Details

Time bar (total: 1.6m)

sample1.4s

Algorithm
intervals
Results
390.0ms39×body5120valid
389.0ms87×body2560valid
355.0ms126×body1280valid
139.0ms80×body640valid
36.0ms29×body320valid
24.0ms64×body80valid
16.0ms19×body160valid

simplify233.0ms

Calls
1 calls:
Slowest
233.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.9b

localize418.0ms

Local error

Found 4 expressions with local error:

27.6b
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
0.9b
(/ t (* (/ l t) (/ l t)))
0.8b
(* (tan k) (/ t (* (/ l t) (/ l t))))
0.8b
(* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))

rewrite39.0ms

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
19.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
13.0ms
(* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))
5.0ms
(* (tan k) (/ t (* (/ l t) (/ l t))))
1.0ms
(/ t (* (/ l t) (/ l t)))

series552.0ms

Calls
4 calls:
Slowest
221.0ms
(/ (/ 2 (* (/ k t) (/ k t))) (* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k)))
174.0ms
(* (* (tan k) (/ t (* (/ l t) (/ l t)))) (sin k))
141.0ms
(* (tan k) (/ t (* (/ l t) (/ l t))))
17.0ms
(/ t (* (/ l t) (/ l t)))

simplify13.6s

Calls
70 calls:
Slowest
1.5s
(/ (* (* (/ 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))))
1.3s
(/ (* (* (/ 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))))
1.1s
(/ (* (* (/ 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))))
665.0ms
(/ (/ 2 (* (/ k t) k)) (* (tan k) (/ t (* (/ l t) (/ l t)))))
610.0ms
(/ (/ 2 (* k (/ k t))) (* (tan k) (/ t (* (/ l t) (/ l t)))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))
5.6b
(* (* k k) t)
0.3b
(/ (cos k) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))))
0.3b
(* (/ l (sin k)) (/ l (sin k)))

rewrite45.0ms

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
17.0ms
(/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))
16.0ms
(/ (cos k) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))))
5.0ms
(* (* k k) t)
4.0ms
(* (/ l (sin k)) (/ l (sin k)))

series366.0ms

Calls
4 calls:
Slowest
181.0ms
(/ (cos k) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))))
89.0ms
(/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))
80.0ms
(* (/ l (sin k)) (/ l (sin k)))
16.0ms
(* (* k k) t)

simplify19.0s

Calls
104 calls:
Slowest
1.2s
(/ (* (* (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))))))
1.2s
(/ (* (* (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))))))
833.0ms
(/ (* (* (cos k) (cos k)) (cos k)) (* (* (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k)))) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))) (/ (* (* k k) t) (* (/ l (sin k)) (/ l (sin k))))))
833.0ms
(/ (* (* (* (* 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)))))
809.0ms
(/ (* (* (* (* 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)))))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

7.3b
(* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
0.3b
(/ (/ (cos k) 1) (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))))
0.3b
(* (/ k l) (sin k))
0.3b
(* (/ k l) (sin k))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l/
10×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
8×pow1 associate-*l* associate-*r/
7×associate-*r*
5×div-inv
4×times-frac insert-posit16 associate-/l* add-log-exp
3×associate-/r/ *-commutative
2×frac-times pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv clear-num associate-/r* frac-2neg div-exp associate-/l/
Calls
4 calls:
Slowest
36.0ms
(* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
30.0ms
(/ (/ (cos k) 1) (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))))
7.0ms
(* (/ k l) (sin k))
5.0ms
(* (/ k l) (sin k))

series438.0ms

Calls
4 calls:
Slowest
202.0ms
(/ (/ (cos k) 1) (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))))
115.0ms
(* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
69.0ms
(* (/ k l) (sin k))
52.0ms
(* (/ k l) (sin k))

simplify5.1s

Calls
48 calls:
Slowest
551.0ms
(/ (* (* (/ (cos k) 1) (/ (cos k) 1)) (/ (cos k) 1)) (* (* (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))) (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))) (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))))
483.0ms
(/ (cbrt (/ (cos k) 1)) (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
455.0ms
(/ (/ 1 1) (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
415.0ms
(/ (sqrt (/ (cos k) 1)) (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
279.0ms
(* (* (* (/ k l) (/ k l)) (/ k l)) (* (* (sin k) (sin k)) (sin k)))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

7.3b
(* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
0.3b
(/ 1 (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))))
0.3b
(* (/ k l) (sin k))
0.3b
(* (/ k l) (sin k))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l/
9×pow1 add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cbrt-cube associate-*l* associate-*r/ add-cube-cbrt
7×associate-*r*
4×insert-posit16 add-log-exp
3×associate-/r/ *-commutative div-inv
2×frac-times pow-prod-down prod-exp cbrt-unprod
1×rec-exp clear-num associate-/r* frac-2neg pow-flip inv-pow
Calls
4 calls:
Slowest
37.0ms
(/ 1 (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))))
21.0ms
(* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
4.0ms
(* (/ k l) (sin k))
4.0ms
(* (/ k l) (sin k))

series413.0ms

Calls
4 calls:
Slowest
165.0ms
(/ 1 (* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k)))))
131.0ms
(* t (* (* (/ k l) (sin k)) (* (/ k l) (sin k))))
66.0ms
(* (/ k l) (sin k))
50.0ms
(* (/ k l) (sin k))

simplify2.7s

Calls
35 calls:
Slowest
291.0ms
(* (* (/ k l) (sin k)) (* (/ k l) (sin k)))
261.0ms
(- (+ (* 2/45 (/ (* t (pow k 8)) (pow l 2))) (/ (* t (pow k 4)) (pow l 2))) (* 1/3 (/ (* t (pow k 6)) (pow l 2))))
249.0ms
(* (* (* (/ k l) (/ k l)) (/ k l)) (* (* (sin k) (sin k)) (sin k)))
228.0ms
(/ (* t (* (pow (sin k) 2) (pow k 2))) (pow l 2))
226.0ms
(* (* (* (/ k l) (/ k l)) (/ k l)) (* (* (sin k) (sin k)) (sin k)))

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.0b

regimes657.0ms

Accuracy

44.9% (4.0b remaining)

Error of 4.3b against oracle of 0.3b and baseline of 7.5b

bsearch2.8s

end0.0ms

sample40.8s

Algorithm
intervals
Results
12.8s4006×body1280valid
11.1s2241×body2560valid
8.9s1009×body5120valid
5.0s2586×body640valid
1.4s1012×body320valid
835.0ms1997×body80valid
377.0ms445×body160valid