Details

sample413.0ms

Algorithm

intervals

Results

133.0ms	76×	body	2560	valid
103.0ms	32×	body	5120	valid
101.0ms	145×	body	1280	valid
39.0ms	86×	body	640	valid
8.0ms	24×	body	320	valid
5.0ms	53×	body	80	valid
2.0ms	12×	body	160	valid

simplify27.0ms

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
20.6b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.0b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite56.0ms

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)
6.0ms	(* (pow t 3.0) (tan k))
19.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series925.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ k t) 2.0)
242.0ms	(* (pow t 3.0) (tan k))
374.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
243.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify40.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune486.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.4b	(* (pow k 2.0) (pow t 1.0))
14.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite111.0ms

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:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
22.0ms	(* (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:

344.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
336.0ms	(* (pow k 2.0) (pow t 1.0))
654.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify148.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (85.0ms)

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

prune677.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 15.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.9b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.3b	(* (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)))

rewrite289.0ms

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:

3.0ms	(pow (sin k) 2)
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
12.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
38.0ms	(* (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)
344.0ms	(/ 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))
661.0ms	(* (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)))

simplify293.0ms

Algorithm

egg-herbie

Counts

1480 → 1480

Iterations

Useful iterations: 2 (86.0ms)

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

prune621.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin k))
0.9b	(pow (cbrt (sin k)) 4)
1.6b	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
14.3b	(* (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)))

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

28001×	`times-frac`
11422×	`add-sqr-sqrt`
10969×	`add-cube-cbrt` `*-un-lft-identity`
10259×	`add-exp-log`
7729×	`unpow-prod-down`
6416×	`div-exp`
5073×	`prod-exp`
4256×	`pow-exp`
3846×	`cbrt-prod`
3557×	`associate-r`
2489×	`pow-to-exp`
1342×	`sqr-pow`
668×	`unpow2`
589×	`rec-exp` `1-exp`
323×	`associate-/l*`
302×	`div-inv`
108×	`unswap-sqr`
38×	`add-cbrt-cube`
23×	`associate-/r/`
20×	`cbrt-undiv`
11×	`associate-l` `associate-/r*`
5×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `pow1/3`
1×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 9474

Calls

4 calls:

2.0ms	(cbrt (sin k))
4.0ms	(pow (cbrt (sin k)) 4)
143.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.3s	(* (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)))

series983.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (sin k))
133.0ms	(pow (cbrt (sin k)) 4)
91.0ms	(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
657.0ms	(* (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)))

simplify2.6s

Algorithm

egg-herbie

Counts

9486 → 9486

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	10719	264382

prune55.4s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 4.9b

regimes591.0ms

Accuracy

17.1% (3.9b remaining)

Error of 11.0b against oracle of 7.1b and baseline of 11.8b

bsearch637.0ms

Steps

Iters	Range		Point
8	-2.131125377017844e-152	-1.333102075632568e-156	-7.585502794490059e-156
8	-3.8975250219793675e+142	-5.828232727961281e+138	-3.0011853703712436e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	45
1	61	45

end0.0ms

sample13.2s

Algorithm

intervals

Results

4.3s	2306×	body	2560	valid
3.7s	963×	body	5120	valid
2.9s	4084×	body	1280	valid
1.2s	2528×	body	640	valid
333.0ms	1023×	body	320	valid
213.0ms	2032×	body	80	valid
98.0ms	433×	body	160	valid