Details

Time bar (total: 31.9s)

sample481.0ms

Algorithm
intervals
Results
146.0ms78×body2560valid
143.0ms33×body5120valid
107.0ms131×body1280valid
40.0ms79×body640valid
16.0ms40×body320valid
7.0ms61×body80valid
1.0ms5×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (657.0ms)

IterNodesCost
01925
14425
214325
371023
4377821
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.5b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
1.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
17.6b
(/ (pow t 3.0) (* l l))
30.3b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
272×add-exp-log
153×unpow-prod-down
144×add-sqr-sqrt
137×add-cube-cbrt *-un-lft-identity
128×div-exp
103×prod-exp
59×add-cbrt-cube
58×associate-*l/
54×associate-/r/
38×tan-quot
34×pow-exp
32×div-inv
24×pow-to-exp
21×cbrt-unprod
19×cbrt-undiv frac-times associate-*r/
18×associate-/r*
17×associate-/l*
15×sqr-pow
12×associate-*l*
11×pow1
6×associate-*r*
4×pow-prod-down add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 354
Calls
4 calls:
14.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
34.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
5.0ms
(/ (pow t 3.0) (* l l))
52.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
306.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
174.0ms
(/ (pow t 3.0) (* l l))
556.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify640.0ms

Counts
366 → 366
Iterations

Useful iterations: done (622.0ms)

IterNodesCost
066210242
116369739
done50009711

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.3b
(* (pow k 2.0) (pow t 1.0))
8.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
10.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms
(* (pow k 2.0) (pow t 1.0))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
34.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts
4 → 12
Calls
4 calls:
324.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
314.0ms
(* (pow k 2.0) (pow t 1.0))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
622.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Counts
612 → 612
Iterations

Useful iterations: 2 (575.0ms)

IterNodesCost
048315017
1122313295
2327412599
done500112599

prune636.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1460
Calls
4 calls:
1.0ms
(pow (sin k) 2)
25.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
57.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
330.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
645.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.2s

Counts
1472 → 1472
Iterations

Useful iterations: 2 (617.0ms)

IterNodesCost
059750343
1168633112
2357731574
done500031574

prune580.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.1b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
8.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.4b
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
41×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
12×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×unpow2 unswap-sqr
2×frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 5762
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
144.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
6.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
36.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
328.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
372.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
84.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
373.0ms
(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify1.7s

Counts
5774 → 5774
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01477226017
14285201321
done5001190555

prune842.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.6b

regimes435.0ms

Accuracy

32.1% (4.5b remaining)

Error of 16.0b against oracle of 11.5b and baseline of 18.1b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04374
15374
done5374

end0.0ms

sample14.0s

Algorithm
intervals
Results
4.2s2286×body2560valid
3.9s950×body5120valid
3.4s4108×body1280valid
1.3s2436×body640valid
379.0ms978×body320valid
259.0ms2156×body80valid
126.0ms465×body160valid