Details

sample401.0ms

Algorithm

intervals

Results

149.0ms	73×	body	2560	valid
103.0ms	130×	body	1280	valid
50.0ms	17×	body	5120	valid
45.0ms	76×	body	640	valid
13.0ms	38×	body	320	valid
7.0ms	61×	body	80	valid
4.0ms	15×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune18.0ms

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: 38.2b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.1b	(* (pow t 3.0) (tan k))
19.6b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.0b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite52.0ms

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×	`associate-r` `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 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
5.0ms	(* (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)))
14.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series919.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ k t) 2.0)
237.0ms	(* (pow t 3.0) (tan k))
366.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
251.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify133.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune600.0ms

Filtered

191 candidates to 88 candidates (46.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	183	8	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Merged error: 20.7b

Counts

193 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.7b	(* (pow k 2.0) (pow t 1.0))
15.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite104.0ms

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)))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
23.0ms	(* (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:

337.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
330.0ms	(* (pow k 2.0) (pow t 1.0))
646.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify157.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1316	7192
1	4162	7023
2	5002	7016

prune800.0ms

Filtered

612 candidates to 99 candidates (16.2%)

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: 16.9b

Counts

620 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.6b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.7b	(* (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)))

rewrite258.0ms

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:

2.0ms	(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))
40.0ms	(* (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)))

series1.3s

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin k) 2)
345.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
881.0ms	(* (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)))

simplify299.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	1742	23541
1	4574	19109
2	5002	17856

prune718.0ms

Filtered

1472 candidates to 85 candidates (5.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	1465	7	1472
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	1471	13	1484

Merged error: 13.7b

Counts

1484 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (sin k))
0.6b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.1b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
15.7b	(* (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))))

rewrite189.0ms

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)))
35.0ms	(* (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:

19.0ms	(/ (cos k) (sin k))
345.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
672.0ms	(* (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))))

simplify176.0ms

Algorithm

egg-herbie

Counts

943 → 943

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	2147	15095
1	5002	12257

prune931.0ms

Filtered

943 candidates to 133 candidates (14.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	935	8	943
Fresh	8	3	11
Picked	1	0	1
Done	1	0	1
Total	945	11	956

Merged error: 9.8b

Counts

956 → 11

regimes378.0ms

Accuracy

44.2% (3.9b remaining)

Error of 12.5b against oracle of 8.6b and baseline of 15.7b

bsearch1.6s

Steps

Iters	Range		Point
10	6.635454334326372e+102	2.1988364261229182e+113	2.0675160110253756e+113
9	1.2213256053674497e-216	3.162643837825275e-207	4.079239898132412e-211
10	-3.3105721778341776e-130	-5.360054782405147e-144	-3.176794358632659e-134
10	-4.4717271713542035e+153	-3.70834960042386e+143	-1.9692685096305275e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	82
1	64	82

end0.0ms

sample14.5s

Algorithm

intervals

Results

4.5s	2299×	body	2560	valid
4.2s	930×	body	5120	valid
3.2s	4073×	body	1280	valid
1.2s	2410×	body	640	valid
367.0ms	998×	body	320	valid
260.0ms	2037×	body	80	valid
111.0ms	454×	body	160	valid

Details

sample401.0ms

simplify27.0ms

prune18.0ms

localize19.0ms

rewrite52.0ms

series919.0ms

simplify133.0ms

prune600.0ms

localize24.0ms

rewrite104.0ms

series1.4s

simplify157.0ms

prune800.0ms

localize25.0ms

rewrite258.0ms

series1.3s

simplify299.0ms

prune718.0ms

localize25.0ms

rewrite189.0ms

series1.1s

simplify176.0ms

prune931.0ms

regimes378.0ms

bsearch1.6s

simplify2.0ms

end0.0ms

sample14.5s

Profiling