Details

sample163.0ms

Algorithm

intervals

Results

52.0ms	151×	body	80	valid
38.0ms	44×	body	1280	valid
24.0ms	38×	body	640	valid
8.0ms	17×	body	320	valid
2.0ms	6×	body	160	valid

simplify3.5s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize55.0ms

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)
7.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite443.0ms

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:

39.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
24.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
266.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
107.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series830.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
223.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
287.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
210.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

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

prune824.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize39.0ms

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))))
7.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite199.0ms

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)))
42.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
38.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
77.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
69.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
123.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
764.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.9s

Counts

100 → 100

Iterations

Useful iterations: 2 (480.0ms)

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

prune710.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.6b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
7.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

21.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
41.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
22.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
54.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

685.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
95.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
176.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
737.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify1.7s

Counts

101 → 101

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	206	2273
1	535	2248
2	3018	1771
done	5002	1766

prune833.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
0.0b	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
0.1b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
7.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative`
1×	`hypot-udef` `frac-2neg` `clear-num` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
9.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
16.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
48.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series2.3s

Counts

4 → 12

Calls

4 calls:

656.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
696.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
127.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
840.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify2.1s

Counts

116 → 116

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	250	2841
1	623	2768
2	3044	2304
done	5001	2303

prune878.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

regimes630.0ms

Accuracy

0% (0.3b remaining)

Error of 8.6b against oracle of 8.3b and baseline of 8.6b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	23	26
done	23	26

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.2s	1469×	body	1280	valid
1.1s	1244×	body	640	valid
794.0ms	4392×	body	80	valid
289.0ms	598×	body	320	valid
117.0ms	299×	body	160	valid