Details

sample149.0ms

Algorithm

intervals

Results

55.0ms	75×	body	1280	valid
31.0ms	58×	body	640	valid
23.0ms	172×	body	80	valid
16.0ms	32×	body	320	valid
2.0ms	9×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5086	25

prune15.0ms

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: 29.0b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
4.8b	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
7.1b	(* (/ 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))))))

rewrite104.0ms

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:

21.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
29.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
25.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
21.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
132.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
205.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
112.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5029	3715

prune317.0ms

Filtered

92 candidates to 164 candidates (-78.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	9	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	156	10	166

Merged error: 22.0b

Counts

166 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
4.8b	(* 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))
7.1b	(* (/ 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)
15.4b	(* (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))))

rewrite137.0ms

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:

19.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
34.0ms	(* 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))
33.0ms	(* (/ 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)
29.0ms	(* (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))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
145.0ms	(* 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))
230.0ms	(* (/ 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)
124.0ms	(* (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))))

simplify67.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5005	6558

prune397.0ms

Filtered

90 candidates to 222 candidates (-146.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	213	9	222
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	216	16	232

Merged error: 18.6b

Counts

232 → 16

localize33.0ms

Local error

Found 4 expressions with local error:

4.5b	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
4.8b	(* 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))
5.4b	(* (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)))))
7.1b	(* (/ 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)

rewrite209.0ms

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:

24.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
50.0ms	(* 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))
33.0ms	(* (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)))))
45.0ms	(* (/ 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)

series579.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
145.0ms	(* 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))
125.0ms	(* (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)))))
233.0ms	(* (/ 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)

simplify136.0ms

Algorithm

egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5102	14009

prune433.0ms

Filtered

86 candidates to 403 candidates (-368.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	397	6	403
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	400	19	419

Merged error: 15.5b

Counts

419 → 19

localize33.0ms

Local error

Found 4 expressions with local error:

4.8b	(* 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)))))))))
5.1b	(* (/ 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))))))))
5.7b	(* (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)))))
10.1b	(* 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)))))))

rewrite321.0ms

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:

61.0ms	(* 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)))))))))
42.0ms	(* (/ 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))))))))
30.0ms	(* (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)))))
32.0ms	(* 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)))))))

series628.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* 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)))))))))
199.0ms	(* (/ 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))))))))
121.0ms	(* (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)))))
165.0ms	(* 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)))))))

simplify260.0ms

Algorithm

egg-herbie

Counts

900 → 900

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5431	33261

prune392.0ms

Filtered

96 candidates to 900 candidates (-837.5%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	893	7	900
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	896	23	919

Merged error: 14.5b

Counts

919 → 23

regimes1.4s

Accuracy

21.5% (5.3b remaining)

Error of 18.4b against oracle of 13.2b and baseline of 19.8b

bsearch221.0ms

Steps

Iters	Range	Point
2	2.559599023499027e+108	3.113903656401177e+108	2.7674632608373334e+108
9	-5.0994168056953787e-154	-6.728240533841265e-160	-6.836749431022513e-160
8	-5.219179957878739e+123	-5.590082551980238e+120	-1.0049859230952732e+123

Iters

Range

Point

2.559599023499027e+108

3.113903656401177e+108

2.7674632608373334e+108

-5.0994168056953787e-154

-6.728240533841265e-160

-6.836749431022513e-160

-5.219179957878739e+123

-5.590082551980238e+120

-1.0049859230952732e+123

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	142	222
1	142	222

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.6s	2155×	body	1280	valid
936.0ms	1718×	body	640	valid
751.0ms	5734×	body	80	valid
341.0ms	853×	body	320	valid
116.0ms	435×	body	160	valid

Details

sample149.0ms

simplify24.0ms

prune15.0ms

localize21.0ms

rewrite104.0ms

series586.0ms

simplify55.0ms

prune317.0ms

localize26.0ms

rewrite137.0ms

series582.0ms

simplify67.0ms

prune397.0ms

localize33.0ms

rewrite209.0ms

series579.0ms

simplify136.0ms

prune433.0ms

localize33.0ms

rewrite321.0ms

series628.0ms

simplify260.0ms

prune392.0ms

regimes1.4s

bsearch221.0ms

simplify2.0ms

end0.0ms

sample4.3s

Profiling