Details

Time bar (total: 3.8m)

sample5.5s

Algorithm
intervals
Results
2.9s113×body1280valid
1.9s38×body5120valid
397.0ms61×body2560valid
234.0ms86×body640valid
68.0ms39×body320valid
31.0ms69×body80valid
13.0ms13×body160valid

simplify1.3s

Calls
1 calls:
Slowest
1.3s
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.4b

localize179.0ms

Local error

Found 4 expressions with local error:

26.7b
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
1.5b
(/ t (* (/ l t) (/ l t)))
0.9b
(* (tan k) (/ t (* (/ l t) (/ l t))))
0.4b
(/ 2 (* (/ k t) (/ k t)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-/r/
15×add-cbrt-cube add-exp-log
10×associate-*l/
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×frac-times times-frac associate-*r* associate-*r/ associate-/l*
6×pow1 div-inv
4×prod-exp tan-quot cbrt-unprod insert-posit16 add-log-exp
3×cbrt-undiv clear-num associate-/r* frac-2neg div-exp associate-*l*
1×pow-prod-down *-commutative associate-/l/
Calls
4 calls:
Slowest
30.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
11.0ms
(* (tan k) (/ t (* (/ l t) (/ l t))))
2.0ms
(/ 2 (* (/ k t) (/ k t)))
2.0ms
(/ t (* (/ l t) (/ l t)))

series1.1s

Calls
4 calls:
Slowest
647.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
403.0ms
(* (tan k) (/ t (* (/ l t) (/ l t))))
33.0ms
(/ t (* (/ l t) (/ l t)))
30.0ms
(/ 2 (* (/ k t) (/ k t)))

simplify21.6s

Calls
59 calls:
Slowest
4.9s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (* (tan k) (tan k)) (tan k)) (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (sin k)) (sin k))))
1.8s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (* (tan k) (/ t (* (/ l t) (/ l t))))) (* (tan k) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (sin k)) (sin k))))
1.6s
(/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))))
1.1s
(/ (* (cbrt (/ 2 (* (/ k t) (/ k t)))) (cbrt (/ 2 (* (/ k t) (/ k t))))) (* (tan k) (/ t (* (/ l t) (/ l t)))))
1.0s
(/ (/ 2 (* k (/ k t))) (* (tan k) (/ t (* (/ l t) (/ l t)))))

prune3.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize40.0ms

Local error

Found 4 expressions with local error:

16.0b
(/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))
7.4b
(* (* k k) t)
0.5b
(/ (cos k) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))))
0.3b
(* (/ l (sin k)) (/ l (sin k)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
29×times-frac
20×add-cbrt-cube add-exp-log
19×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/r/
9×pow1 associate-/r*
8×div-inv
7×cbrt-undiv div-exp
6×frac-times associate-*l/ associate-*r/
5×associate-*l*
4×associate-*r* insert-posit16 associate-/l* add-log-exp
3×prod-exp cbrt-unprod
2×clear-num frac-2neg *-commutative
1×pow2 pow-plus pow-prod-down pow-prod-up
Calls
4 calls:
Slowest
46.0ms
(/ (cos k) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))))
17.0ms
(/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))
6.0ms
(* (/ l (sin k)) (/ l (sin k)))
5.0ms
(* (* k k) t)

series536.0ms

Calls
4 calls:
Slowest
271.0ms
(/ (cos k) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))))
160.0ms
(/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))
88.0ms
(* (/ l (sin k)) (/ l (sin k)))
16.0ms
(* (* k k) t)

simplify34.4s

Calls
104 calls:
Slowest
3.0s
(/ (* (* (* (* k k) t) (* (* k k) t)) (* (* k k) t)) (* (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k)))))
2.7s
(/ (* (* (cos k) (cos k)) (cos k)) (/ (* (* (* (* k k) t) (* (* k k) t)) (* (* k k) t)) (* (* (* (/ l (sin k)) (/ l (sin k))) (* (/ l (sin k)) (/ l (sin k)))) (* (/ l (sin k)) (/ l (sin k))))))
2.3s
(/ (* (* (* (* k k) t) (* (* k k) t)) (* (* k k) t)) (* (* (* (/ l (sin k)) (/ l (sin k))) (* (/ l (sin k)) (/ l (sin k)))) (* (/ l (sin k)) (/ l (sin k)))))
1.8s
(/ (* (* (cos k) (cos k)) (cos k)) (/ (* (* (* (* k k) t) (* (* k k) t)) (* (* k k) t)) (* (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))))))
1.3s
(/ (* (cbrt (cos k)) (cbrt (cos k))) (/ (* (* k k) t) (* l l)))

prune3.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize83.0ms

Local error

Found 4 expressions with local error:

6.8b
(/ (* (/ l k) (/ l k)) (* t (sin k)))
0.9b
(* (/ (* (/ l k) (/ l k)) (* t (sin k))) (/ (cos k) (sin k)))
0.3b
(/ (cos k) (sin k))
0.2b
(* (/ l k) (/ l k))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
34×add-cbrt-cube add-exp-log
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×times-frac
17×associate-*r*
11×pow1
10×cbrt-undiv div-exp prod-exp cbrt-unprod
9×associate-*l*
6×div-inv
4×associate-/r* insert-posit16 associate-/l* add-log-exp
3×frac-times associate-*l/ associate-*r/ associate-/l/
2×clear-num frac-2neg pow-prod-down *-commutative
1×pow2 pow-plus pow-prod-up
Calls
4 calls:
Slowest
27.0ms
(* (/ (* (/ l k) (/ l k)) (* t (sin k))) (/ (cos k) (sin k)))
16.0ms
(/ (* (/ l k) (/ l k)) (* t (sin k)))
11.0ms
(/ (cos k) (sin k))
8.0ms
(* (/ l k) (/ l k))

series432.0ms

Calls
4 calls:
Slowest
187.0ms
(* (/ (* (/ l k) (/ l k)) (* t (sin k))) (/ (cos k) (sin k)))
180.0ms
(/ (* (/ l k) (/ l k)) (* t (sin k)))
33.0ms
(/ (cos k) (sin k))
31.0ms
(* (/ l k) (/ l k))

simplify31.6s

Calls
97 calls:
Slowest
2.7s
(* (/ (* (* (* (/ l k) (/ l k)) (* (/ l k) (/ l k))) (* (/ l k) (/ l k))) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k)))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (sin k) (sin k)) (sin k))))
2.2s
(* (/ (* (* (* (/ l k) (/ l k)) (/ l k)) (* (* (/ l k) (/ l k)) (/ l k))) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k)))) (* (* (/ (cos k) (sin k)) (/ (cos k) (sin k))) (/ (cos k) (sin k))))
2.2s
(* (/ (* (* (* (/ l k) (/ l k)) (* (/ l k) (/ l k))) (* (/ l k) (/ l k))) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k)))) (* (* (/ (cos k) (sin k)) (/ (cos k) (sin k))) (/ (cos k) (sin k))))
2.2s
(+ (- (+ (log (/ l k)) (log (/ l k))) (log (* t (sin k)))) (- (log (cos k)) (log (sin k))))
2.1s
(* (/ (* (* (* (/ l k) (/ l k)) (/ l k)) (* (* (/ l k) (/ l k)) (/ l k))) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k)))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (sin k) (sin k)) (sin k))))

prune4.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

5.3b
(/ (/ l k) t)
0.9b
(* (* (/ (/ l k) t) (/ (/ l k) (sin k))) (/ (cos k) (sin k)))
0.7b
(* (/ (/ l k) t) (/ (/ l k) (sin k)))
0.3b
(/ (cos k) (sin k))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube add-exp-log
30×times-frac
29×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
12×prod-exp cbrt-unprod
11×pow1
9×div-inv
7×cbrt-undiv div-exp associate-/l*
6×frac-times associate-*l/
5×associate-*l*
4×pow-prod-down associate-*r/ insert-posit16 add-log-exp
3×associate-/r*
2×clear-num frac-2neg *-commutative
1×associate-/l/
Calls
4 calls:
Slowest
156.0ms
(* (* (/ (/ l k) t) (/ (/ l k) (sin k))) (/ (cos k) (sin k)))
8.0ms
(* (/ (/ l k) t) (/ (/ l k) (sin k)))
6.0ms
(/ (/ l k) t)
6.0ms
(/ (cos k) (sin k))

series404.0ms

Calls
4 calls:
Slowest
177.0ms
(* (* (/ (/ l k) t) (/ (/ l k) (sin k))) (/ (cos k) (sin k)))
169.0ms
(* (/ (/ l k) t) (/ (/ l k) (sin k)))
36.0ms
(/ (cos k) (sin k))
20.0ms
(/ (/ l k) t)

simplify22.5s

Calls
105 calls:
Slowest
1.6s
(* (* (/ (/ l k) t) (/ (/ l k) (sin k))) (/ (cos k) (sin k)))
1.6s
(* (* (* (* (/ (/ l k) t) (/ (/ l k) (sin k))) (* (/ (/ l k) t) (/ (/ l k) (sin k)))) (* (/ (/ l k) t) (/ (/ l k) (sin k)))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (sin k) (sin k)) (sin k))))
1.5s
(+ (+ (log (/ (/ l k) t)) (- (log (/ l k)) (log (sin k)))) (- (log (cos k)) (log (sin k))))
1.4s
(* (* (* (* (/ (/ l k) t) (/ (/ l k) t)) (/ (/ l k) t)) (/ (* (* (/ l k) (/ l k)) (/ l k)) (* (* (sin k) (sin k)) (sin k)))) (/ (* (* (cos k) (cos k)) (cos k)) (* (* (sin k) (sin k)) (sin k))))
1.2s
(* (* (/ (/ l k) t) (/ (/ l k) (sin k))) (/ (cos k) (sin k)))

prune2.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0b

regimes1.6s

Accuracy

18.6% (1.4b remaining)

Error of 1.5b against oracle of 0.1b and baseline of 1.8b

bsearch3.1s

end0.0ms

sample1.5m

Algorithm
intervals
Results
27.7s4052×body1280valid
23.1s2249×body2560valid
21.8s927×body5120valid
13.0s2563×body640valid
2.5s1037×body320valid
2.1s2062×body80valid
823.0ms424×body160valid