Details

sample505.0ms

Algorithm

intervals

Results

143.0ms	64×	body	2560	valid
129.0ms	116×	body	1280	valid
107.0ms	23×	body	5120	valid
74.0ms	93×	body	640	valid
16.0ms	31×	body	320	valid
10.0ms	55×	body	80	valid
4.0ms	12×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.8b

localize22.0ms

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)))

rewrite91.0ms

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:

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)))
22.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (/ k t) 2.0)
51.0ms	(* (pow t 3.0) (tan k))
118.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
66.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify130.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (20.0ms)

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

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.9b

localize22.0ms

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)))

rewrite127.0ms

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:

8.0ms	(/ 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))
36.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series438.0ms

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))
125.0ms	(* (pow k 2.0) (pow t 1.0))
163.0ms	(* (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

612 → 612

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1316	7194
1	4162	7025
2	5002	7018

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite138.0ms

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:

8.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
31.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
9.0ms	(* (pow k 2.0) (pow t 1.0))
41.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
29.0ms	(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
128.0ms	(* (pow k 2.0) (pow t 1.0))
162.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify84.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1743	6193
1	5001	5828

prune2.4s

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) (fabs (sin k))) l)) (/ (fabs (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) (fabs (sin k))) l))

rewrite120.0ms

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×	`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 → 462

Calls

4 calls:

8.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
25.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l)) (/ (fabs (sin k)) l))
8.0ms	(* (pow k 2.0) (pow t 1.0))
28.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l))

series528.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
161.0ms	(/ (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l)) (/ (fabs (sin k)) l))
125.0ms	(* (pow k 2.0) (pow t 1.0))
119.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (* (/ (cos k) (fabs (sin k))) l))

simplify84.0ms

Algorithm

egg-herbie

Counts

474 → 474

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1659	6516
1	5002	6151

prune1.6s

Pruning

18 alts after pruning (18 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

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	39
1	46	39

end0.0ms

sample17.2s

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
534.0ms	990×	body	320	valid
354.0ms	2037×	body	80	valid
159.0ms	416×	body	160	valid