Details

Time bar (total: 6.2m)

sample1.7s

Algorithm
intervals
Results
875.0ms93×body2560valid
354.0ms116×body1280valid
227.0ms24×body5120valid
145.0ms80×body640valid
31.0ms20×body320valid
23.0ms55×body80valid
11.0ms13×body160valid

simplify325.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
325.0ms
(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (- (+ 1 (pow (/ k t) 2)) 1)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.7b

localize34.0ms

Local error

Found 4 expressions with local error:

30.3b
(/ (/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (tan k)) (* (/ k t) (/ k t)))
1.7b
(* (/ 2 t) (* (/ l t) (/ l t)))
1.4b
(/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))
1.2b
(/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (tan k))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
668×add-cbrt-cube add-exp-log
370×cbrt-undiv div-exp
196×prod-exp cbrt-unprod
132×times-frac
60×add-sqr-sqrt
57×*-un-lft-identity add-cube-cbrt
34×associate-/l*
16×div-inv
13×associate-*l*
11×frac-times associate-*r/
9×pow1 associate-/l/
7×associate-/r* associate-*l/
6×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-prod-down tan-quot
2×unswap-sqr
1×associate-*r* *-commutative
Counts
4 → 375
Calls
4 calls:
Slowest
75.0ms
(/ (/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (tan k)) (* (/ k t) (/ k t)))
56.0ms
(/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))
32.0ms
(/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (tan k))
29.0ms
(* (/ 2 t) (* (/ l t) (/ l t)))

series931.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
392.0ms
(/ (/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (tan k)) (* (/ k t) (/ k t)))
346.0ms
(/ (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (tan k))
127.0ms
(/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))
65.0ms
(* (/ 2 t) (* (/ l t) (/ l t)))

simplify2.1m

Counts
444 → 387
Calls
444 calls:
Slowest
1.5s
(/ (/ (/ (* (* (* (/ 2 t) (* (/ l t) (/ l t))) (* (/ 2 t) (* (/ l t) (/ l t)))) (* (/ 2 t) (* (/ l t) (/ l t)))) (* (* (sin k) (sin k)) (sin k))) (* (* (tan k) (tan k)) (tan k))) (* (* (* (/ k t) (/ k t)) (* (/ k t) (/ k t))) (* (/ k t) (/ k t))))
1.2s
(/ (/ (* (* (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))) (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))) (* (* (tan k) (tan k)) (tan k))) (* (/ (* (* k k) k) (* (* t t) t)) (/ (* (* k k) k) (* (* t t) t))))
1.2s
(/ (/ (* (* (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k)) (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))) (/ (* (/ 2 t) (* (/ l t) (/ l t))) (sin k))) (* (* (tan k) (tan k)) (tan k))) (* (* (* (/ k t) (/ k t)) (/ k t)) (/ (* (* k k) k) (* (* t t) t))))
1.2s
(/ (/ (* (/ (* (* 2 2) 2) (* (* t t) t)) (* (* (* (/ l t) (/ l t)) (/ l t)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (sin k) (sin k)) (sin k))) (* (* (tan k) (tan k)) (tan k)))
1.2s
(/ (/ (* (/ (* (* 2 2) 2) (* (* t t) t)) (* (/ (* (* l l) l) (* (* t t) t)) (* (* (/ l t) (/ l t)) (/ l t)))) (* (* (sin k) (sin k)) (sin k))) (* (* (tan k) (tan k)) (tan k)))

prune5.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.0b

localize53.0ms

Local error

Found 4 expressions with local error:

8.2b
(* (/ (cos k) t) (* (/ l (* (sin k) k)) (/ l (* (sin k) k))))
2.7b
(/ l (* (sin k) k))
2.7b
(/ l (* (sin k) k))
0.3b
(* (/ l (* (sin k) k)) (/ l (* (sin k) k)))

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
154×add-cbrt-cube add-exp-log
67×prod-exp cbrt-unprod
50×cbrt-undiv div-exp
28×add-sqr-sqrt times-frac
23×*-un-lft-identity add-cube-cbrt
20×associate-*l*
16×pow1
8×associate-*r*
7×swap-sqr div-inv
6×frac-times associate-*r/ associate-/l*
4×expm1-log1p-u pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
2×clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up
Counts
4 → 183
Calls
4 calls:
Slowest
149.0ms
(* (/ (cos k) t) (* (/ l (* (sin k) k)) (/ l (* (sin k) k))))
43.0ms
(* (/ l (* (sin k) k)) (/ l (* (sin k) k)))
17.0ms
(/ l (* (sin k) k))
15.0ms
(/ l (* (sin k) k))

series505.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
284.0ms
(* (/ (cos k) t) (* (/ l (* (sin k) k)) (/ l (* (sin k) k))))
82.0ms
(* (/ l (* (sin k) k)) (/ l (* (sin k) k)))
71.0ms
(/ l (* (sin k) k))
68.0ms
(/ l (* (sin k) k))

simplify1.1m

Counts
214 → 195
Calls
214 calls:
Slowest
2.3s
(* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (* (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k))) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))))
2.0s
(* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (* (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k))) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))))
1.8s
(* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (* (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k))) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))))
1.5s
(* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (* (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k))) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))))
1.5s
(* (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k))) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k))))

prune2.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 1.0b

localize38.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (cos k) t) (/ l (* (sin k) k)))
2.7b
(/ l (* (sin k) k))
2.7b
(/ l (* (sin k) k))
0.2b
(* (* (/ (cos k) t) (/ l (* (sin k) k))) (/ l (* (sin k) k)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
143×add-cbrt-cube add-exp-log
62×prod-exp cbrt-unprod
46×cbrt-undiv div-exp
24×add-sqr-sqrt
22×times-frac
19×*-un-lft-identity add-cube-cbrt
14×associate-*r* associate-*l*
11×pow1
6×frac-times associate-*l/ associate-/l*
5×div-inv
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
2×clear-num associate-/r* frac-2neg *-commutative unswap-sqr
Counts
4 → 167
Calls
4 calls:
Slowest
95.0ms
(* (* (/ (cos k) t) (/ l (* (sin k) k))) (/ l (* (sin k) k)))
33.0ms
(* (/ (cos k) t) (/ l (* (sin k) k)))
7.0ms
(/ l (* (sin k) k))
7.0ms
(/ l (* (sin k) k))

series692.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
296.0ms
(* (* (/ (cos k) t) (/ l (* (sin k) k))) (/ l (* (sin k) k)))
229.0ms
(* (/ (cos k) t) (/ l (* (sin k) k)))
87.0ms
(/ l (* (sin k) k))
81.0ms
(/ l (* (sin k) k))

simplify58.5s

Counts
191 → 179
Calls
191 calls:
Slowest
1.9s
(* (* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k))))
1.9s
(* (* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k))))
1.8s
(* (* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k))))
1.6s
(* (* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k))))
1.4s
(* (* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))) (* (* (/ l (* (sin k) k)) (/ l (* (sin k) k))) (/ l (* (sin k) k))))

prune2.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (cos k) t) (/ l (* (sin k) k)))
2.7b
(/ l (* (sin k) k))
0.2b
(* (* (/ (cos k) t) (/ l (* (sin k) k))) (/ (/ l (sin k)) k))
0.2b
(/ (cos k) t)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
140×add-cbrt-cube add-exp-log
91×times-frac
63×add-sqr-sqrt
58×*-un-lft-identity add-cube-cbrt
54×prod-exp cbrt-unprod
52×cbrt-undiv div-exp
50×associate-*r*
14×associate-*l*
11×pow1
8×div-inv
6×frac-times associate-*l/ associate-/l*
4×expm1-log1p-u associate-/r* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative unswap-sqr
Counts
4 → 209
Calls
4 calls:
Slowest
82.0ms
(* (* (/ (cos k) t) (/ l (* (sin k) k))) (/ (/ l (sin k)) k))
31.0ms
(* (/ (cos k) t) (/ l (* (sin k) k)))
16.0ms
(/ (cos k) t)
7.0ms
(/ l (* (sin k) k))

series666.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
289.0ms
(* (* (/ (cos k) t) (/ l (* (sin k) k))) (/ (/ l (sin k)) k))
230.0ms
(* (/ (cos k) t) (/ l (* (sin k) k)))
92.0ms
(/ l (* (sin k) k))
55.0ms
(/ (cos k) t)

simplify1.1m

Counts
239 → 221
Calls
239 calls:
Slowest
1.8s
(* (* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))) (/ (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))) (* (* k k) k)))
1.7s
(* (* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (* (* (/ l (* (sin k) k)) (/ l (* (sin k) k))) (/ l (* (sin k) k)))) (/ (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))) (* (* k k) k)))
1.5s
(* (* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))) (/ (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))) (* (* k k) k)))
1.4s
(* (* (/ (* (* (cos k) (cos k)) (cos k)) (* (* t t) t)) (/ (* (* l l) l) (* (* (* (sin k) (sin k)) (sin k)) (* (* k k) k)))) (/ (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))) (* (* k k) k)))
1.3s
(* (* (* (* (/ (cos k) t) (/ (cos k) t)) (/ (cos k) t)) (/ (* (* l l) l) (* (* (* (sin k) k) (* (sin k) k)) (* (sin k) k)))) (/ (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))) (* (* k k) k)))

prune2.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0b

regimes342.0ms

Accuracy

20.8% (1.7b remaining)

Error of 1.7b against oracle of 0.1b and baseline of 2.2b

bsearch897.0ms

end0.0ms

sample40.4s

Algorithm
intervals
Results
12.6s4115×body1280valid
11.1s2192×body2560valid
8.3s910×body5120valid
5.2s2506×body640valid
1.4s971×body320valid
912.0ms2040×body80valid
379.0ms436×body160valid