Details

sample447.0ms

Algorithm

intervals

Results

155.0ms	31×	body	5120	valid
118.0ms	61×	body	2560	valid
94.0ms	134×	body	1280	valid
36.0ms	70×	body	640	valid
12.0ms	38×	body	320	valid
7.0ms	64×	body	80	valid
4.0ms	18×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	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: 38.9b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
0.2b	(pow (/ k t) 2.0)
19.0b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.1b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

390×	`add-exp-log`
262×	`prod-exp`
75×	`div-exp`
72×	`add-cbrt-cube`
62×	`pow-exp`
41×	`pow-to-exp`
39×	`cbrt-unprod`
26×	`unpow-prod-down`
21×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-l`
12×	`cbrt-undiv`
7×	`pow1`
6×	`associate-*r/`
4×	`associate-r` `add-log-exp`
3×	`tan-quot` `pow-unpow` `div-inv`
2×	`associate-l/` `-commutative` `sqr-pow`
1×	`pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 187

Calls

4 calls:

12.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
7.0ms	(pow (/ k t) 2.0)
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)))

series921.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
64.0ms	(pow (/ k t) 2.0)
353.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
239.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify139.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	935	2182
1	4992	1803
2	5001	1803

prune395.0ms

Filtered

199 candidates to 80 candidates (40.2%)

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: 20.5b

Counts

201 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.5b	(* (pow k 2.0) (pow t 1.0))
14.6b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite97.0ms

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:

7.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
7.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
20.0ms	(* (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:

326.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
84.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
316.0ms	(* (pow k 2.0) (pow t 1.0))
626.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify161.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (88.0ms)

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

prune553.0ms

Filtered

612 candidates to 100 candidates (16.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	603	9	612
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	608	12	620

Merged error: 16.3b

Counts

620 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin k) 2)
0.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.6b	(* (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)))

rewrite474.0ms

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×	`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 → 1460

Calls

4 calls:

8.0ms	(pow (sin k) 2)
11.0ms	(/ 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))
34.0ms	(* (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:

17.0ms	(pow (sin k) 2)
326.0ms	(/ 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))
631.0ms	(* (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)))

simplify324.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1742	23543
1	4574	19111
2	5002	17858

prune496.0ms

Filtered

1472 candidates to 85 candidates (5.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	1464	8	1472
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	1470	14	1484

Merged error: 12.8b

Counts

1484 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos k) (sin k))
0.4b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.9b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
14.6b	(* (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))))

rewrite186.0ms

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×	`associate-/r*` `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 → 931

Calls

4 calls:

4.0ms	(/ (cos k) (sin k))
11.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
20.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
33.0ms	(* (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))
332.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
645.0ms	(* (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))))

simplify177.0ms

Algorithm

egg-herbie

Counts

943 → 943

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2147	15097
1	5002	12259

prune658.0ms

Filtered

943 candidates to 135 candidates (14.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	936	7	943
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	942	15	957

Merged error: 7.5b

Counts

957 → 15

regimes293.0ms

Accuracy

24.5% (5.5b remaining)

Error of 14.0b against oracle of 8.6b and baseline of 15.8b

bsearch279.0ms

Steps

Iters	Range		Point
4	-5.843560698527696e-70	-3.5516785375926374e-70	-4.756510568443509e-70
9	-1.1834517464687555e+151	-2.790188816684615e+142	-3.6285153497394795e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	51
1	66	51

end0.0ms

sample13.0s

Algorithm

intervals

Results

4.0s	2182×	body	2560	valid
3.7s	884×	body	5120	valid
3.0s	4102×	body	1280	valid
1.2s	2443×	body	640	valid
344.0ms	1010×	body	320	valid
218.0ms	1989×	body	80	valid
102.0ms	457×	body	160	valid

Details

sample447.0ms

simplify27.0ms

prune11.0ms

localize18.0ms

rewrite59.0ms

series921.0ms

simplify139.0ms

prune395.0ms

localize22.0ms

rewrite97.0ms

series1.4s

simplify161.0ms

prune553.0ms

localize28.0ms

rewrite474.0ms

series1.1s

simplify324.0ms

prune496.0ms

localize23.0ms

rewrite186.0ms

series1.1s

simplify177.0ms

prune658.0ms

regimes293.0ms

bsearch279.0ms

simplify2.0ms

end0.0ms

sample13.0s

Profiling