Details

sample588.0ms

Algorithm

intervals

Results

177.0ms	88×	body	2560	valid
138.0ms	28×	body	5120	valid
134.0ms	119×	body	1280	valid
64.0ms	84×	body	640	valid
25.0ms	39×	body	320	valid
19.0ms	80×	body	80	valid
5.0ms	12×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
18.0b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.1b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite87.0ms

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:

3.0ms	(pow (/ k t) 2.0)
10.0ms	(* (pow t 3.0) (tan k))
42.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
21.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series922.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ k t) 2.0)
239.0ms	(* (pow t 3.0) (tan k))
369.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
247.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify42.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune502.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0b	(* (pow k 2.0) (pow t 1.0))
13.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite113.0ms

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:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0ms	(* (pow k 2.0) (pow t 1.0))
33.0ms	(* (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:

333.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
320.0ms	(* (pow k 2.0) (pow t 1.0))
650.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify154.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (83.0ms)

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

prune660.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.3b	(* (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)))

rewrite291.0ms

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:

1.0ms	(pow (sin k) 2)
21.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
60.0ms	(* (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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin k) 2)
328.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
842.0ms	(* (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)))

simplify285.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (88.0ms)

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

prune604.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos k) (sin k))
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.1b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
13.3b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 939

Calls

4 calls:

3.0ms	(/ (cos k) (sin k))
21.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
31.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
63.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (cos k) (sin k))
337.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
653.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify169.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2402	15175
1	5001	12337

prune775.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

regimes552.0ms

Accuracy

53.2% (3.3b remaining)

Error of 11.8b against oracle of 8.4b and baseline of 15.6b

bsearch2.4s

Steps

Iters	Range		Point
10	4.040826535236262e+132	1.7408175636706706e+142	1.6455364292447533e+142
12	1.3794177633234925e-189	2.7802313010617128e-146	2.7112574226970215e-148
10	-5.941234367780267e-121	-7.33641120008535e-133	-5.866557080506545e-121
8	-1.2600048194356575e+137	-2.1321545243619132e+133	-6.757516663156314e+136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	84
1	77	84

end0.0ms

sample17.4s

Algorithm

intervals

Results

4.9s	2211×	body	2560	valid
4.7s	4177×	body	1280	valid
4.2s	896×	body	5120	valid
1.9s	2486×	body	640	valid
579.0ms	1006×	body	320	valid
460.0ms	2002×	body	80	valid
177.0ms	446×	body	160	valid