Details

sample478.0ms

Algorithm

intervals

Results

170.0ms	87×	body	2560	valid
108.0ms	132×	body	1280	valid
98.0ms	21×	body	5120	valid
52.0ms	102×	body	640	valid
10.0ms	28×	body	320	valid
6.0ms	59×	body	80	valid
6.0ms	25×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
20.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 187

Calls

4 calls:

6.0ms	(pow (/ k t) 2.0)
16.0ms	(* (pow t 3.0) (tan k))
89.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
44.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (/ k t) 2.0)
241.0ms	(* (pow t 3.0) (tan k))
378.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
248.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune467.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.9b	(* (pow k 2.0) (pow t 1.0))
16.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 608

Calls

4 calls:

17.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms	(* (pow k 2.0) (pow t 1.0))
71.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

345.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
341.0ms	(* (pow k 2.0) (pow t 1.0))
656.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify152.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1439	7252
1	4296	7083
2	5003	7076

prune653.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1468

Calls

4 calls:

4.0ms	(pow (sin k) 2)
45.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
133.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin k) 2)
345.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
666.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify274.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1997	23615
1	4854	19182
2	5002	17933

prune597.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
3.5b	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

13925×	`add-exp-log`
10128×	`prod-exp`
8234×	`pow-exp`
5894×	`div-exp`
4214×	`pow-to-exp`
910×	`rec-exp` `1-exp`
84×	`unpow-prod-down`
61×	`times-frac` `associate-l`
49×	`add-sqr-sqrt`
44×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
21×	`sqrt-prod`
13×	`associate-r` `cbrt-unprod` `sqr-pow`
8×	`associate-/r*`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `unpow2` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 3178

Calls

4 calls:

3.0ms	(pow (sin k) 2)
175.0ms	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
77.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin k) 2)
648.0ms	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
95.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
663.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify538.0ms

Algorithm

egg-herbie

Counts

3190 → 3190

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	3293	60241
1	5001	59966

prune929.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

regimes291.0ms

Accuracy

38.1% (3.3b remaining)

Error of 16.0b against oracle of 12.8b and baseline of 18.0b

bsearch560.0ms

Steps

Iters	Range		Point
8	1.048707475731352e-109	1.233250811945564e-106	7.86864403713139e-109
8	-2.803464213148836e-142	-1.382633121979521e-146	-4.767926568016393e-144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	68
1	67	68

end0.0ms

sample14.1s

Algorithm

intervals

Results

4.1s	2224×	body	2560	valid
3.9s	921×	body	5120	valid
3.4s	4121×	body	1280	valid
1.3s	2573×	body	640	valid
391.0ms	1027×	body	320	valid
244.0ms	1998×	body	80	valid
116.0ms	496×	body	160	valid