Details

Time bar (total: 37.5s)

sample486.0ms

Algorithm
intervals
Results
135.0ms57×body2560valid
134.0ms142×body1280valid
120.0ms30×body5120valid
46.0ms80×body640valid
14.0ms34×body320valid
8.0ms63×body80valid
4.0ms16×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (388.0ms)

IterNodesCost
01925
14425
214325
371023
4378721
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.5b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (pow t 3.0) (sin k))
4.7b
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
7.8b
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
30.7b
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
376×add-exp-log
181×prod-exp
144×div-exp
94×add-cbrt-cube
43×pow-exp
38×cbrt-unprod
31×pow-to-exp
30×cbrt-undiv
25×times-frac
23×add-sqr-sqrt
20×associate-*l*
16×add-cube-cbrt *-un-lft-identity
11×pow1
9×associate-*r*
8×associate-/l*
5×div-inv
4×unpow-prod-down pow-prod-down add-log-exp unswap-sqr
3×tan-quot associate-*r/ associate-*l/ associate-/r/ *-commutative
2×sqr-pow
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 190
Calls
4 calls:
6.0ms
(* (pow t 3.0) (sin k))
102.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
36.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
13.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

series1.7s

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (pow t 3.0) (sin k))
727.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
529.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
321.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

simplify995.0ms

Counts
202 → 202
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
02924965
18404526
232063678
done50013678

prune445.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.9b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(/ (* (cos k) l) (pow (sin k) 2))
4.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
5.0b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
8.5b
(* (pow k 2.0) (pow t 1.0))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
2134×add-exp-log
1515×prod-exp
826×pow-exp
682×div-exp
406×pow-to-exp
140×rec-exp 1-exp
40×add-cbrt-cube
36×add-sqr-sqrt
29×unpow-prod-down
22×associate-*r*
19×add-cube-cbrt *-un-lft-identity times-frac associate-*l* cbrt-unprod
13×sqr-pow
12×unswap-sqr
9×pow1
8×associate-/r*
6×cbrt-undiv
4×add-log-exp
3×associate-*r/ pow-prod-down *-commutative div-inv unpow2
1×frac-2neg associate-*l/ clear-num associate-/l*
Counts
4 → 598
Calls
4 calls:
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
125.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
30.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
8.0ms
(* (pow k 2.0) (pow t 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (* (cos k) l) (pow (sin k) 2))
700.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
484.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
340.0ms
(* (pow k 2.0) (pow t 1.0))

simplify1.6s

Counts
610 → 610
Iterations

Useful iterations: 2 (811.0ms)

IterNodesCost
059716175
1172114076
2419113392
done500113392

prune567.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.5b
(/ (* (cos k) l) (pow (sin k) 2))
4.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
5.0b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))

rewrite543.0ms

Algorithm
rewrite-expression-head
Rules
7247×add-exp-log
5835×prod-exp
2962×pow-exp
2088×div-exp
1660×pow-to-exp
465×rec-exp 1-exp
47×add-cbrt-cube
22×add-sqr-sqrt times-frac
21×cbrt-unprod
17×add-cube-cbrt unpow-prod-down *-un-lft-identity
15×associate-*r*
12×associate-*l*
10×pow1
9×cbrt-undiv associate-/r*
5×sqr-pow
4×div-inv associate-/l* add-log-exp
3×associate-*r/ pow-prod-down unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*l/ inv-pow
Counts
4 → 1554
Calls
4 calls:
21.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
188.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
54.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
347.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
92.0ms
(/ (* (cos k) l) (pow (sin k) 2))
693.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)
479.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))

simplify1.0s

Counts
1566 → 1566
Iterations

Useful iterations: done (927.0ms)

IterNodesCost
090055558
1280435946
done500135204

prune545.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.5b
(/ (* (cos k) l) (pow (sin k) 2))
3.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
4.7b
(* (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
15926×add-exp-log
12183×prod-exp
6198×pow-exp
4798×div-exp
2706×pow-to-exp
710×rec-exp 1-exp
50×add-cbrt-cube
25×cbrt-unprod
22×add-sqr-sqrt times-frac
17×add-cube-cbrt unpow-prod-down *-un-lft-identity
15×associate-*r*
12×associate-*l*
10×pow1
9×associate-/r*
8×cbrt-undiv
5×sqr-pow
4×associate-*r/ div-inv associate-/l* add-log-exp
3×pow-prod-down unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*l/ inv-pow
Counts
4 → 2466
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
33.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
515.0ms
(* (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

series1.6s

Counts
4 → 12
Calls
4 calls:
351.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
94.0ms
(/ (* (cos k) l) (pow (sin k) 2))
490.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
708.0ms
(* (* 2.0 (* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2))))) l)

simplify1.1s

Counts
2478 → 2478
Iterations

Useful iterations: 0 (545.0ms)

IterNodesCost
01992112944
done5000112944

prune5.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.7b

regimes345.0ms

Accuracy

34.4% (2.1b remaining)

Error of 6.9b against oracle of 4.8b and baseline of 8.0b

bsearch513.0ms

Steps
ItersRangePoint
5
1.7730613794721092e+90
3.8878908855898174e+90
1.9403210429628964e+90
5
-8.187910929615223e+207
-2.115940709473092e+207
-2.1549948150372896e+207

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
040149
156100
done56100

end0.0ms

sample14.0s

Algorithm
intervals
Results
4.1s2242×body2560valid
4.0s940×body5120valid
3.3s4083×body1280valid
1.4s2589×body640valid
344.0ms990×body320valid
235.0ms1930×body80valid
100.0ms393×body160valid