Details

sample611.0ms

Algorithm

intervals

Results

200.0ms	89×	body	2560	valid
154.0ms	31×	body	5120	valid
142.0ms	134×	body	1280	valid
55.0ms	73×	body	640	valid
15.0ms	29×	body	320	valid
13.0ms	74×	body	80	valid
8.0ms	23×	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: 43.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
24.6b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.7b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite85.0ms

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)
6.0ms	(* (pow t 3.0) (tan k))
44.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
20.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ k t) 2.0)
231.0ms	(* (pow t 3.0) (tan k))
356.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
240.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify40.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune507.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b	(* (pow k 2.0) (pow t 1.0))
6.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.8b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite117.0ms

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)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
6.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms	(* (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:

325.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
326.0ms	(* (pow k 2.0) (pow t 1.0))
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
629.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify155.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (87.0ms)

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

prune673.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
2.5b	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
5.0b	(* (pow k 2.0) (pow t 1.0))
18.8b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

1169×	`add-exp-log`
660×	`prod-exp`
466×	`div-exp`
367×	`pow-exp`
157×	`pow-to-exp`
90×	`times-frac`
88×	`add-sqr-sqrt`
80×	`rec-exp` `1-exp`
61×	`add-cbrt-cube`
55×	`add-cube-cbrt` `*-un-lft-identity`
52×	`associate-r`
31×	`associate-l`
21×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`unpow-prod-down`
15×	`unswap-sqr`
9×	`sqr-pow`
7×	`pow1` `div-inv`
5×	`associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`frac-times` `associate-*l/`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `associate-/r/` `inv-pow`

Counts

4 → 448

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
29.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
39.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1.3s

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
72.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
328.0ms	(* (pow k 2.0) (pow t 1.0))
607.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify90.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1866	6263
1	5002	5898

prune861.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.3b	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
5.0b	(* (pow k 2.0) (pow t 1.0))
9.8b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

1274×	`add-exp-log`
782×	`prod-exp`
448×	`div-exp`
416×	`pow-exp`
176×	`pow-to-exp`
90×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
20×	`cbrt-unprod`
19×	`unpow-prod-down`
18×	`associate-l`
14×	`cbrt-undiv`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unswap-sqr` `sqr-pow`
8×	`associate-r`
7×	`times-frac`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`pow-flip` `associate-*r/` `associate-/r/` `inv-pow`

Counts

4 → 412

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
23.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
21.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

series1.8s

Counts

4 → 12

Calls

4 calls:

332.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
600.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
315.0ms	(* (pow k 2.0) (pow t 1.0))
556.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

simplify131.0ms

Algorithm

egg-herbie

Counts

424 → 424

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1474	5430
1	4801	4873
2	5001	4873

prune488.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

regimes352.0ms

Accuracy

46% (4.0b remaining)

Error of 10.4b against oracle of 6.3b and baseline of 13.8b

bsearch883.0ms

Steps

Iters	Range		Point
6	4.5499695502683e+145	2.454733387000712e+146	1.9070107828136717e+146
8	1.2133077999293584e-86	1.9551407955890144e-82	7.029524427665179e-84
10	-5.176101993223403e-98	-7.860763033875255e-112	-1.1514252442459826e-102

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	57	84
1	60	42
2	63	42
3	63	42

end0.0ms

sample17.3s

Algorithm

intervals

Results

5.1s	2302×	body	2560	valid
4.5s	963×	body	5120	valid
4.3s	4069×	body	1280	valid
1.8s	2521×	body	640	valid
489.0ms	949×	body	320	valid
389.0ms	2077×	body	80	valid
161.0ms	449×	body	160	valid