Details

Time bar (total: 38.0s)

sample480.0ms

Algorithm
intervals
Results
149.0ms78×body2560valid
143.0ms33×body5120valid
103.0ms131×body1280valid
40.0ms79×body640valid
15.0ms40×body320valid
7.0ms61×body80valid
1.0ms5×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (389.0ms)

IterNodesCost
01925
14425
214325
371023
4378721
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (pow (/ k t) 2.0) (tan k))
6.7b
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
10.3b
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
27.4b
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
379×add-exp-log
182×prod-exp
145×div-exp
94×add-cbrt-cube
44×pow-exp
38×cbrt-unprod
35×times-frac
32×add-sqr-sqrt
31×pow-to-exp
30×cbrt-undiv associate-*l*
22×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
11×pow1
9×associate-*r*
8×associate-/l*
6×div-inv
5×unswap-sqr
4×tan-quot associate-*r/ pow-prod-down add-log-exp
3×associate-*l/ associate-/r/ *-commutative
2×sqr-pow
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 203
Calls
4 calls:
16.0ms
(* (pow (/ k t) 2.0) (tan k))
104.0ms
(* (* (/ (/ 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:
217.0ms
(* (pow (/ k t) 2.0) (tan k))
705.0ms
(* (* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l) l)
501.0ms
(* (/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k))) l)
316.0ms
(/ (/ 2.0 (* (pow (/ k t) 2.0) (tan k))) (* (pow t 3.0) (sin k)))

simplify1.0s

Counts
215 → 215
Iterations

Useful iterations: 2 (392.0ms)

IterNodesCost
03355196
19264753
233863891
done50003891

prune519.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.0b

localize23.0ms

Local error

Found 4 expressions with local error:

2.5b
(/ (* (cos k) l) (pow (sin k) 2))
5.3b
(* (pow k 2.0) (pow t 1.0))
5.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
6.7b
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)

rewrite244.0ms

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))
8.0ms
(* (pow k 2.0) (pow t 1.0))
33.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (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)

series1.6s

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (* (cos k) l) (pow (sin k) 2))
346.0ms
(* (pow k 2.0) (pow t 1.0))
480.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
697.0ms
(* (* 2.0 (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))) l)

simplify1.4s

Counts
610 → 610
Iterations

Useful iterations: 2 (628.0ms)

IterNodesCost
059716175
1172114076
2416513392
done500013392

prune796.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.2b

localize26.0ms

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))))
2.5b
(/ (* (cos k) l) (pow (sin k) 2))
5.5b
(* (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)))
6.7b
(* (* 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)

rewrite537.0ms

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:
25.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
52.0ms
(* (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)))
198.0ms
(* (* 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)

series1.6s

Counts
4 → 12
Calls
4 calls:
345.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (* (cos k) l) (pow (sin k) 2))
483.0ms
(* (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)))
680.0ms
(* (* 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)

simplify1.1s

Counts
1566 → 1566
Iterations

Useful iterations: done (966.0ms)

IterNodesCost
090055558
1280335946
done500235204

prune562.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.5b
(/ (* (cos k) l) (pow (sin k) 2))
6.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
6.7b
(* (* 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:
10.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
5.0ms
(/ (* (cos k) l) (pow (sin k) 2))
31.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
533.0ms
(* (* 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:
334.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
90.0ms
(/ (* (cos k) l) (pow (sin k) 2))
479.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) l) (pow (sin k) 2)))
697.0ms
(* (* 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)

simplify796.0ms

Counts
2478 → 2478
Iterations

Useful iterations: 0 (333.0ms)

IterNodesCost
01992112944
done5000112944

prune5.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.1b

regimes315.0ms

Accuracy

39.2% (2.2b remaining)

Error of 6.9b against oracle of 4.8b and baseline of 8.3b

bsearch678.0ms

Steps
ItersRangePoint
8
1.8802742352016126e+87
9.018108319142249e+89
4.290368852676071e+88
8
-4.947555866969207e+135
-2.5791006095191983e+132
-4.360789912444986e+133

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
042139
15895
done5895

end0.0ms

sample14.2s

Algorithm
intervals
Results
4.3s2286×body2560valid
3.9s950×body5120valid
3.5s4108×body1280valid
1.3s2436×body640valid
356.0ms978×body320valid
272.0ms2156×body80valid
118.0ms465×body160valid