Details

sample505.0ms

Algorithm

intervals

Results

172.0ms	40×	body	5120	valid
144.0ms	71×	body	2560	valid
95.0ms	115×	body	1280	valid
47.0ms	93×	body	640	valid
9.0ms	26×	body	320	valid
7.0ms	61×	body	80	valid
6.0ms	23×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

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: 39.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
22.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.5b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite178.0ms

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:

6.0ms	(pow (/ k t) 2.0)
15.0ms	(* (pow t 3.0) (tan k))
97.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
49.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow (/ k t) 2.0)
217.0ms	(* (pow t 3.0) (tan k))
337.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
232.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune482.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
6.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.3b	(* (pow k 2.0) (pow t 1.0))
17.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 575

Calls

4 calls:

4.0ms	(pow (sin k) 2)
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms	(* (pow k 2.0) (pow t 1.0))
77.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (sin k) 2)
79.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
312.0ms	(* (pow k 2.0) (pow t 1.0))
608.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify140.0ms

Algorithm

egg-herbie

Counts

587 → 587

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1304	6971
1	3873	6815
2	5003	6814

prune782.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.3b	(pow (sin k) 2)
6.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.9b	(* (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)))

rewrite425.0ms

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:

50.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.0ms	(pow (sin k) 2)
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
144.0ms	(* (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)))

series985.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
19.0ms	(pow (sin k) 2)
74.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
579.0ms	(* (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)))

simplify301.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (87.0ms)

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

prune592.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
0.8b	(pow (cbrt (sin k)) 4)
2.0b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
17.9b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

29087×	`times-frac`
11908×	`add-sqr-sqrt`
11455×	`add-cube-cbrt` `*-un-lft-identity`
10275×	`add-exp-log`
7945×	`unpow-prod-down`
6428×	`div-exp`
5073×	`prod-exp`
4257×	`pow-exp`
3951×	`cbrt-prod`
3557×	`associate-r`
2490×	`pow-to-exp`
1378×	`sqr-pow`
668×	`unpow2`
589×	`rec-exp` `1-exp`
326×	`associate-/l*`
319×	`div-inv`
117×	`associate-/r*`
108×	`unswap-sqr`
47×	`add-cbrt-cube`
26×	`cbrt-undiv`
24×	`associate-/r/`
11×	`associate-l`
5×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`pow1/3` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 9909

Calls

4 calls:

42.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
4.0ms	(pow (cbrt (sin k)) 4)
176.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.4s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series991.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
122.0ms	(pow (cbrt (sin k)) 4)
77.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
619.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.4s

Algorithm

egg-herbie

Counts

9921 → 9921

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	10818	276445

prune1.2m

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 7.8b

regimes852.0ms

Accuracy

33.3% (3.9b remaining)

Error of 10.7b against oracle of 6.9b and baseline of 12.7b

bsearch8.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	102
1	83	102

end0.0ms

sample14.7s

Algorithm

intervals

Results

4.3s	2225×	body	2560	valid
4.3s	991×	body	5120	valid
3.5s	4062×	body	1280	valid
1.4s	2524×	body	640	valid
378.0ms	965×	body	320	valid
257.0ms	2013×	body	80	valid
126.0ms	484×	body	160	valid