Details

Time bar (total: 26.8s)

sample506.0ms

Algorithm
intervals
Results
154.0ms34×body5120valid
154.0ms86×body2560valid
104.0ms132×body1280valid
48.0ms86×body640valid
10.0ms30×body320valid
8.0ms65×body80valid
3.0ms15×body160valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111
done500111

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 39.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
19.6b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.0b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
337×add-exp-log
220×prod-exp
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
30×unpow-prod-down
28×add-sqr-sqrt
24×associate-*l*
23×add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
5×pow1 associate-*r/
4×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp sqr-pow
3×tan-quot pow-unpow div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 187
Calls
4 calls:
6.0ms
(pow (/ k t) 2.0)
15.0ms
(* (pow t 3.0) (tan k))
96.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
44.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series960.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ k t) 2.0)
246.0ms
(* (pow t 3.0) (tan k))
392.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
255.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify40.0ms

Counts
199 → 199
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09912005
150011672
done50011672

prune484.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.4b
(* (pow k 2.0) (pow t 1.0))
15.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite189.0ms

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:
18.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
17.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms
(* (pow k 2.0) (pow t 1.0))
74.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
359.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
95.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
354.0ms
(* (pow k 2.0) (pow t 1.0))
671.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify149.0ms

Counts
620 → 620
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
014397252
142967083
250037076
done50037076

prune652.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.4b
(* (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)))

rewrite424.0ms

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:
4.0ms
(pow (sin k) 2)
48.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
141.0ms
(* (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:
19.0ms
(pow (sin k) 2)
361.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
95.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
687.0ms
(* (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)))

simplify267.0ms

Counts
1480 → 1480
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933
done500217933

prune610.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (sin k))
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.2b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
15.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite379.0ms

Algorithm
rewrite-expression-head
Rules
3841×add-exp-log
2622×prod-exp
1370×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
99×times-frac
80×add-sqr-sqrt
65×add-cbrt-cube
59×add-cube-cbrt *-un-lft-identity
45×associate-*r*
24×associate-*l*
22×cbrt-undiv cbrt-unprod
8×div-inv
7×pow1 unpow-prod-down
6×associate-/l* unswap-sqr
5×associate-*r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down associate-/r/ inv-pow sqr-pow
Counts
4 → 939
Calls
4 calls:
9.0ms
(/ (cos k) (sin k))
48.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
45.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
151.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.4s

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (cos k) (sin k))
364.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
95.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
906.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify150.0ms

Counts
951 → 951
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0240215175
1500112337
done500112337

prune767.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

regimes288.0ms

Accuracy

55.3% (3.2b remaining)

Error of 11.9b against oracle of 8.7b and baseline of 15.8b

bsearch2.4s

Steps
ItersRangePoint
6
2.0253598023400303e+141
1.185049118930683e+142
1.122770281998579e+142
11
8.128130995100578e-170
1.610239390119146e-144
8.218377655060683e-159
9
-1.299221172874282e-153
-1.8234627852955154e-160
-1.4760655038412053e-156
4
-1.2053858483217588e+154
-6.220397902907621e+153
-1.1856453275643411e+154

simplify5.0ms

Iterations

Useful iterations: 2 (1.0ms)

IterNodesCost
062100
165100
27138
37438
48038
59138
69838
79938
89938
done9938

end0.0ms

sample14.2s

Algorithm
intervals
Results
4.2s2232×body2560valid
4.1s982×body5120valid
3.4s4157×body1280valid
1.3s2479×body640valid
345.0ms932×body320valid
227.0ms1999×body80valid
104.0ms427×body160valid