Details

sample49.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
11.0ms	200×	body	80	overflowed

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite247.0ms

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:

17.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
20.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
143.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
63.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
120.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
171.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
130.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	543	1085
1	2466	960
2	5002	960

prune302.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)
0.6b	(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
5.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
63×	`times-frac`
42×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
34×	`div-exp`
27×	`add-cbrt-cube`
26×	`unpow-prod-down`
24×	`prod-exp`
17×	`pow1`
13×	`pow-exp`
9×	`cbrt-unprod` `div-inv`
8×	`rec-exp` `1-exp` `sqrt-prod`
7×	`cbrt-undiv` `associate-r` `associate-/r*`
6×	`pow-prod-down`
4×	`sqrt-div` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-/l*`
2×	`pow-flip` `flip3-+` `associate-*r/` `associate-/r/` `flip-+` `distribute-lft-out` `inv-pow`
1×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `*-commutative` `sqr-pow`

Counts

4 → 157

Calls

4 calls:

30.0ms	(pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)
27.0ms	(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
129.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
53.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))

series518.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)
82.0ms	(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
173.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
133.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))

simplify101.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	833	1909
1	4099	1717
2	5001	1646

prune345.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.7b

localize23.0ms

Local error

Found 4 expressions with local error:

5.5b	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
5.5b	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
8.7b	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

53.0ms	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
52.0ms	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
51.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
53.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))

series657.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
199.0ms	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
125.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
130.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	154	1086
1	366	1034
2	1239	1034
3	5001	1016

prune319.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.7b

localize26.0ms

Local error

Found 4 expressions with local error:

5.5b	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
8.7b	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
12.6b	(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))) 3))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

42×	`sqrt-prod`
26×	`cbrt-prod`
25×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`sqrt-div`
10×	`unpow-prod-down` `cube-prod`
8×	`pow1`
6×	`sqrt-pow1`
5×	`distribute-lft-out`
4×	`add-exp-log` `rem-sqrt-square` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`cube-div` `cbrt-div`
1×	`cube-mult` `pow1/3` `unpow3` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

52.0ms	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
50.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
51.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
57.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))) 3))

series678.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0))))
129.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
128.0ms	(sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))
205.0ms	(cbrt (pow (sqrt (sqrt (+ 1.0 (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) 2.0)))) 3))

simplify162.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (148.0ms)

Iter	Nodes	Cost
0	273	1404
1	823	1351
2	3639	1333
3	5001	1324

prune364.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 10.7b

regimes213.0ms

Accuracy

71.6% (1.5b remaining)

Error of 14.1b against oracle of 12.5b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	51
1	56	51

end0.0ms

sample1.4s

Algorithm

intervals

Results

573.0ms	7988×	body	80	valid
378.0ms	6967×	body	80	overflowed
2.0ms	12×	body	160	valid