Details

sample509.0ms

Algorithm

intervals

Results

138.0ms	64×	body	2560	valid
133.0ms	116×	body	1280	valid
113.0ms	23×	body	5120	valid
71.0ms	93×	body	640	valid
16.0ms	31×	body	320	valid
10.0ms	55×	body	80	valid
4.0ms	12×	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

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
18.4b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.8b	(* (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)
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)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ k t) 2.0)
48.0ms	(* (pow t 3.0) (tan k))
116.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
69.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify42.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.8b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.8b	(* (pow k 2.0) (pow t 1.0))
15.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite119.0ms

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:

10.0ms	(/ 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))
34.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
25.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
127.0ms	(* (pow k 2.0) (pow t 1.0))
156.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify150.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1439	7260
1	4421	7083
2	5002	7083

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
1.7b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
4.8b	(* (pow k 2.0) (pow t 1.0))
15.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite125.0ms

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:

10.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
28.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
8.0ms	(* (pow k 2.0) (pow t 1.0))
42.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
26.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
125.0ms	(* (pow k 2.0) (pow t 1.0))
162.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify82.0ms

Algorithm

egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1868	5492
1	5001	5177

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.5b	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l)) (/ (sin k) l))
4.8b	(* (pow k 2.0) (pow t 1.0))
5.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

1420×	`add-exp-log`
774×	`prod-exp`
599×	`div-exp`
465×	`pow-exp`
195×	`pow-to-exp`
100×	`rec-exp` `1-exp`
52×	`add-cbrt-cube`
39×	`add-sqr-sqrt`
37×	`times-frac`
27×	`add-cube-cbrt` `*-un-lft-identity`
19×	`unpow-prod-down`
18×	`associate-l`
17×	`cbrt-undiv` `cbrt-unprod`
14×	`associate-/r*`
9×	`unswap-sqr` `sqr-pow`
8×	`associate-r`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `*-commutative`
1×	`pow-flip` `associate-/r/` `associate-/l/` `inv-pow`

Counts

4 → 470

Calls

4 calls:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
26.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l)) (/ (sin k) l))
8.0ms	(* (pow k 2.0) (pow t 1.0))
26.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l))

series526.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
157.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l)) (/ (sin k) l))
124.0ms	(* (pow k 2.0) (pow t 1.0))
121.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (sin k)) l))

simplify83.0ms

Algorithm

egg-herbie

Counts

482 → 482

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1747	5905
1	5001	5586

prune1.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.8b

regimes1.9s

Accuracy

-3.3% (4.4b remaining)

Error of 11.1b against oracle of 6.7b and baseline of 11.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	35
1	45	35

end0.0ms

sample17.3s

Algorithm

intervals

Results

4.9s	2191×	body	2560	valid
4.6s	4113×	body	1280	valid
4.4s	941×	body	5120	valid
1.9s	2435×	body	640	valid
536.0ms	990×	body	320	valid
361.0ms	2037×	body	80	valid
149.0ms	416×	body	160	valid