Details

sample549.0ms

Algorithm

intervals

Results

202.0ms	135×	body	1280	valid
138.0ms	58×	body	2560	valid
97.0ms	19×	body	5120	valid
59.0ms	86×	body	640	valid
13.0ms	28×	body	320	valid
9.0ms	61×	body	80	valid
4.0ms	12×	body	160	valid

simplify25.0ms

Counts: 1 → 1

prune56.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
1.1b	(* (pow t 3.0) (tan k))
21.2b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.6b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite239.0ms

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:

7.0ms	(pow (/ k t) 2.0)
19.0ms	(* (pow t 3.0) (tan k))
132.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
69.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.3s

Counts

4 → 12

Calls

4 calls:

96.0ms	(pow (/ k t) 2.0)
321.0ms	(* (pow t 3.0) (tan k))
536.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
395.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify131.0ms

Counts: 191 → 191

prune632.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.8b	(* (pow k 2.0) (pow t 1.0))
17.3b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite271.0ms

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:

27.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
27.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
27.0ms	(* (pow k 2.0) (pow t 1.0))
86.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.9s

Counts

4 → 12

Calls

4 calls:

491.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
146.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
513.0ms	(* (pow k 2.0) (pow t 1.0))
783.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify167.0ms

Counts: 612 → 612

prune855.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.5b	(/ 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))
17.3b	(* (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)))

rewrite537.0ms

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:

4.0ms	(pow (sin k) 2)
60.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
21.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
194.0ms	(* (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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sin k) 2)
506.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
108.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
873.0ms	(* (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)))

simplify287.0ms

Counts: 1472 → 1472

prune801.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.0b	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
3.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.5b	(* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

5981×	`add-exp-log`
3859×	`prod-exp`
3047×	`pow-exp`
2534×	`div-exp`
1627×	`pow-to-exp`
84×	`unpow-prod-down`
70×	`times-frac`
64×	`associate-l`
52×	`add-sqr-sqrt`
47×	`add-cube-cbrt` `*-un-lft-identity`
37×	`add-cbrt-cube`
30×	`sqrt-prod`
14×	`cbrt-unprod`
13×	`associate-r`
12×	`sqr-pow`
9×	`associate-/r*`
8×	`cbrt-undiv`
7×	`associate-/l*`
5×	`div-inv`
4×	`pow1` `add-log-exp`
3×	`associate-*r/` `unpow2` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`

Counts

4 → 1370

Calls

4 calls:

14.0ms	(/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
217.0ms	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
366.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
92.0ms	(* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

415.0ms	(/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
789.0ms	(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
98.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
908.0ms	(* (pow (/ (sqrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify362.0ms

Counts: 1382 → 1382

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

regimes727.0ms

Accuracy

30.7% (3.5b remaining)

Error of 16.2b against oracle of 12.7b and baseline of 17.7b

bsearch1.1s

Steps

Iters	Range		Point
9	1.2896822248683738e-160	3.5672657208799707e-153	1.0543460049915535e-155
8	-1.219730356203349e-148	-7.621802709561935e-152	-2.7986257638741188e-151

simplify51.0ms

end0.0ms

sample32.7s

Algorithm

intervals

Results

9.4s	4079×	body	1280	valid
9.0s	2274×	body	2560	valid
8.1s	956×	body	5120	valid
3.3s	2510×	body	640	valid
857.0ms	983×	body	320	valid
767.0ms	2062×	body	80	valid
293.0ms	445×	body	160	valid