Details

analyze2.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample130.0ms

Algorithm

intervals

Results

47.0ms	54×	body	1280	valid
34.0ms	61×	body	640	valid
13.0ms	103×	body	80	valid
10.0ms	27×	body	320	valid
5.0ms	40×	body	80	invalid
3.0ms	6×	body	640	invalid
3.0ms	11×	body	160	valid
1.0ms	3×	body	320	invalid
1.0ms	2×	body	160	invalid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5086	25

prune13.0ms

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: 30.3b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
3.6b	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
8.1b	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
22.4b	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
106×	`prod-exp`
74×	`add-cbrt-cube`
40×	`cbrt-unprod`
37×	`associate-*r/`
30×	`div-exp`
22×	`associate-l`
14×	`add-sqr-sqrt`
12×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `pow-exp`
11×	`pow1`
10×	`associate-/r/`
9×	`tan-quot`
6×	`frac-times` `flip3-+` `times-frac` `flip-+`
5×	`associate-r` `associate-*l/`
4×	`pow-prod-down` `add-log-exp`
3×	`unpow-prod-down` `-commutative` `associate-/l`
2×	`div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*` `unswap-sqr` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

18.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
22.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
24.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
18.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

series522.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
116.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
182.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
103.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5089	3723

prune279.0ms

Filtered

92 candidates to 164 candidates (-78.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	8	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	9	166

Merged error: 21.6b

Counts

166 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
3.6b	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
8.1b	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
17.0b	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

551×	`add-exp-log`
424×	`prod-exp`
85×	`add-cbrt-cube`
74×	`pow-exp`
66×	`div-exp`
52×	`cbrt-unprod`
50×	`pow-to-exp`
27×	`associate-*r/`
21×	`associate-l`
20×	`associate-*l/`
15×	`associate-r`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`cbrt-undiv`
9×	`tan-quot`
7×	`unpow-prod-down`
6×	`frac-times` `flip3-+` `flip-+`
5×	`associate-/r/`
4×	`pow-prod-down` `*-commutative` `add-log-exp`
3×	`cbrt-prod` `times-frac`
2×	`sqr-pow`
1×	`div-inv` `unswap-sqr`

Counts

4 → 210

Calls

4 calls:

20.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
29.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
27.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
26.0ms	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

series517.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
129.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
204.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
111.0ms	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

simplify85.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5027	6570

prune549.0ms

Filtered

90 candidates to 222 candidates (-146.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	214	8	222
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	215	16	231

Merged error: 17.3b

Counts

231 → 16

localize34.0ms

Local error

Found 4 expressions with local error:

3.6b	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
4.3b	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
6.3b	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
8.1b	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

1830×	`add-exp-log`
1542×	`prod-exp`
314×	`pow-exp`
183×	`pow-to-exp`
178×	`div-exp`
112×	`add-cbrt-cube`
73×	`cbrt-unprod`
32×	`associate-*l/`
27×	`associate-*r/`
21×	`associate-l`
12×	`cbrt-undiv` `add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`tan-quot`
6×	`frac-times` `flip3-+` `flip-+`
5×	`associate-/r/`
4×	`pow-prod-down` `*-commutative` `add-log-exp`
3×	`times-frac`
2×	`unpow-prod-down` `sqr-pow`
1×	`div-inv` `unswap-sqr`

Counts

4 → 391

Calls

4 calls:

43.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
20.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
28.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
37.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

series515.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
70.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
109.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
207.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

simplify142.0ms

Algorithm

egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5003	14021

prune407.0ms

Filtered

86 candidates to 403 candidates (-368.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	397	6	403
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	399	20	419

Merged error: 14.4b

Counts

419 → 20

localize36.0ms

Local error

Found 4 expressions with local error:

3.6b	(* l (* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
4.9b	(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
6.6b	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
10.4b	(* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

5308×	`add-exp-log`
4102×	`prod-exp`
1107×	`div-exp`
772×	`pow-exp`
442×	`pow-to-exp`
216×	`rec-exp` `1-exp`
215×	`add-cbrt-cube`
133×	`cbrt-unprod`
39×	`cbrt-undiv`
34×	`associate-*r/`
30×	`associate-l`
20×	`pow1` `add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
15×	`associate-r`
12×	`associate-*l/`
10×	`pow-prod-down`
6×	`tan-quot` `frac-times`
5×	`associate-/r/`
4×	`unpow-prod-down` `flip3-+` `*-commutative` `flip-+` `add-log-exp` `sqr-pow`
2×	`div-inv`
1×	`unswap-sqr`

Counts

4 → 888

Calls

4 calls:

51.0ms	(* l (* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
37.0ms	(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
24.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
30.0ms	(* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* l (* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
173.0ms	(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
107.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
140.0ms	(* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

simplify256.0ms

Algorithm

egg-herbie

Counts

900 → 900

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5064	33283

prune391.0ms

Filtered

96 candidates to 900 candidates (-837.5%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	890	10	900
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	893	27	920

Merged error: 13.6b

Counts

920 → 27

regimes1.5s

Accuracy

22.9% (4.6b remaining)

Error of 17.7b against oracle of 13.1b and baseline of 19.1b

bsearch2.0s

Steps

Iters	Range		Point
10	4.800631009828841e-106	7.708879833570746e-94	2.2844510146699535e-95
7	-3.1646382374424315e-251	-1.6395643651991098e-253	-3.3013132694615146e-252

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	156
1	83	156

end0.0ms

analyze2.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample3.9s

Algorithm

intervals

Results

1.6s	2059×	body	1280	valid
866.0ms	1590×	body	640	valid
420.0ms	3245×	body	80	valid
310.0ms	785×	body	320	valid
185.0ms	1452×	body	80	invalid
84.0ms	321×	body	160	valid
73.0ms	132×	body	640	invalid
40.0ms	106×	body	320	invalid
23.0ms	87×	body	160	invalid
23.0ms	30×	body	1280	invalid

Details

analyze2.1s

sample130.0ms

simplify23.0ms

prune13.0ms

localize20.0ms

rewrite88.0ms

series522.0ms

simplify49.0ms

prune279.0ms

localize27.0ms

rewrite117.0ms

series517.0ms

simplify85.0ms

prune549.0ms

localize34.0ms

rewrite179.0ms

series515.0ms

simplify142.0ms

prune407.0ms

localize36.0ms

rewrite289.0ms

series550.0ms

simplify256.0ms

prune391.0ms

regimes1.5s

bsearch2.0s

simplify2.0ms

end0.0ms

analyze2.1s

sample3.9s

Profiling