Details

sample604.0ms

Algorithm

intervals

Results

198.0ms	89×	body	2560	valid
149.0ms	134×	body	1280	valid
148.0ms	31×	body	5120	valid
50.0ms	73×	body	640	valid
14.0ms	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	147	13
2	857	12
3	5002	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)))

rewrite86.0ms

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×	`associate-r` `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 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
45.0ms	(/ (* 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)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(pow (/ k t) 2.0)
234.0ms	(* (pow t 3.0) (tan k))
367.0ms	(/ (* 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)))

simplify140.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune457.0ms

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)))

rewrite118.0ms

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×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

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))
37.0ms	(* (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:

338.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
330.0ms	(* (pow k 2.0) (pow t 1.0))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
641.0ms	(* (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

612 → 612

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1316	7202
1	4287	7025
2	5001	7018

prune608.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.2b

localize22.0ms

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))))

rewrite124.0ms

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×	`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 → 440

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
27.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
43.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1.5s

Counts

4 → 12

Calls

4 calls:

332.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
66.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
324.0ms	(* (pow k 2.0) (pow t 1.0))
798.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify89.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1743	6193
1	5001	5828

prune807.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.3b

localize23.0ms

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))

rewrite95.0ms

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×	`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 → 404

Calls

4 calls:

10.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
19.0ms	(/ (* (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))

series1.7s

Counts

4 → 12

Calls

4 calls:

348.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
616.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l)) (* (fabs (sin k)) (/ (fabs (sin k)) l)))
331.0ms	(* (pow k 2.0) (pow t 1.0))
375.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (cos k) l))

simplify137.0ms

Algorithm

egg-herbie

Counts

416 → 416

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1431	5362
1	4747	4805
2	5001	4805

prune437.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

regimes355.0ms

Accuracy

46% (4.0b remaining)

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

bsearch865.0ms

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

simplify2.0ms

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

sample17.0s

Algorithm

intervals

Results

5.0s	2302×	body	2560	valid
4.4s	963×	body	5120	valid
4.3s	4069×	body	1280	valid
1.8s	2521×	body	640	valid
487.0ms	949×	body	320	valid
366.0ms	2077×	body	80	valid
154.0ms	449×	body	160	valid