Details

sample64.0ms

Algorithm

intervals

Results

18.0ms	49×	body	1280	valid
15.0ms	48×	body	640	valid
9.0ms	123×	body	80	valid
6.0ms	29×	body	320	valid
1.0ms	7×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	13
1	74	13
2	138	13
3	203	13
4	368	13
5	1361	13
6	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.1b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`pow1`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `prod-exp`
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` `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` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `associate-/r` `-commutative` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

7.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
57.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
26.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series555.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
135.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
188.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
145.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	543	1086
1	2465	960
2	5001	960

prune303.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.7b

localize21.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-div`
7×	`pow1` `cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

12.0ms	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
25.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
25.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
139.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
140.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
139.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	183	942
1	410	899
2	1386	895
3	5001	884

prune335.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.7b

localize36.0ms

Local error

Found 4 expressions with local error:

10.1b	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

30.0ms	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series894.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
228.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
221.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
220.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify98.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	210	1282
1	564	1214
2	2574	1208
3	5001	1182

prune502.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 12.7b

localize44.0ms

Local error

Found 4 expressions with local error:

15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.7b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod` `*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

14.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series899.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
231.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
223.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
225.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	150	968
1	344	900
2	1231	884
3	5002	872

prune527.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 12.7b

regimes326.0ms

Accuracy

91.2% (0.5b remaining)

Error of 13.2b against oracle of 12.7b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

sample1.7s

Algorithm

intervals

Results

614.0ms	1573×	body	1280	valid
344.0ms	1243×	body	640	valid
302.0ms	4243×	body	80	valid
125.0ms	629×	body	320	valid
43.0ms	315×	body	160	valid