Details

sample212.0ms

Algorithm

intervals

Results

67.0ms	49×	body	1280	valid
64.0ms	39×	body	640	valid
37.0ms	141×	body	80	valid
15.0ms	20×	body	320	valid
3.0ms	7×	body	160	valid

simplify803.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	2093
4	624
3	188
2	81
1	36
0	17

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2 J) (cos (/ K 2)))
0.2b	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
6.1b	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
8.5b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l` `associate-r/` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

32.0ms	(* (* -2 J) (cos (/ K 2)))
37.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
212.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
96.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* -2 J) (cos (/ K 2)))
109.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
191.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
146.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify3.2s

Counts

102 → 102

Iterations

Iter	Nodes
3	5702
2	1419
1	436
0	179

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* J (cos (/ K 2)))
0.2b	(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
6.2b	(* (* -2 J) (* (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))) (cos (/ K 2))))
8.5b	(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-cbrt-cube` `add-exp-log`
88×	`times-frac`
60×	`cbrt-undiv` `div-exp`
54×	`prod-exp` `cbrt-unprod`
44×	`add-sqr-sqrt`
39×	`*-un-lft-identity` `add-cube-cbrt`
26×	`pow1`
21×	`associate-r` `associate-l`
17×	`swap-sqr`
10×	`pow-prod-down`
8×	`div-inv`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-l/` `associate-r/` `*-commutative` `sqrt-prod`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 179

Calls

4 calls:

14.0ms	(* J (cos (/ K 2)))
44.0ms	(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
42.0ms	(* (* -2 J) (* (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))) (cos (/ K 2))))
5.0ms	(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* J (cos (/ K 2)))
158.0ms	(* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))
219.0ms	(* (* -2 J) (* (sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2))))))) (cos (/ K 2))))
163.0ms	(sqrt (+ 1 (* (/ (/ U 2) (* J (cos (/ K 2)))) (/ (/ U 2) (* J (cos (/ K 2)))))))

simplify1.8s

Counts

191 → 191

Iterations

Iter	Nodes
2	4490
1	1014
0	327

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
6.1b	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
8.5b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite585.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
487.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
96.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (cos (/ K 2)))
146.0ms	(cbrt (cos (/ K 2)))
208.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
141.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify4.6s

Counts

90 → 90

Iterations

Iter	Nodes
3	7230
2	1463
1	375
0	147

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.5b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (cos (/ K 2))))
0.3b	(cbrt (cbrt (cos (/ K 2))))
6.1b	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (* (cbrt (cbrt (cos (/ K 2)))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
8.5b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite774.0ms

Algorithm

rewrite-expression-head

Rules

91×	`pow1`
90×	`add-exp-log`
70×	`pow-prod-down` `prod-exp` `cbrt-unprod`
58×	`add-cbrt-cube`
18×	`cbrt-prod`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
8×	`sqrt-prod`
7×	`associate-r`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`flip3-+` `pow1/3` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt (cbrt (cos (/ K 2))))
1.0ms	(cbrt (cbrt (cos (/ K 2))))
686.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (* (cbrt (cbrt (cos (/ K 2)))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
82.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series638.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (cbrt (cos (/ K 2))))
168.0ms	(cbrt (cbrt (cos (/ K 2))))
191.0ms	(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (* (cbrt (cbrt (cos (/ K 2)))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
116.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
2	2579
1	550
0	207

prune2.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.5b

regimes720.0ms

Accuracy

88% (1.0b remaining)

Error of 9.7b against oracle of 8.7b and baseline of 17.2b

bsearch3.0ms

simplify12.0ms

Iterations

Iter	Nodes
2	47
1	47
0	32

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.5s	1499×	body	1280	valid
1.4s	4296×	body	80	valid
1.2s	1279×	body	640	valid
444.0ms	635×	body	320	valid
162.0ms	295×	body	160	valid