Details

sample182.0ms

Algorithm

intervals

Results

68.0ms	63×	body	1280	valid
34.0ms	44×	body	640	valid
28.0ms	126×	body	80	valid
17.0ms	6×	body	160	valid
11.0ms	17×	body	320	valid

simplify961.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2067
4	616
3	185
2	79
1	34
0	17

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* J 2) (cos (/ K 2)))
0.2b	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
6.2b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite782.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-cbrt-cube` `add-exp-log`
49×	`prod-exp` `cbrt-unprod`
26×	`pow1`
24×	`cbrt-undiv` `div-exp`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l`
12×	`times-frac`
11×	`associate-r`
10×	`pow-prod-down`
7×	`swap-sqr`
6×	`sqrt-prod`
4×	`sqrt-div` `insert-posit16` `div-inv` `add-log-exp`
3×	`associate-l/` `-commutative`
2×	`flip3-+` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*r/` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

17.0ms	(* (* J 2) (cos (/ K 2)))
128.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
410.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
223.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series572.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* J 2) (cos (/ K 2)))
127.0ms	(* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2)))))
249.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
134.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.3s

Counts

145 → 145

Iterations

Iter	Nodes
2	3067
1	664
0	231

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.4b

localize72.0ms

Local error

Found 4 expressions with local error:

6.2b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
6.2b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite697.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

134.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
162.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
158.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
241.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series884.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
263.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
159.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
151.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify21.9s

Counts

88 → 88

Iterations

Iter	Nodes
4	15942
3	1864
2	449
1	182
0	92

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.4b

localize55.0ms

Local error

Found 4 expressions with local error:

6.2b	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
7.9b	(log (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

178.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
113.0ms	(log (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
183.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
138.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series792.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(sqrt (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
172.0ms	(log (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)))
165.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
144.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify1.1s

Counts

86 → 86

Iterations

Iter	Nodes
3	2275
2	548
1	223
0	118

prune1.7s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.4b

localize63.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
9.2b	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

rewrite902.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-*l/`
1×	`associate-r` `*-commutative`

Counts

4 → 75

Calls

4 calls:

415.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
145.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
152.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
187.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

series699.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1)) (* (cos (/ K 2)) (* -2 J)))
165.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
140.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))
154.0ms	(sqrt (+ (* (/ U (* (* J 2) (cos (/ K 2)))) (/ U (* (* J 2) (cos (/ K 2))))) 1))

simplify2.3s

Counts

87 → 87

Iterations

Iter	Nodes
3	4507
2	868
1	247
0	102

prune1.8s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 6.4b

regimes540.0ms

Accuracy

-2% (8.7b remaining)

Error of 17.3b against oracle of 8.6b and baseline of 17.1b

bsearch283.0ms

Steps

Iters	Range		Point
9	-2.9071946876675688e-233	-1.0814405530977078e-239	-3.513211526895522e-238
9	-2.3090392327040577e-173	-1.4449598187689686e-179	-2.1661330982400293e-176

simplify22.0ms

Iterations

Iter	Nodes
2	33
1	33
0	24

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.4s	1538×	body	1280	valid
1.5s	4354×	body	80	valid
1.4s	1243×	body	640	valid
482.0ms	591×	body	320	valid
142.0ms	275×	body	160	valid