Details

analyze2.8s

Algorithm: search

sample482.0ms

Algorithm

intervals

Results

131.0ms	27×	body	5120	invalid
99.0ms	115×	body	1280	valid
93.0ms	35×	body	2560	invalid
38.0ms	27×	body	2560	valid
37.0ms	60×	body	640	valid
25.0ms	33×	body	1280	invalid
8.0ms	22×	body	320	valid
7.0ms	3×	body	5120	valid
6.0ms	11×	body	640	invalid
6.0ms	16×	body	320	invalid
4.0ms	28×	body	80	invalid
3.0ms	10×	body	160	valid
3.0ms	19×	body	80	valid
2.0ms	8×	body	160	invalid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (23.0ms)

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

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 36.2b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
17.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite49.0ms

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))
18.0ms	(/ (* 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)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ k t) 2.0)
56.0ms	(* (pow t 3.0) (tan k))
115.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
76.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1123	2068
1	5002	1738

prune292.0ms

Filtered

93 candidates to 191 candidates (-105.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	181	10	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	182	11	193

Merged error: 26.2b

Counts

193 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow t 3.0) (tan k))
15.3b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
17.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
19.2b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1168×	`prod-exp`
346×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
55×	`cbrt-unprod`
41×	`associate-l`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`cbrt-undiv`
9×	`associate-*r/`
5×	`associate-r`
4×	`tan-quot` `pow1` `add-log-exp` `sqr-pow`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 408

Calls

4 calls:

5.0ms	(* (pow t 3.0) (tan k))
17.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
28.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (pow t 3.0) (tan k))
71.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
113.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
75.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify86.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5002	5612

prune407.0ms

Filtered

110 candidates to 420 candidates (-281.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	417	3	420
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	419	12	431

Merged error: 26.2b

Counts

431 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
9.9b	(* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
15.3b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
17.5b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (sin k)))

rewrite685.0ms

Algorithm

rewrite-expression-head

Rules

18119×	`add-exp-log`
13949×	`prod-exp`
5103×	`pow-exp`
4242×	`div-exp`
2137×	`pow-to-exp`
578×	`rec-exp` `1-exp`
131×	`add-cbrt-cube`
82×	`cbrt-unprod`
54×	`associate-l`
42×	`unpow-prod-down`
31×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-undiv`
13×	`associate-*r/`
9×	`cbrt-prod`
4×	`tan-quot` `pow1` `div-inv` `add-log-exp`
3×	`associate-r` `*-commutative` `sqr-pow`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 2764

Calls

4 calls:

19.0ms	(* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
13.0ms	(* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
44.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
95.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (sin k)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
96.0ms	(* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
88.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
134.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (sin k)))

simplify629.0ms

Algorithm

egg-herbie

Counts

2776 → 2776

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5002	77059

prune853.0ms

Filtered

165 candidates to 2776 candidates (-1582.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	2773	3	2776
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	2774	14	2788

Merged error: 25.7b

Counts

2788 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
9.9b	(* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
14.5b	(* (pow (/ 1 t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
17.5b	(/ (* 2.0 (* l l)) (* (* (pow k (/ 2.0 2)) (* (pow (/ 1 t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))) (sin k)))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

75889×	`add-exp-log`
62068×	`prod-exp`
22794×	`pow-exp`
17759×	`div-exp`
9752×	`pow-to-exp`
3614×	`rec-exp` `1-exp`
158×	`add-cbrt-cube`
103×	`cbrt-unprod`
54×	`associate-l`
42×	`unpow-prod-down`
31×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
21×	`cbrt-undiv`
14×	`associate-*r/`
9×	`cbrt-prod`
4×	`tan-quot` `pow1` `div-inv` `add-log-exp`
3×	`associate-r` `*-commutative` `sqr-pow`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 9552

Calls

4 calls:

33.0ms	(* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
13.0ms	(* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
39.0ms	(* (pow (/ 1 t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
344.0ms	(/ (* 2.0 (* l l)) (* (* (pow k (/ 2.0 2)) (* (pow (/ 1 t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))) (sin k)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
95.0ms	(* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
101.0ms	(* (pow (/ 1 t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))
134.0ms	(/ (* 2.0 (* l l)) (* (* (pow k (/ 2.0 2)) (* (pow (/ 1 t) (/ 2.0 2)) (* (pow (/ 1 (* (cbrt t) (cbrt t))) (/ 2.0 2)) (* (pow (/ k (cbrt t)) (/ 2.0 2)) (* (pow t 3.0) (tan k)))))) (sin k)))

simplify3.2s

Algorithm

egg-herbie

Counts

9564 → 9564

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5013	334766

prune36.6s

Filtered

3070 candidates to 9564 candidates (-211.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	9559	5	9564
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	9561	17	9578

Merged error: 23.8b

Counts

9578 → 17

regimes921.0ms

Accuracy

52.5% (4.6b remaining)

Error of 30.8b against oracle of 26.2b and baseline of 35.9b

bsearch3.3s

Steps

Iters	Range	Point
7	9.42820227542079e-137	6.122624504769368e-135	5.993295287220876e-135
9	-1.439896126589276e-306	8.391718756410277e-302	-5.07998190631281e-309
8	-1.3635869151008458e-104	-1.7912848569799995e-108	-2.435112747370758e-108

Iters

Range

Point

9.42820227542079e-137

6.122624504769368e-135

5.993295287220876e-135

-1.439896126589276e-306

8.391718756410277e-302

-5.07998190631281e-309

-1.3635869151008458e-104

-1.7912848569799995e-108

-2.435112747370758e-108

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	111	116
1	111	116

end0.0ms

analyze2.6s

Algorithm: search

sample14.8s

Algorithm

intervals

Results

3.3s	1229×	body	2560	invalid
3.3s	710×	body	5120	invalid
3.0s	3321×	body	1280	valid
1.4s	982×	body	2560	valid
1.1s	1970×	body	640	valid
628.0ms	773×	body	1280	invalid
619.0ms	194×	body	5120	valid
269.0ms	521×	body	640	invalid
262.0ms	641×	body	320	valid
142.0ms	340×	body	320	invalid
124.0ms	885×	body	80	invalid
87.0ms	642×	body	80	valid
68.0ms	250×	body	160	valid
49.0ms	197×	body	160	invalid

Details

analyze2.8s

sample482.0ms

simplify25.0ms

prune18.0ms

localize19.0ms

rewrite49.0ms

series259.0ms

simplify45.0ms

prune292.0ms

localize24.0ms

rewrite105.0ms

series312.0ms

simplify86.0ms

prune407.0ms

localize35.0ms

rewrite685.0ms

series421.0ms

simplify629.0ms

prune853.0ms

localize35.0ms

rewrite2.8s

series430.0ms

simplify3.2s

prune36.6s

regimes921.0ms

bsearch3.3s

simplify3.0ms

end0.0ms

analyze2.6s

sample14.8s

Profiling