Details

sample131.0ms

Algorithm

intervals

Results

35.0ms	43×	body	640	valid
29.0ms	40×	body	1280	valid
20.0ms	139×	body	80	valid
10.0ms	22×	body	320	valid
3.0ms	12×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	136	24
4	214	24
5	498	24
6	3356	24
done	5002	24

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite530.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`pow1`
12×	`add-cube-cbrt` `prod-exp`
9×	`cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
7×	`associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `hypot-def` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `associate-/r` `-commutative`

Counts

4 → 101

Calls

4 calls:

35.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
43.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
299.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
147.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
272.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
363.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
282.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.7s

Counts

113 → 113

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	222	2298
1	613	2082
2	2883	1877
done	5001	1875

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
6.7b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `-commutative` `associate-/l`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 88

Calls

4 calls:

37.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
40.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
43.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
116.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.3s

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
83.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
174.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
921.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify2.5s

Counts

100 → 100

Iterations

Useful iterations: 2 (646.0ms)

Iter	Nodes	Cost
0	193	1843
1	498	1816
2	2978	1437
done	5001	1437

prune993.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
6.7b	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite789.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r`
1×	`associate-l` `*-commutative`

Counts

4 → 71

Calls

4 calls:

2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
779.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.9s

Counts

4 → 12

Calls

4 calls:

304.0ms	(cbrt (cos (/ K 2.0)))
308.0ms	(cbrt (cos (/ K 2.0)))
301.0ms	(cbrt (cos (/ K 2.0)))
991.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify2.3s

Counts

83 → 83

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	162	2214
1	420	2172
2	2076	1444
done	5000	1291

prune876.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize86.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
6.8b	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1` `add-exp-log`
32×	`add-cbrt-cube`
31×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 81

Calls

4 calls:

2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
256.0ms	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt (cos (/ K 2.0)))
304.0ms	(cbrt (cos (/ K 2.0)))
304.0ms	(cbrt (cos (/ K 2.0)))
1.0s	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify1.9s

Counts

93 → 93

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	157	2877
1	427	2810
2	1892	1747
done	5000	1541

prune743.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes771.0ms

Accuracy

0% (0.2b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	24	26
done	24	26

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.8s	1542×	body	1280	valid
936.0ms	4303×	body	80	valid
871.0ms	1237×	body	640	valid
263.0ms	595×	body	320	valid
106.0ms	330×	body	160	valid