Details

sample934.0ms

Algorithm

intervals

Results

275.0ms	135×	body	1280	valid
210.0ms	84×	body	640	valid
194.0ms	61×	body	2560	valid
176.0ms	30×	body	5120	valid
25.0ms	26×	body	320	valid
24.0ms	78×	body	80	valid
7.0ms	11×	body	160	valid

simplify113.0ms

Calls

1 calls:

Slowest

113.0ms

(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.7b

localize50.0ms

Local error

Found 4 expressions with local error:

34.5b	(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1))
14.0b	(/ (pow t 3) (* l l))
1.0b	(* (/ (pow t 3) (* l l)) (sin k))
0.9b	(- (+ 1 (pow (/ k t) 2)) 1)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
25×	`add-cbrt-cube`
15×	`prod-exp`
15×	`pow1`
13×	`associate-*l/`
12×	`add-sqr-sqrt`
11×	`cbrt-unprod`
10×	`add-cube-cbrt`
10×	`associate-l`
10×	`times-frac`
10×	`*-un-lft-identity`
9×	`frac-times`
7×	`pow-prod-down`
7×	`associate-r`
6×	`tan-quot`
6×	`div-exp`
5×	`associate-/l*`
5×	`flip--`
5×	`associate-*r/`
5×	`flip3--`
4×	`add-log-exp`
3×	`associate--l+`
3×	`unpow3`
3×	`distribute-lft-in`
3×	`sub-neg`
3×	`cbrt-undiv`
3×	`pow-to-exp`
3×	`cube-mult`
3×	`distribute-rgt-in`
2×	`div-inv`
2×	`*-commutative`
2×	`difference-of-sqr-1`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`

Calls

4 calls:

Slowest

58.0ms	(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1))
9.0ms	(* (/ (pow t 3) (* l l)) (sin k))
8.0ms	(- (+ 1 (pow (/ k t) 2)) 1)
5.0ms	(/ (pow t 3) (* l l))

series451.0ms

Calls

4 calls:

Slowest

325.0ms	(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1))
78.0ms	(* (/ (pow t 3) (* l l)) (sin k))
27.0ms	(/ (pow t 3) (* l l))
21.0ms	(- (+ 1 (pow (/ k t) 2)) 1)

simplify15.2s

Calls

87 calls:

Slowest

855.0ms	(* (* (* (pow t 3) (sin k)) (sin k)) (- (+ 1 (pow (/ k t) 2)) 1))
825.0ms	(* (* (* (pow t 3) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1))
664.0ms	(* (* (* (pow t 3) (sin k)) (tan k)) (- (pow (+ 1 (pow (/ k t) 2)) 3) (pow 1 3)))
580.0ms	(- (+ 1 (pow (/ k t) 2)) 1)
573.0ms	(* (* (* (/ (* (* (pow t 3) (pow t 3)) (pow t 3)) (* (* (* l l) (* l l)) (* l l))) (* (* (sin k) (sin k)) (sin k))) (* (* (tan k) (tan k)) (tan k))) (* (* (- (+ 1 (pow (/ k t) 2)) 1) (- (+ 1 (pow (/ k t) 2)) 1)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.8b

localize37.0ms

Local error

Found 4 expressions with local error:

19.6b	(/ (* t (* (pow k 2) (pow (sin k) 2))) (* (pow l 2) (cos k)))
5.0b	(* t (* (pow k 2) (pow (sin k) 2)))
0.4b	(* (pow k 2) (pow (sin k) 2))
0.4b	(pow (sin k) 2)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`add-cube-cbrt`
8×	`prod-exp`
8×	`associate-r`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`pow-to-exp`
6×	`unpow-prod-down`
5×	`pow1`
4×	`add-log-exp`
4×	`associate-l`
3×	`unpow2`
3×	`pow-exp`
3×	`div-exp`
2×	`cbrt-unprod`
2×	`*-commutative`
2×	`cbrt-undiv`
1×	`associate-/l*`
1×	`div-inv`
1×	`pow-prod-down`
1×	`times-frac`
1×	`frac-2neg`
1×	`pow-pow`
1×	`associate-/r*`
1×	`clear-num`

Calls

4 calls:

Slowest

9.0ms	(/ (* t (* (pow k 2) (pow (sin k) 2))) (* (pow l 2) (cos k)))
7.0ms	(* (pow k 2) (pow (sin k) 2))
7.0ms	(* t (* (pow k 2) (pow (sin k) 2)))
2.0ms	(pow (sin k) 2)

series360.0ms

Calls

4 calls:

Slowest

196.0ms	(/ (* t (* (pow k 2) (pow (sin k) 2))) (* (pow l 2) (cos k)))
96.0ms	(* t (* (pow k 2) (pow (sin k) 2)))
43.0ms	(* (pow k 2) (pow (sin k) 2))
25.0ms	(pow (sin k) 2)

simplify3.7s

Calls

43 calls:

Slowest

551.0ms	(/ (* (* (* t (* (pow k 2) (pow (sin k) 2))) (* t (* (pow k 2) (pow (sin k) 2)))) (* t (* (pow k 2) (pow (sin k) 2)))) (* (* (* (pow l 2) (pow l 2)) (pow l 2)) (* (* (cos k) (cos k)) (cos k))))
492.0ms	(/ (* t (* (pow k 2) (pow (sin k) 2))) (* (pow l 2) (cos k)))
454.0ms	(/ (* (* (* t (* (pow k 2) (pow (sin k) 2))) (* t (* (pow k 2) (pow (sin k) 2)))) (* t (* (pow k 2) (pow (sin k) 2)))) (* (* (* (pow l 2) (cos k)) (* (pow l 2) (cos k))) (* (pow l 2) (cos k))))
437.0ms	(/ (* t (* (pow k 2) (pow (sin k) 2))) (* (pow l 2) (cos k)))
425.0ms	(- (log (* t (* (pow k 2) (pow (sin k) 2)))) (log (* (pow l 2) (cos k))))

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.2b

localize11.0ms

Local error

Found 4 expressions with local error:

19.6b	(/ (* (* t (pow k 2)) (pow (sin k) 2)) (* (pow l 2) (cos k)))
4.7b	(* t (pow k 2))
0.4b	(pow (sin k) 2)
0.4b	(/ 2 (/ (* (* t (pow k 2)) (pow (sin k) 2)) (* (pow l 2) (cos k))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
17×	`prod-exp`
16×	`add-cbrt-cube`
12×	`div-exp`
8×	`pow-to-exp`
7×	`add-cube-cbrt`
7×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
6×	`associate-/r*`
5×	`pow1`
4×	`add-log-exp`
4×	`cbrt-unprod`
4×	`pow-exp`
4×	`associate-r`
4×	`cbrt-undiv`
3×	`div-inv`
3×	`unpow-prod-down`
2×	`unpow2`
2×	`times-frac`
2×	`frac-2neg`
2×	`clear-num`
1×	`associate-/l*`
1×	`*-commutative`
1×	`associate-/r/`
1×	`pow-pow`

Calls

4 calls:

Slowest

12.0ms	(/ (* (* t (pow k 2)) (pow (sin k) 2)) (* (pow l 2) (cos k)))
2.0ms	(/ 2 (/ (* (* t (pow k 2)) (pow (sin k) 2)) (* (pow l 2) (cos k))))
2.0ms	(* t (pow k 2))
2.0ms	(pow (sin k) 2)

series534.0ms

Calls

4 calls:

Slowest

266.0ms	(/ 2 (/ (* (* t (pow k 2)) (pow (sin k) 2)) (* (pow l 2) (cos k))))
229.0ms	(/ (* (* t (pow k 2)) (pow (sin k) 2)) (* (pow l 2) (cos k)))
21.0ms	(pow (sin k) 2)
18.0ms	(* t (pow k 2))

simplify6.9s

Calls

46 calls:

Slowest

888.0ms	(/ (* (* (* (* t (pow k 2)) (* t (pow k 2))) (* t (pow k 2))) (* (* (pow (sin k) 2) (pow (sin k) 2)) (pow (sin k) 2))) (* (* (* (pow l 2) (cos k)) (* (pow l 2) (cos k))) (* (pow l 2) (cos k))))
600.0ms	(- (+ (log (* t (pow k 2))) (* (log (sin k)) 2)) (log (* (pow l 2) (cos k))))
543.0ms	(- (+ (log (* t (pow k 2))) (* (log (sin k)) 2)) (log (* (pow l 2) (cos k))))
516.0ms	(/ (* (* (* (* t (pow k 2)) (* t (pow k 2))) (* t (pow k 2))) (* (* (pow (sin k) 2) (pow (sin k) 2)) (pow (sin k) 2))) (* (* (* (pow l 2) (pow l 2)) (pow l 2)) (* (* (cos k) (cos k)) (cos k))))
499.0ms	(/ (* (* (* (* t (pow k 2)) (pow (sin k) 2)) (* (* t (pow k 2)) (pow (sin k) 2))) (* (* t (pow k 2)) (pow (sin k) 2))) (* (* (* (pow l 2) (pow l 2)) (pow l 2)) (* (* (cos k) (cos k)) (cos k))))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.1b

localize24.0ms

Local error

Found 4 expressions with local error:

19.6b	(/ (* (* (* t k) k) (pow (sin k) 2)) (* (pow l 2) (cos k)))
0.4b	(pow (sin k) 2)
0.4b	(/ 2 (/ (* (* (* t k) k) (pow (sin k) 2)) (* (pow l 2) (cos k))))
0.4b	(* (* (* t k) k) (pow (sin k) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
20×	`prod-exp`
18×	`add-cbrt-cube`
12×	`div-exp`
9×	`pow-to-exp`
8×	`add-cube-cbrt`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`associate-r`
6×	`unpow-prod-down`
6×	`associate-/r*`
5×	`cbrt-unprod`
5×	`pow-exp`
5×	`pow1`
4×	`add-log-exp`
4×	`cbrt-undiv`
3×	`div-inv`
2×	`unpow2`
2×	`times-frac`
2×	`frac-2neg`
2×	`clear-num`
1×	`associate-/l*`
1×	`*-commutative`
1×	`associate-/r/`
1×	`associate-l`
1×	`pow-pow`

Calls

4 calls:

Slowest

19.0ms	(/ (* (* (* t k) k) (pow (sin k) 2)) (* (pow l 2) (cos k)))
8.0ms	(* (* (* t k) k) (pow (sin k) 2))
1.0ms	(/ 2 (/ (* (* (* t k) k) (pow (sin k) 2)) (* (pow l 2) (cos k))))
1.0ms	(pow (sin k) 2)

series535.0ms

Calls

4 calls:

Slowest

232.0ms	(/ 2 (/ (* (* (* t k) k) (pow (sin k) 2)) (* (pow l 2) (cos k))))
202.0ms	(/ (* (* (* t k) k) (pow (sin k) 2)) (* (pow l 2) (cos k)))
84.0ms	(* (* (* t k) k) (pow (sin k) 2))
17.0ms	(pow (sin k) 2)

simplify7.0s

Calls

55 calls:

Slowest

601.0ms	(/ (* (* (* (* (* t k) k) (pow (sin k) 2)) (* (* (* t k) k) (pow (sin k) 2))) (* (* (* t k) k) (pow (sin k) 2))) (* (* (* (pow l 2) (pow l 2)) (pow l 2)) (* (* (cos k) (cos k)) (cos k))))
592.0ms	(* (* (* (* (* t k) k) (* (* t k) k)) (* (* t k) k)) (* (* (pow (sin k) 2) (pow (sin k) 2)) (pow (sin k) 2)))
576.0ms	(/ (* (* (* (* (* t k) k) (* (* t k) k)) (* (* t k) k)) (* (* (pow (sin k) 2) (pow (sin k) 2)) (pow (sin k) 2))) (* (* (* (pow l 2) (cos k)) (* (pow l 2) (cos k))) (* (pow l 2) (cos k))))
543.0ms	(/ (* (* (* (* (* t k) k) (* (* t k) k)) (* (* t k) k)) (* (* (pow (sin k) 2) (pow (sin k) 2)) (pow (sin k) 2))) (* (* (* (pow l 2) (pow l 2)) (pow l 2)) (* (* (cos k) (cos k)) (cos k))))
536.0ms	(/ (* t (* (pow k 2) (pow (sin k) 2))) (* (pow l 2) (cos k)))

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.5b

regimes617.0ms

Accuracy

17.1% (6.1b remaining)

Error of 18.7b against oracle of 12.6b and baseline of 20.0b

bsearch727.0ms

end0.0ms

sample40.4s

Algorithm

intervals

Results

11.5s	2187×	body	2560	valid
11.2s	4121×	body	1280	valid
9.4s	995×	body	5120	valid
5.1s	2526×	body	640	valid
1.5s	1023×	body	320	valid
863.0ms	2059×	body	80	valid
374.0ms	451×	body	160	valid