Details

Time bar (total: 1.7m)

sample1.2s

Algorithm
intervals
Results
323.0ms33×body5120valid
323.0ms74×body2560valid
279.0ms125×body1280valid
220.0ms92×body640valid
30.0ms24×body320valid
23.0ms64×body80valid
12.0ms13×body160valid

simplify581.0ms

Calls
1 calls:
Slowest
581.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize55.0ms

Local error

Found 4 expressions with local error:

31.0b
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
1.5b
(/ t (* (/ l t) (/ l t)))
1.0b
(* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))
0.8b
(* (tan k) (/ t (* (/ l t) (/ l t))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
15×associate-/r/
13×associate-*l/
11×pow1
10×associate-*r*
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×frac-times times-frac prod-exp associate-*r/ cbrt-unprod associate-/l*
6×tan-quot
5×div-inv
4×associate-*l* pow-prod-down insert-posit16 add-log-exp
3×cbrt-undiv div-exp
2×clear-num associate-/r* frac-2neg *-commutative
1×associate-/l/
Calls
4 calls:
Slowest
18.0ms
(* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))
15.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
10.0ms
(* (tan k) (/ t (* (/ l t) (/ l t))))
1.0ms
(/ t (* (/ l t) (/ l t)))

series554.0ms

Calls
4 calls:
Slowest
233.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
152.0ms
(* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))
143.0ms
(* (tan k) (/ t (* (/ l t) (/ l t))))
26.0ms
(/ t (* (/ l t) (/ l t)))

simplify14.7s

Calls
70 calls:
Slowest
1.7s
(/ (* (* (/ 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))))
1.4s
(/ (* (* (/ 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))))
1.0s
(/ (* (* (/ 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))))
660.0ms
(/ (/ 2 (* (/ k t) k)) (* (tan k) (/ t (* (/ l t) (/ l t)))))
612.0ms
(/ (/ 2 (* k (/ k t))) (* (tan k) (/ t (* (/ l t) (/ l t)))))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.5b

localize37.0ms

Local error

Found 4 expressions with local error:

11.4b
(* (/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k) (/ t (sin k)))
7.0b
(* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t))))
3.8b
(/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k)
0.3b
(* (/ l t) (/ l t))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*r/
13×pow1 associate-*l*
12×frac-times
10×add-cbrt-cube add-exp-log
9×add-sqr-sqrt *-un-lft-identity associate-*r* associate-*l/ add-cube-cbrt
7×associate-/l/
6×div-inv
4×insert-posit16 add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod
1×pow2 clear-num frac-2neg pow-plus tan-quot associate-/r/ pow-prod-up associate-/l*
Calls
4 calls:
Slowest
25.0ms
(* (/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k) (/ t (sin k)))
21.0ms
(/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k)
14.0ms
(* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t))))
8.0ms
(* (/ l t) (/ l t))

series532.0ms

Calls
4 calls:
Slowest
197.0ms
(* (/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k) (/ t (sin k)))
180.0ms
(* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t))))
140.0ms
(/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k)
14.0ms
(* (/ l t) (/ l t))

simplify7.3s

Calls
64 calls:
Slowest
603.0ms
(* (* (* (/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k) (/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k)) (/ (* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) (/ l t)))) k)) (* (* (/ t (sin k)) (/ t (sin k))) (/ t (sin k))))
386.0ms
(- (* 2 (/ (pow l 2) (* t (pow k 4)))) (* 1/3 (/ (pow l 2) (* t (pow k 2)))))
345.0ms
(* 2 (* 1 (* (/ l t) (/ l t))))
322.0ms
(* 2 (* 1 (* (/ l t) (/ l t))))
320.0ms
(* (/ 2 (* (tan k) k)) (* 1 (* (/ l t) l)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.9b

localize29.0ms

Local error

Found 4 expressions with local error:

11.4b
(* (/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k) (/ t (sin k)))
7.9b
(* (/ l t) (/ (/ (cos k) (sin k)) k))
3.8b
(/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k)
0.4b
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*l/
13×pow1 add-cbrt-cube add-exp-log
12×frac-times associate-*l* associate-*r/
9×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
7×associate-/l/
6×div-inv
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×*-commutative
1×clear-num frac-2neg associate-/l*
Calls
4 calls:
Slowest
106.0ms
(* (/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k) (/ t (sin k)))
65.0ms
(/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k)
16.0ms
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))
14.0ms
(* (/ l t) (/ (/ (cos k) (sin k)) k))

series827.0ms

Calls
4 calls:
Slowest
262.0ms
(* (/ l t) (/ (/ (cos k) (sin k)) k))
214.0ms
(* (/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k) (/ t (sin k)))
177.0ms
(/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k)
174.0ms
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))

simplify10.3s

Calls
63 calls:
Slowest
545.0ms
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))
511.0ms
(* (* (* (/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k) (/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k)) (/ (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) k)) (* (* (/ t (sin k)) (/ t (sin k))) (/ t (sin k))))
506.0ms
(* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2)
468.0ms
(* (* l (* (/ l t) (/ (cos k) (sin k)))) 2)
461.0ms
(* (* (/ l t) (* l (/ (cos k) (sin k)))) 2)

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.2b

localize6.0ms

Local error

Found 4 expressions with local error:

11.1b
(* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k)))
7.9b
(* (/ l t) (/ (/ (cos k) (sin k)) k))
5.6b
(/ (* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k))) k)
0.4b
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
58×associate-*l/
40×frac-times
28×associate-*r/
15×associate-/l/
13×pow1 add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow-prod-down prod-exp cbrt-unprod div-inv
4×insert-posit16 add-log-exp
3×*-commutative
1×clear-num frac-2neg associate-/l*
Calls
4 calls:
Slowest
129.0ms
(/ (* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k))) k)
113.0ms
(* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k)))
23.0ms
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))
8.0ms
(* (/ l t) (/ (/ (cos k) (sin k)) k))

series829.0ms

Calls
4 calls:
Slowest
249.0ms
(* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k)))
201.0ms
(* (/ l t) (/ (/ (cos k) (sin k)) k))
200.0ms
(/ (* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k))) k)
179.0ms
(* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k)))

simplify15.5s

Calls
87 calls:
Slowest
637.0ms
(* (* (* (/ l t) (* l (/ (cos k) (sin k)))) 2) (/ t (sin k)))
592.0ms
(* (* (* (/ l t) (* l (/ (cos k) (sin k)))) 2) (/ t (sin k)))
545.0ms
(* (* (* l (* (/ l t) (/ (cos k) (sin k)))) 2) (/ t (sin k)))
536.0ms
(* (* (* l (* l (/ (/ (cos k) (sin k)) k))) 2) (/ t (sin k)))
528.0ms
(* (* (* (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2) (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2)) (* (* (/ l t) (* (/ l t) (/ (/ (cos k) (sin k)) k))) 2)) (* (* (/ t (sin k)) (/ t (sin k))) (/ t (sin k))))

prune1.8s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 2.9b

regimes692.0ms

Accuracy

48.7% (6.2b remaining)

Error of 8.2b against oracle of 2.0b and baseline of 14.1b

bsearch3.3s

end0.0ms

sample40.4s

Algorithm
intervals
Results
12.4s4050×body1280valid
10.4s2154×body2560valid
9.5s1000×body5120valid
5.1s2526×body640valid
1.2s990×body320valid
962.0ms2053×body80valid
343.0ms457×body160valid