valid
12.0ms	15×	body	1280	valid
7.0ms	10×	body	640	valid
6.0ms	4×	body	5120	valid
3.0ms	7×	body	320	valid
1.0ms	2×	body	160	valid

simplify7.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
59	2004
58	1998
57	1980
56	1947
55	1929
54	1896
53	1878
52	1845
51	1827
50	1794
49	1776
48	1743
47	1725
46	1692
45	1674
44	1641
43	1623
42	1590
41	1572
40	1539
39	1521
38	1488
37	1470
36	1437
35	1419
34	1386
33	1368
32	1335
31	1317
30	1284
29	1266
28	1233
27	1215
26	1182
25	1164
24	1131
23	1113
22	1080
21	1062
20	1029
19	1011
18	978
17	960
16	927
15	909
14	876
13	858
12	825
11	786
10	745
9	598
8	441
7	301
6	200
5	145
4	104
3	76
2	51
1	29
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
0.0b	(+ (* x x) (* p (* 4 p)))
0.6b	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `associate-/r/` `flip-+` `insert-posit16`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft1-in` `sqrt-pow1` `distribute-rgt-out` `pow1/2` `distribute-lft-out`

Counts

4 → 62

Calls

4 calls:

37.0ms	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
20.0ms	(+ (* x x) (* p (* 4 p)))
44.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
61.0ms	(+ (* x x) (* p (* 4 p)))
101.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
57.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify1.0s

Counts

74 → 74

Iterations

Iter	Nodes
done	2036
3	2036
2	721
1	236
0	100

prune370.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* p (* 4 p)))
0.6b	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
0.6b	(log (exp (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)))
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite464.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`log-pow` `add-cube-cbrt`
6×	`pow1` `exp-prod`
4×	`log-prod` `add-cbrt-cube` `add-exp-log` `associate-/r/` `insert-posit16`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`+-commutative` `sum-log` `distribute-lft1-in` `distribute-rgt-out` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `exp-sum`

Counts

4 → 63

Calls

4 calls:

9.0ms	(+ (* x x) (* p (* 4 p)))
342.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
106.0ms	(log (exp (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)))
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series266.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (* x x) (* p (* 4 p)))
86.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
88.0ms	(log (exp (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)))
49.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify898.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	2000
3	2000
2	755
1	258
0	109

prune430.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`+-commutative` `sum-log` `distribute-lft1-in` `distribute-rgt-out` `distribute-lft-out`

Counts

4 → 63

Calls

4 calls:

30.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
9.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series209.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
43.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
46.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
44.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify947.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	2000
4	2000
3	1506
2	479
1	172
0	71

prune422.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
7.7b	(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))
15.3b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
50×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`*-un-lft-identity`
18×	`pow1/2` `add-cube-cbrt`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16`
2×	`rem-sqrt-square` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `+-commutative` `sum-log` `rem-square-sqrt` `distribute-lft1-in` `pow-plus` `distribute-rgt-out` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`

Counts

4 → 131

Calls

4 calls:

35.0ms	(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
18.0ms	(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
10.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
73.0ms	(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
48.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
43.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify829.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	2011
3	2011
2	772
1	323
0	146

prune422.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.2b

regimes142.0ms

Accuracy

0% (0.2b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

894.0ms	6083×	body	80	valid
484.0ms	751×	body	2560	valid
285.0ms	580×	body	1280	valid
254.0ms	8000×	pre	80	true
122.0ms	309×	body	640	valid
56.0ms	150×	body	320	valid
36.0ms	55×	body	5120	valid
12.0ms	72×	body	160	valid