Details

Time bar (total: 59.4s)

sample789.0ms

Algorithm
intervals
Results
238.0ms146×body1280valid
218.0ms75×body2560valid
145.0ms22×body5120valid
109.0ms71×body640valid
19.0ms32×body320valid
15.0ms73×body80valid
6.0ms15×body160valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01925
14425
214825
384123
done500121

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.2b

localize34.0ms

Local error

Found 4 expressions with local error:

1.1b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
17.0b
(/ (pow t 3.0) (* l l))
28.9b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite341.0ms

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×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 362
Calls
4 calls:
88.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
37.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
15.0ms
(/ (pow t 3.0) (* l l))
176.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series2.0s

Counts
4 → 12
Calls
4 calls:
526.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
380.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
262.0ms
(/ (pow t 3.0) (* l l))
812.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.3s

Counts
374 → 374
Iterations

Useful iterations: done (1.3s)

IterNodesCost
067010352
117859880
done50009414

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b
(* (pow k 2.0) (pow t 1.0))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.1b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite218.0ms

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:
19.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
20.0ms
(* (pow k 2.0) (pow t 1.0))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
95.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.9s

Counts
4 → 12
Calls
4 calls:
509.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
434.0ms
(* (pow k 2.0) (pow t 1.0))
99.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
823.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify750.0ms

Counts
620 → 620
Iterations

Useful iterations: done (723.0ms)

IterNodesCost
049115125
1148213001
done500012725

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.4b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.1b
(* (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)))

rewrite720.0ms

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:
8.0ms
(pow (sin k) 2)
78.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
18.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
246.0ms
(* (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)))

series1.7s

Counts
4 → 12
Calls
4 calls:
37.0ms
(pow (sin k) 2)
522.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
134.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1000.0ms
(* (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)))

simplify1.1s

Counts
1480 → 1480
Iterations

Useful iterations: done (1.0s)

IterNodesCost
060550477
1205133540
done500131701

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.3b
(* (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))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.1b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
13973×add-exp-log
10155×prod-exp
8251×pow-exp
5914×div-exp
4231×pow-to-exp
920×rec-exp 1-exp
81×unpow-prod-down
64×times-frac
61×associate-*l*
49×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-cbrt-cube
21×sqrt-prod
14×cbrt-unprod
13×associate-*r*
12×sqr-pow
9×associate-/r*
8×cbrt-undiv
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 3211
Calls
4 calls:
23.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
258.0ms
(* (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))))
21.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
165.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.7s

Counts
4 → 12
Calls
4 calls:
587.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
939.0ms
(* (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))))
123.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.4s

Counts
3223 → 3223
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01021126601
13660106485
done5001103329

prune1.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.1b

regimes580.0ms

Accuracy

28.6% (4.8b remaining)

Error of 16.3b against oracle of 11.5b and baseline of 18.3b

bsearch1.9s

Steps
ItersRangePoint
9
4.1368702715426593e+145
3.8281298477808404e+154
1.1478743484480851e+154
7
-4.073943833331379e+185
-1.8779889896941352e+183
-1.9100655647147183e+183

simplify58.0ms

Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
048111
16179
26377
36577
done6577

end0.0ms

sample32.5s

Algorithm
intervals
Results
9.4s956×body5120valid
8.8s4089×body1280valid
8.2s2230×body2560valid
3.2s2533×body640valid
1.0s1025×body320valid
622.0ms2045×body80valid
217.0ms480×body160valid