Details

sample59.0ms

Algorithm

intervals

Results

19.0ms	50×	body	1280	valid
10.0ms	144×	body	80	valid
10.0ms	38×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	13
1	75	13
2	139	13
3	207	13
4	375	13
5	1373	13
6	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.8b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
56.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
30.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
138.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
194.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
148.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	464	1076
1	1988	966
2	5001	965

prune346.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
8.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite46.0ms

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:

7.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
6.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
6.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
24.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
47.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
51.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
503.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	489	993
1	2344	770
2	5001	770

prune333.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (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)))
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite31.0ms

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:

7.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
3.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
9.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
10.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
440.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
49.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
501.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	524	1240
1	2426	964
2	5002	963

prune333.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) (/ 2.0 2))))
0.1b	(/ U (cos (/ K 2.0)))
0.2b	(* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0))))
8.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-exp-log`
41×	`add-cbrt-cube`
30×	`add-sqr-sqrt`
29×	`prod-exp`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
20×	`pow1`
17×	`associate-r` `cbrt-unprod`
16×	`div-exp`
11×	`associate-l`
10×	`pow-prod-down`
8×	`cbrt-undiv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 129

Calls

4 calls:

3.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) (/ 2.0 2))))
2.0ms	(/ U (cos (/ K 2.0)))
27.0ms	(* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0))))
19.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

497.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) (/ 2.0 2))))
66.0ms	(/ U (cos (/ K 2.0)))
75.0ms	(* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0))))
511.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (* (/ 1 (* 2.0 J)) (/ U (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	752	1658
1	3753	1326
2	5001	1323

prune444.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.8b

regimes265.0ms

Accuracy

0% (0.4b remaining)

Error of 7.8b against oracle of 7.4b and baseline of 7.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	15
1	28	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

599.0ms	1578×	body	1280	valid
326.0ms	1232×	body	640	valid
311.0ms	4280×	body	80	valid
120.0ms	606×	body	320	valid
41.0ms	307×	body	160	valid