Details

sample474.0ms

Algorithm

intervals

Results

169.0ms	87×	body	2560	valid
106.0ms	132×	body	1280	valid
98.0ms	21×	body	5120	valid
50.0ms	102×	body	640	valid
10.0ms	28×	body	320	valid
7.0ms	59×	body	80	valid
6.0ms	25×	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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.0b	(* (pow t 3.0) (tan k))
20.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.8b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite170.0ms

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:

8.0ms	(pow (/ k t) 2.0)
15.0ms	(* (pow t 3.0) (tan k))
92.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
45.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series928.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ k t) 2.0)
239.0ms	(* (pow t 3.0) (tan k))
381.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
246.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify44.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune468.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.9b	(* (pow k 2.0) (pow t 1.0))
16.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite184.0ms

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:

17.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms	(* (pow k 2.0) (pow t 1.0))
72.0ms	(* (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:

342.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
338.0ms	(* (pow k 2.0) (pow t 1.0))
643.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify153.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (86.0ms)

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

prune658.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0b	(* (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)))

rewrite414.0ms

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:

4.0ms	(pow (sin k) 2)
47.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
136.0ms	(* (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin k) 2)
350.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
665.0ms	(* (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)))

simplify274.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (88.0ms)

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

prune606.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
3.5b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.6b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

24975×	`add-exp-log`
19170×	`prod-exp`
16882×	`pow-exp`
11120×	`div-exp`
7942×	`pow-to-exp`
2980×	`rec-exp` `1-exp`
54×	`unpow-prod-down`
40×	`times-frac` `associate-l`
36×	`add-sqr-sqrt`
32×	`add-cbrt-cube`
31×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r` `cbrt-unprod`
10×	`sqr-pow`
8×	`associate-/r*`
6×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `unpow2` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 5737

Calls

4 calls:

4.0ms	(pow (sin k) 2)
192.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
78.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin k) 2)
658.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
92.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
664.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify984.0ms

Algorithm

egg-herbie

Counts

5749 → 5749

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5001	119837

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.8b

regimes360.0ms

Accuracy

27.4% (4.7b remaining)

Error of 16.0b against oracle of 11.3b and baseline of 17.8b

bsearch515.0ms

Steps

Iters	Range		Point
7	6.932449966890243e-135	1.6902561201493824e-133	7.03262491694227e-135
8	-2.803464213148836e-142	-1.382633121979521e-146	-4.767926568016393e-144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	63
1	67	63

end0.0ms

sample14.2s

Algorithm

intervals

Results

4.2s	2224×	body	2560	valid
3.9s	921×	body	5120	valid
3.4s	4121×	body	1280	valid
1.4s	2573×	body	640	valid
376.0ms	1027×	body	320	valid
239.0ms	1998×	body	80	valid
117.0ms	496×	body	160	valid