Details

Time bar (total: 39.3s)

sample307.0ms

Algorithm
intervals
Results
112.0ms57×body640valid
95.0ms62×body1280valid
40.0ms183×body80valid
22.0ms27×body320valid
8.0ms16×body160valid

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5032
44037
3735
2153
148
019

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize38.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.3b
(* (/ (pow t 3.0) (* l l)) (sin k))
15.4b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.6b
(/ (pow t 3.0) (* l l))

rewrite714.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×pow-to-exp cbrt-undiv pow-exp tan-quot
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in
Counts
4 → 144
Calls
4 calls:
83.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
42.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
575.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
9.0ms
(/ (pow t 3.0) (* l l))

series2.0s

Counts
4 → 12
Calls
4 calls:
439.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
345.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
945.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
244.0ms
(/ (pow t 3.0) (* l l))

simplify2.5s

Counts
156 → 156
Iterations
IterNodes
done5007
23583
1804
0254

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.4b

localize78.0ms

Local error

Found 4 expressions with local error:

3.4b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
4.3b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
8.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.4b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
203×prod-exp
97×div-exp
82×add-cbrt-cube
55×associate-*l/
46×cbrt-unprod
41×pow-exp
35×frac-times
32×pow1
28×pow-to-exp
22×*-un-lft-identity
19×pow-prod-down
17×add-sqr-sqrt add-cube-cbrt
16×tan-quot
15×times-frac associate-*r/
13×cbrt-undiv
11×associate-*r*
8×flip3-+ flip-+
5×associate-/l*
4×unpow-prod-down add-log-exp sqr-pow
3×associate-/r* associate-*l* *-commutative distribute-lft-out
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in div-inv
Counts
4 → 204
Calls
4 calls:
251.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
91.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
15.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.4s

Counts
4 → 12
Calls
4 calls:
555.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
425.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
311.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify2.4s

Counts
216 → 216
Iterations
IterNodes
done5000
11165
0370

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.5b

localize77.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 2.0 (+ (/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))) (* 2.0 (* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l))))))
1.9b
(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
7.4b
(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
20.0b
(* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

rewrite358.0ms

Algorithm
rewrite-expression-head
Rules
263×add-cbrt-cube add-exp-log
115×prod-exp cbrt-unprod
92×cbrt-undiv div-exp
27×associate-*r/
21×add-sqr-sqrt
20×frac-times
19×times-frac
18×*-un-lft-identity add-cube-cbrt
17×associate-/r/
15×associate-*l*
14×pow1
12×associate-*l/
7×frac-add
6×pow-prod-down associate-/l*
4×associate-/r* div-inv add-log-exp
3×unswap-sqr
2×clear-num frac-2neg associate-*r* *-commutative
1×flip3-+ flip-+ sin-mult
Counts
4 → 216
Calls
4 calls:
123.0ms
(/ 2.0 (+ (/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))) (* 2.0 (* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l))))))
57.0ms
(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
74.0ms
(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
84.0ms
(* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

series1.3s

Counts
4 → 12
Calls
4 calls:
694.0ms
(/ 2.0 (+ (/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))) (* 2.0 (* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l))))))
170.0ms
(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
266.0ms
(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
210.0ms
(* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

simplify2.2s

Counts
228 → 228
Iterations
IterNodes
done5001
11265
0441

prune1.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 1.2b

localize60.0ms

Local error

Found 4 expressions with local error:

2.2b
(* t (* (* t (/ (sin k) l)) (* t (/ (sin k) l))))
3.7b
(* t (/ (sin k) l))
3.7b
(* t (/ (sin k) l))
7.4b
(/ t (/ (* (/ l k) (* (/ l k) (/ (cos k) (sin k)))) (sin k)))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
127×add-cbrt-cube add-exp-log
53×times-frac prod-exp cbrt-unprod
48×add-sqr-sqrt
44×cbrt-undiv div-exp
37×*-un-lft-identity add-cube-cbrt
27×associate-*r*
26×pow1
15×pow-prod-down
10×associate-*r/
9×associate-*l*
7×associate-/r* div-inv
5×unswap-sqr
4×add-log-exp
3×*-commutative associate-/l*
1×frac-times clear-num frac-2neg associate-*l/ associate-/r/
Counts
4 → 171
Calls
4 calls:
158.0ms
(* t (* (* t (/ (sin k) l)) (* t (/ (sin k) l))))
11.0ms
(* t (/ (sin k) l))
11.0ms
(* t (/ (sin k) l))
32.0ms
(/ t (/ (* (/ l k) (* (/ l k) (/ (cos k) (sin k)))) (sin k)))

series689.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(* t (* (* t (/ (sin k) l)) (* t (/ (sin k) l))))
94.0ms
(* t (/ (sin k) l))
71.0ms
(* t (/ (sin k) l))
387.0ms
(/ t (/ (* (/ l k) (* (/ l k) (/ (cos k) (sin k)))) (sin k)))

simplify1.6s

Counts
183 → 183
Iterations
IterNodes
done5000
11084
0346

prune1.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.7b

regimes772.0ms

Accuracy

29.4% (2.3b remaining)

Error of 2.6b against oracle of 0.4b and baseline of 3.6b

bsearch335.0ms

Steps
ItersRangePoint
8
2.0642034119818884e-52
1.2908862423629985e-48
3.049035263999028e-50
9
-6.816939173909149e-88
-1.3799188861238731e-95
-5.5160361380203745e-90

simplify23.0ms

Iterations
IterNodes
done57
157
041

end0.0ms

sample10.6s

Algorithm
intervals
Results
5.0s2026×body1280valid
2.3s1748×body640valid
2.0s5830×body80valid
671.0ms834×body320valid
199.0ms407×body160valid