Details

sample141.0ms

Algorithm

intervals

Results

54.0ms	67×	body	1280	valid
27.0ms	52×	body	640	valid
20.0ms	187×	body	80	valid
18.0ms	36×	body	320	valid
3.0ms	11×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	25
1	47	25
2	153	25
3	759	25
4	3754	25
done	5001	25

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize20.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (/ (pow t 3.0) (* l l)) (sin k))
3.1b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.3b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.1b	(/ (pow t 3.0) (* l l))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`tan-quot` `cbrt-undiv` `pow-to-exp` `pow-exp`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r*`

Counts

4 → 144

Calls

4 calls:

15.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
35.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
295.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms	(/ (pow t 3.0) (* l l))

series1.4s

Counts

4 → 12

Calls

4 calls:

253.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
325.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
636.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
183.0ms	(/ (pow t 3.0) (* l l))

simplify1.5s

Counts

156 → 156

Iterations

Useful iterations: 2 (671.0ms)

Iter	Nodes	Cost
0	255	3209
1	786	3070
2	3733	2565
done	5000	2565

prune512.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.8b

localize26.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.9b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.3b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

304×	`add-exp-log`
184×	`prod-exp`
78×	`add-cbrt-cube`
77×	`div-exp`
50×	`add-sqr-sqrt`
49×	`times-frac`
44×	`associate-*l/` `cbrt-unprod`
42×	`*-un-lft-identity`
37×	`add-cube-cbrt`
36×	`associate-l`
34×	`frac-times`
33×	`pow-exp`
29×	`pow1`
24×	`unpow-prod-down`
22×	`pow-to-exp`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
12×	`cbrt-undiv`
11×	`associate-r`
10×	`cbrt-prod`
8×	`flip3-+` `flip-+` `sqr-pow`
5×	`associate-/l*` `unswap-sqr`
4×	`add-log-exp`
3×	`associate-/r` `-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 229

Calls

4 calls:

78.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
18.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
450.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

371.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
248.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
201.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
744.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify484.0ms

Counts

241 → 241

Iterations

Useful iterations: done (475.0ms)

Iter	Nodes	Cost
0	429	6958
1	1345	6583
done	5001	6450

prune981.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
3.1b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.3b	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

773×	`add-exp-log`
437×	`prod-exp`
291×	`div-exp`
115×	`add-cbrt-cube`
98×	`pow-to-exp` `pow-exp`
63×	`cbrt-unprod`
44×	`associate-*l/`
43×	`add-sqr-sqrt`
36×	`associate-l`
35×	`*-un-lft-identity`
34×	`frac-times` `times-frac`
30×	`pow1` `add-cube-cbrt`
26×	`unpow-prod-down`
25×	`cbrt-undiv`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
13×	`cbrt-prod`
11×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`unswap-sqr` `sqr-pow`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative` `distribute-lft-out`
2×	`pow-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `pow1/3` `div-inv`

Counts

4 → 298

Calls

4 calls:

2.0ms	(pow (cbrt t) 3.0)
170.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
20.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
825.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

313.0ms	(pow (cbrt t) 3.0)
373.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
241.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
749.0ms	(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify546.0ms

Counts

310 → 310

Iterations

Useful iterations: done (534.0ms)

Iter	Nodes	Cost
0	458	10217
1	1550	9300
done	5000	8534

prune980.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 10.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt t) 3.0)
0.8b	(pow (cbrt t) 3.0)
3.8b	(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.8b	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite395.0ms

Algorithm

rewrite-expression-head

Rules

772×	`add-exp-log`
436×	`prod-exp`
291×	`div-exp`
113×	`add-cbrt-cube`
99×	`pow-to-exp` `pow-exp`
62×	`cbrt-unprod`
44×	`add-sqr-sqrt`
35×	`associate-l`
34×	`times-frac`
32×	`unpow-prod-down`
31×	`add-cube-cbrt` `*-un-lft-identity`
29×	`pow1` `frac-times`
26×	`associate-*l/`
25×	`cbrt-undiv`
19×	`associate-*r/`
16×	`cbrt-prod` `pow-prod-down`
12×	`tan-quot`
8×	`flip3-+` `flip-+`
6×	`pow-unpow` `sqr-pow`
5×	`unswap-sqr`
4×	`distribute-rgt-in` `pow-pow` `distribute-lft-in` `associate-r` `add-log-exp`
2×	`pow1/3` `*-commutative`
1×	`div-inv`

Counts

4 → 295

Calls

4 calls:

2.0ms	(pow (cbrt t) 3.0)
2.0ms	(pow (cbrt t) 3.0)
19.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
344.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

314.0ms	(pow (cbrt t) 3.0)
314.0ms	(pow (cbrt t) 3.0)
237.0ms	(* (/ (pow (cbrt t) 3.0) l) (sin k))
763.0ms	(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify561.0ms

Counts

307 → 307

Iterations

Useful iterations: done (549.0ms)

Iter	Nodes	Cost
0	434	10620
1	1489	9713
done	5001	9020

prune773.0ms

Pruning

31 alts after pruning (31 fresh and 0 done)

Merged error: 10.0b

regimes846.0ms

Accuracy

22.6% (5.8b remaining)

Error of 15.7b against oracle of 10.0b and baseline of 17.4b

bsearch401.0ms

Steps

Iters	Range		Point
8	1.8922008845293637e+84	1.1034845283378316e+89	7.584383525453802e+84
8	4.112353450980103e+50	2.35982203985993e+54	1.991576021297121e+52
10	-7.081229578003571e-128	-1.1063856190541223e-137	-2.8340176235482552e-136

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	158
1	71	158
done	71	158

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.7s	2039×	body	1280	valid
859.0ms	1636×	body	640	valid
656.0ms	6034×	body	80	valid
304.0ms	853×	body	320	valid
107.0ms	435×	body	160	valid