Details

sample78.0ms

Algorithm

intervals

Results

21.0ms	35×	body	2560	valid
19.0ms	190×	body	80	valid
9.0ms	256×	pre	80	true
8.0ms	17×	body	1280	valid
4.0ms	8×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	5120	valid
0.0ms	1×	body	320	valid

simplify5.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
54	1972
53	1939
52	1874
51	1851
50	1806
49	1788
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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize47.0ms

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)))
0.9b	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
16.3b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite126.0ms

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:

45.0ms	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
14.0ms	(+ (* x x) (* p (* 4 p)))
52.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
15.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(sqrt (+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5))
38.0ms	(+ (* x x) (* p (* 4 p)))
87.0ms	(+ (/ x (/ (sqrt (+ (* x x) (* p (* 4 p)))) 0.5)) 0.5)
57.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify462.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	2005
2	721
1	236
0	100

prune349.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 13.5b

localize57.0ms

Local error

Found 4 expressions with local error:

16.3b	(sqrt (* (* (cbrt (+ (* x x) (* p (* 4 p)))) (cbrt (+ (* x x) (* p (* 4 p))))) (cbrt (+ (* x x) (* p (* 4 p))))))
17.1b	(cbrt (+ (* x x) (* p (* 4 p))))
17.1b	(cbrt (+ (* x x) (* p (* 4 p))))
17.1b	(cbrt (+ (* x x) (* p (* 4 p))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 93

Calls

4 calls:

71.0ms	(sqrt (* (* (cbrt (+ (* x x) (* p (* 4 p)))) (cbrt (+ (* x x) (* p (* 4 p))))) (cbrt (+ (* x x) (* p (* 4 p))))))
8.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
4.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
6.0ms	(cbrt (+ (* x x) (* p (* 4 p))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (* (* (cbrt (+ (* x x) (* p (* 4 p)))) (cbrt (+ (* x x) (* p (* 4 p))))) (cbrt (+ (* x x) (* p (* 4 p))))))
129.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
133.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
123.0ms	(cbrt (+ (* x x) (* p (* 4 p))))

simplify947.0ms

Counts

105 → 105

Iterations

Iter	Nodes
done	2011
3	1638
2	572
1	307
0	174

prune511.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
8.7b	(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
16.3b	(sqrt (+ (* x x) (* p (* 4 p))))
16.3b	(sqrt (+ (* x x) (* p (* 4 p))))

rewrite93.0ms

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:

48.0ms	(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
24.0ms	(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
11.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
8.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p))))))
94.0ms	(+ (/ x (/ (* (sqrt (sqrt (+ (* x x) (* p (* 4 p))))) (sqrt (sqrt (+ (* x x) (* p (* 4 p)))))) 0.5)) 0.5)
47.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
54.0ms	(sqrt (+ (* x x) (* p (* 4 p))))

simplify738.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	2011
2	772
1	323
0	146

prune764.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.5b

localize52.0ms

Local error

Found 4 expressions with local error:

16.3b	(sqrt (+ (* x x) (* p (* 4 p))))
17.1b	(cbrt (+ (* x x) (* p (* 4 p))))
17.1b	(cbrt (+ (* x x) (* p (* 4 p))))
17.1b	(cbrt (+ (* x x) (* p (* 4 p))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

6.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
4.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
4.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
4.0ms	(cbrt (+ (* x x) (* p (* 4 p))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(sqrt (+ (* x x) (* p (* 4 p))))
104.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
107.0ms	(cbrt (+ (* x x) (* p (* 4 p))))
139.0ms	(cbrt (+ (* x x) (* p (* 4 p))))

simplify649.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2004
3	1139
2	413
1	159
0	75

prune612.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.5b

regimes167.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample3.1s

Algorithm

intervals

Results

857.0ms	684×	body	1280	valid
784.0ms	5982×	body	80	valid
655.0ms	740×	body	2560	valid
362.0ms	8000×	pre	80	true
143.0ms	311×	body	640	valid
48.0ms	57×	body	5120	valid
46.0ms	138×	body	320	valid
20.0ms	88×	body	160	valid