Details

sample205.0ms

Algorithm

intervals

Results

78.0ms	63×	body	1280	valid
37.0ms	134×	body	80	valid
35.0ms	35×	body	640	valid
9.0ms	15×	body	320	valid
5.0ms	9×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
0.2b	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
6.6b	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
6.6b	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`pow1`
13×	`add-sqr-sqrt`
12×	`prod-exp` `add-cube-cbrt`
9×	`cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down` `associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`sqrt-div` `pow-exp` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `associate-/r` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `-commutative` `unpow2` `sqr-pow`

Counts

4 → 95

Calls

4 calls:

28.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
35.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
71.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
149.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

series621.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
133.0ms	(pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)
161.0ms	(sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
203.0ms	(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

simplify983.0ms

Counts

107 → 107

Iterations

Iter	Nodes
2	2073
1	517
0	197

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.9b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* (cos (/ K 2)) J) 2))
0.2b	(* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))
6.6b	(sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) 1))
6.7b	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) 1)) (cos (/ K 2))))

rewrite611.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-cbrt-cube` `add-exp-log`
51×	`prod-exp` `cbrt-unprod`
27×	`cbrt-undiv` `div-exp`
24×	`pow1`
18×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
9×	`pow-prod-down`
8×	`associate-r` `associate-l`
7×	`swap-sqr`
5×	`div-inv`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-l/` `associate-r/` `sqrt-prod` `associate-/l*`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`pow2` `frac-times` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `unswap-sqr`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/ U (* (* (cos (/ K 2)) J) 2))
117.0ms	(* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))
153.0ms	(sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) 1))
322.0ms	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) 1)) (cos (/ K 2))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ U (* (* (cos (/ K 2)) J) 2))
146.0ms	(* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))
155.0ms	(sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) 1))
233.0ms	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) 1)) (cos (/ K 2))))

simplify1.4s

Counts

148 → 148

Iterations

Iter	Nodes
2	3120
1	690
0	235

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.3b

localize78.0ms

Local error

Found 4 expressions with local error:

6.7b	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (* (* (cbrt (/ U (* (* (cos (/ K 2)) J) 2))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2)))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2))))) 1)) (cos (/ K 2))))
15.5b	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))
15.5b	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))
15.5b	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
16×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`sqrt-div` `associate-l/` `associate-r/`
1×	`flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 76

Calls

4 calls:

954.0ms	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (* (* (cbrt (/ U (* (* (cos (/ K 2)) J) 2))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2)))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2))))) 1)) (cos (/ K 2))))
22.0ms	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))
23.0ms	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))
23.0ms	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

311.0ms	(* (* -2 J) (* (sqrt (+ (* (/ U (* (* (cos (/ K 2)) J) 2)) (* (* (cbrt (/ U (* (* (cos (/ K 2)) J) 2))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2)))) (cbrt (/ U (* (* (cos (/ K 2)) J) 2))))) 1)) (cos (/ K 2))))
228.0ms	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))
264.0ms	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))
243.0ms	(cbrt (/ U (* (* (cos (/ K 2)) J) 2)))

simplify2.0s

Counts

88 → 88

Iterations

Iter	Nodes
3	4352
2	1010
1	328
0	141

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

localize83.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
11.7b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
11.7b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
11.7b	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`*-un-lft-identity`
12×	`cbrt-prod` `pow1`
9×	`sqrt-pow1` `flip3-+` `pow1/3` `flip-+`
8×	`sqrt-div`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`distribute-lft-out`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 73

Calls

4 calls:

73.0ms	(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
50.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
58.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
36.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

290.0ms	(sqrt (* (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))) (cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))))
318.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
335.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))
264.0ms	(cbrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2)))

simplify3.4s

Counts

85 → 85

Iterations

Iter	Nodes
4	5957
3	1046
2	381
1	199
0	115

prune1.7s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.3b

regimes723.0ms

Accuracy

85.4% (1.3b remaining)

Error of 9.9b against oracle of 8.6b and baseline of 17.4b

bsearch3.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	35
1	35
0	24

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.4s	1543×	body	1280	valid
1.4s	4254×	body	80	valid
1.3s	1260×	body	640	valid
452.0ms	635×	body	320	valid
154.0ms	310×	body	160	valid