Details

Time bar (total: 25.4s)

sample453.0ms

Algorithm
intervals
Results
127.0ms60×body2560valid
125.0ms28×body5120valid
116.0ms137×body1280valid
38.0ms77×body640valid
10.0ms29×body320valid
8.0ms77×body80valid
4.0ms18×body160valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111
done500111

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
25.6b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.1b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite164.0ms

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))
87.0ms
(/ (* 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)))

series946.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (/ k t) 2.0)
243.0ms
(* (pow t 3.0) (tan k))
381.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
254.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify38.0ms

Counts
199 → 199
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09912005
150011672
done50011672

prune469.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 26.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.3b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.4b
(* (pow k 2.0) (pow t 1.0))
21.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite179.0ms

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:
17.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms
(* (pow k 2.0) (pow t 1.0))
69.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
341.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
94.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
345.0ms
(* (pow k 2.0) (pow t 1.0))
663.0ms
(* (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 (84.0ms)

IterNodesCost
014397252
142967083
250037076
done50037076

prune638.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.7b

localize24.0ms

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))))
5.3b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
21.5b
(* (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)))

rewrite403.0ms

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:
3.0ms
(pow (sin k) 2)
45.0ms
(/ 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))
132.0ms
(* (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:
19.0ms
(pow (sin k) 2)
355.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
94.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
665.0ms
(* (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)))

simplify273.0ms

Counts
1480 → 1480
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
0199723615
1485419182
2500217933
done500217933

prune591.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (sin k))
0.8b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.5b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
21.5b
(* (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))))

rewrite577.0ms

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:
10.0ms
(/ (cos k) (sin k))
44.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
41.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
143.0ms
(* (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))))

series1.1s

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (cos k) (sin k))
345.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
656.0ms
(* (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))))

simplify163.0ms

Counts
951 → 951
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0240215175
1500112337
done500112337

prune742.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

regimes288.0ms

Accuracy

51% (3.3b remaining)

Error of 12.3b against oracle of 8.9b and baseline of 15.7b

bsearch1.2s

Steps
ItersRangePoint
8
7.396278648736192e+140
4.065411880217532e+143
1.450138159937342e+142
6
3.22169256823152e-86
3.391562439923427e-85
2.149121323428305e-85
11
-1.2197423548043316e-116
-2.27606886575251e-137
-2.2996756171697746e-136
6
-3.812181010301986e+155
-2.4426674496164293e+154
-2.4840976750367367e+154

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07586
17586
done7586

end0.0ms

sample14.3s

Algorithm
intervals
Results
4.2s990×body5120valid
4.1s2221×body2560valid
3.4s4149×body1280valid
1.3s2459×body640valid
382.0ms981×body320valid
241.0ms2111×body80valid
110.0ms426×body160valid