Details

sample881.0ms

Algorithm

intervals

Results

261.0ms	59×	body	2560	valid
202.0ms	125×	body	1280	valid
177.0ms	27×	body	5120	valid
140.0ms	89×	body	640	valid
35.0ms	37×	body	320	valid
17.0ms	74×	body	80	valid
5.0ms	9×	body	160	valid

simplify32.0ms

Counts: 1 → 1

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
0.6b	(* (pow t 3.0) (tan k))
22.0b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.4b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite400.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-exp-log`
265×	`prod-exp`
74×	`div-exp` `add-cbrt-cube`
61×	`pow-exp`
41×	`pow-to-exp`
40×	`cbrt-unprod`
25×	`associate-l`
21×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv`
10×	`times-frac`
7×	`associate-r/` `associate-r*`
6×	`pow1`
4×	`tan-quot` `add-log-exp`
3×	`*-commutative` `unswap-sqr` `sqr-pow`
2×	`associate-*l/` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 185

Calls

4 calls:

115.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
30.0ms	(* (pow t 3.0) (tan k))
133.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
108.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.4s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
297.0ms	(* (pow t 3.0) (tan k))
429.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
271.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify116.0ms

Counts: 197 → 197

prune535.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.4b

localize35.0ms

Local error

Found 4 expressions with local error:

1.5b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.8b	(* (pow k 2.0) (pow t 1.0))
17.4b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite262.0ms

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:

19.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
25.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
25.0ms	(* (pow k 2.0) (pow t 1.0))
90.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.0s

Counts

4 → 12

Calls

4 calls:

439.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
115.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
458.0ms	(* (pow k 2.0) (pow t 1.0))
958.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify166.0ms

Counts: 612 → 612

prune937.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
1.5b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.4b	(* (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)))

rewrite627.0ms

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:

6.0ms	(pow (sin k) 2)
79.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
30.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
183.0ms	(* (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)))

series1.4s

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sin k) 2)
447.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
113.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
861.0ms	(* (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)))

simplify275.0ms

Counts: 1472 → 1472

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.7b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.0b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

25023×	`add-exp-log`
19197×	`prod-exp`
16899×	`pow-exp`
11140×	`div-exp`
7959×	`pow-to-exp`
2990×	`rec-exp` `1-exp`
51×	`unpow-prod-down`
43×	`times-frac`
40×	`associate-l`
37×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cbrt-unprod`
13×	`associate-r`
9×	`associate-/r*` `sqr-pow`
8×	`cbrt-undiv`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`associate-*r/` `unpow2` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 5762

Calls

4 calls:

20.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
222.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
17.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
123.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.8s

Counts

4 → 12

Calls

4 calls:

549.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1s	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
117.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.1s	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Counts: 5774 → 5774

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

regimes485.0ms

Accuracy

41.8% (3.0b remaining)

Error of 16.1b against oracle of 13.1b and baseline of 18.2b

bsearch998.0ms

Steps

Iters	Range		Point
8	1.5492993701483207e-155	4.2112186859272586e-153	2.0336407093650901e-153
9	-2.308706360310124e-149	-2.163301048683389e-157	-2.987429350833539e-155

simplify96.0ms

end0.0ms

sample31.7s

Algorithm

intervals

Results

8.7s	4089×	body	1280	valid
8.0s	2258×	body	2560	valid
7.6s	932×	body	5120	valid
3.9s	2520×	body	640	valid
1.5s	1029×	body	320	valid
442.0ms	2027×	body	80	valid
234.0ms	414×	body	160	valid