Details

Time bar (total: 45.7s)

sample486.0ms

Algorithm
intervals
Results
157.0ms78×body2560valid
138.0ms33×body5120valid
105.0ms131×body1280valid
41.0ms79×body640valid
15.0ms40×body320valid
7.0ms61×body80valid
1.0ms5×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (286.0ms)

IterNodesCost
01925
14425
214525
372323
4405121
done500021

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (/ (pow t 3.0) (* l l)))
0.8b
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
17.6b
(/ (pow t 3.0) (* l l))
30.1b
(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
424×add-exp-log
226×div-exp
223×times-frac
141×prod-exp
82×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
77×add-cbrt-cube
58×pow-exp
49×unpow-prod-down
48×associate-/l*
40×pow-to-exp
34×cbrt-undiv
20×cbrt-unprod
17×associate-*r*
16×div-inv
13×associate-/r* sqr-pow
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×tan-quot associate-*r/ associate-*l/
1×associate-*l* *-commutative associate-/l/
Counts
4 → 319
Calls
4 calls:
7.0ms
(/ 2.0 (/ (pow t 3.0) (* l l)))
21.0ms
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
5.0ms
(/ (pow t 3.0) (* l l))
26.0ms
(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

series1.4s

Counts
4 → 12
Calls
4 calls:
256.0ms
(/ 2.0 (/ (pow t 3.0) (* l l)))
239.0ms
(* (* (sin k) (tan k)) (pow (/ k t) 2.0))
179.0ms
(/ (pow t 3.0) (* l l))
763.0ms
(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (* (sin k) (tan k)) (pow (/ k t) 2.0)))

simplify491.0ms

Counts
331 → 331
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
04777288
114396729
done50006678

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.9b

localize26.0ms

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)))

rewrite156.0ms

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×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
10.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
12.0ms
(* (pow k 2.0) (pow t 1.0))
12.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
47.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
400.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
358.0ms
(* (pow k 2.0) (pow t 1.0))
94.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
719.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.5s

Counts
620 → 620
Iterations

Useful iterations: 2 (941.0ms)

IterNodesCost
049115125
1141712979
2412312703
done500012703

prune708.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.1b

localize31.0ms

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)))

rewrite356.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 1468
Calls
4 calls:
1.0ms
(pow (sin k) 2)
22.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
7.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
81.0ms
(* (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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
29.0ms
(pow (sin k) 2)
354.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
705.0ms
(* (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)))

simplify6.9s

Counts
1480 → 1480
Iterations

Useful iterations: 2 (3.3s)

IterNodesCost
060550477
1192831970
2452331674
done500031674

prune637.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.1b
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2)))
4.8b
(/ (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2))
15.8b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2)))

rewrite704.0ms

Algorithm
rewrite-expression-head
Rules
13586×add-exp-log
9885×prod-exp
7987×pow-exp
5773×div-exp
4147×pow-to-exp
890×rec-exp 1-exp
93×unpow-prod-down
73×times-frac
70×add-sqr-sqrt
61×associate-*l*
47×*-un-lft-identity
44×add-cube-cbrt
37×add-cbrt-cube
27×sqrt-prod
15×sqr-pow
14×cbrt-unprod
13×associate-*r*
12×unswap-sqr
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 3129
Calls
4 calls:
8.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
128.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2)))
25.0ms
(/ (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2))
27.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2)))

series2.3s

Counts
4 → 12
Calls
4 calls:
382.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
676.0ms
(* (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2)))
684.0ms
(/ (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2))) (pow (sin k) 2))
585.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (* (cos k) (pow l 2)))

simplify5.1s

Counts
3141 → 3141
Iterations

Useful iterations: done (4.9s)

IterNodesCost
0998122680
13270105813
done5001105690

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.3b

regimes449.0ms

Accuracy

5.7% (7.7b remaining)

Error of 18.1b against oracle of 10.4b and baseline of 18.5b

bsearch1.5s

Steps
ItersRangePoint
8
1.6811643068024188e+194
1.4488975596305785e+198
4.0919598199916316e+194
8
7.975119028454442e-98
1.2484941764030143e-94
2.211270174879737e-96
7
8.354898913898953e-165
1.5540079872574706e-162
4.331663927949164e-163
6
3.248240049853562e-200
1.767251733959503e-199
1.7472655777358584e-199
6
-9.125160771875588e-80
-2.0541795503741127e-80
-6.417074703090767e-80
7
-3.898170639313033e+121
-9.443909635795886e+119
-9.580690874421448e+119

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
095275
1113275
done113275

end0.0ms

sample14.9s

Algorithm
intervals
Results
4.5s2286×body2560valid
4.1s950×body5120valid
3.6s4108×body1280valid
1.4s2436×body640valid
384.0ms978×body320valid
268.0ms2156×body80valid
119.0ms465×body160valid