Details

sample425.0ms

Algorithm

intervals

Results

128.0ms	66×	body	2560	valid
111.0ms	142×	body	1280	valid
100.0ms	27×	body	5120	valid
34.0ms	68×	body	640	valid
16.0ms	45×	body	320	valid
10.0ms	79×	body	80	valid
3.0ms	14×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (27.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.4b

Counts

2 → 2

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))
18.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.6b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite53.0ms

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:

5.0ms	(pow (/ k t) 2.0)
6.0ms	(* (pow t 3.0) (tan k))
17.0ms	(/ (* 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)))

series890.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ k t) 2.0)
235.0ms	(* (pow t 3.0) (tan k))
359.0ms	(/ (* 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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	991	2005
1	5001	1672

prune438.0ms

Filtered

199 candidates to 96 candidates (48.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	191	8	199
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	193	8	201

Merged error: 19.5b

Counts

201 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.7b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.0b	(* (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)))
9.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
21.0ms	(* (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:

328.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
322.0ms	(* (pow k 2.0) (pow t 1.0))
633.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify162.0ms

Algorithm

egg-herbie

Counts

620 → 620

Iterations

Useful iterations: 2 (88.0ms)

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

prune593.0ms

Filtered

620 candidates to 108 candidates (17.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	610	10	620
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	616	12	628

Merged error: 15.6b

Counts

628 → 12

localize29.0ms

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))))
4.7b	(/ (* (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)))

rewrite272.0ms

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))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms	(* (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:

18.0ms	(pow (sin k) 2)
334.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
84.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
643.0ms	(* (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 (97.0ms)

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

prune563.0ms

Filtered

1480 candidates to 95 candidates (6.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	1472	8	1480
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	1479	13	1492

Merged error: 12.0b

Counts

1492 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (sin k))
0.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.3b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
14.3b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 939

Calls

4 calls:

4.0ms	(/ (cos k) (sin k))
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
25.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
30.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (cos k) (sin k))
340.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
87.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
639.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify393.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2402	15175
1	5001	12337

prune658.0ms

Filtered

951 candidates to 142 candidates (14.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	945	6	951
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	952	12	964

Merged error: 8.0b

Counts

964 → 12

regimes330.0ms

Accuracy

50.1% (3.6b remaining)

Error of 12.2b against oracle of 8.6b and baseline of 15.8b

bsearch1.5s

Steps

Iters	Range		Point
8	4.220887567316556e+155	7.597600850764516e+158	4.265978622843499e+155
9	1.9964502276303598e-140	5.387884190878717e-133	3.6607201827589383e-140
10	-5.1141962640879435e-120	-4.146171549153613e-130	-4.2051688155039255e-130
10	-6.750681421237088e+158	-7.8545803948048655e+146	-1.3290890488547693e+154

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	60	88
1	63	88
2	69	34
3	72	34
4	78	34
5	89	34
6	96	34
7	97	34
8	97	34

end0.0ms

sample14.0s

Algorithm

intervals

Results

4.4s	2226×	body	2560	valid
3.9s	947×	body	5120	valid
3.2s	4115×	body	1280	valid
1.3s	2528×	body	640	valid
391.0ms	1026×	body	320	valid
262.0ms	2056×	body	80	valid
103.0ms	419×	body	160	valid

Details

sample425.0ms

simplify29.0ms

prune11.0ms

localize18.0ms

rewrite53.0ms

series890.0ms

simplify42.0ms

prune438.0ms

localize23.0ms

rewrite111.0ms

series1.4s

simplify162.0ms

prune593.0ms

localize29.0ms

rewrite272.0ms

series1.1s

simplify301.0ms

prune563.0ms

localize24.0ms

rewrite194.0ms

series1.1s

simplify393.0ms

prune658.0ms

regimes330.0ms

bsearch1.5s

simplify5.0ms

end0.0ms

sample14.0s

Profiling