Details

Time bar (total: 51.5s)

sample303.0ms

Algorithm
intervals
Results
116.0ms73×body1280valid
89.0ms51×body640valid
43.0ms191×body80valid
15.0ms21×body320valid
7.0ms13×body160valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.8s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize35.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.1b
(* (/ (pow t 3.0) (* l l)) (sin k))
16.0b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
16.6b
(/ (pow t 3.0) (* l l))

rewrite372.0ms

Algorithm
rewrite-expression-head
Rules
119×add-exp-log
59×times-frac add-cbrt-cube
49×prod-exp
43×div-exp
39×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
19×cbrt-undiv
17×associate-/l*
16×associate-*l/
12×associate-*l* associate-/r/
11×pow1
10×tan-quot unpow-prod-down
8×pow-to-exp pow-exp
7×div-inv
6×associate-*r*
5×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u add-log-exp unswap-sqr sqr-pow
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 178
Calls
4 calls:
110.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
49.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
181.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
15.0ms
(/ (pow t 3.0) (* l l))

series2.3s

Counts
4 → 12
Calls
4 calls:
519.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
412.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
1.0s
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
312.0ms
(/ (pow t 3.0) (* l l))

simplify2.0s

Counts
190 → 190
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03714464
19304301
233093731
done50013730

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.6b

localize54.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.3b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
16.0b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite608.0ms

Algorithm
rewrite-expression-head
Rules
333×add-exp-log
157×prod-exp
132×div-exp
103×times-frac
88×add-cbrt-cube
72×add-sqr-sqrt
59×add-cube-cbrt *-un-lft-identity
46×associate-*l/
36×cbrt-unprod
35×associate-*l*
33×pow-exp
29×cbrt-undiv
28×associate-/r/
25×frac-times
24×unpow-prod-down
22×pow-to-exp
20×tan-quot
19×associate-/l*
15×pow1 associate-*r/
10×cbrt-prod
8×sqr-pow
7×pow-prod-down div-inv
6×associate-*r* associate-/r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num *-commutative
1×associate-/l/
Counts
4 → 266
Calls
4 calls:
248.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
44.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
10.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
288.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.4s

Counts
4 → 12
Calls
4 calls:
550.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
402.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
303.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify3.1s

Counts
278 → 278
Iterations

Useful iterations: done (3.0s)

IterNodesCost
05638511
114168094
248247039
done50007038

prune2.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 17.4b

localize64.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.0b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.0b
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
1119×add-exp-log
728×times-frac
570×div-exp
487×prod-exp
404×unpow-prod-down
380×associate-*l*
365×add-sqr-sqrt
352×add-cube-cbrt *-un-lft-identity
202×cbrt-prod
164×add-cbrt-cube
145×pow-to-exp pow-exp
68×sqr-pow
67×cbrt-unprod
60×cbrt-undiv
49×associate-*l/
29×associate-/r/
26×frac-times
20×tan-quot pow1
17×div-inv
16×associate-*r/
14×associate-/l*
10×pow-prod-down
7×associate-*r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 747
Calls
4 calls:
242.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
403.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
42.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
477.0ms
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.5s

Counts
4 → 12
Calls
4 calls:
454.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
568.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
355.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(/ (/ 2.0 (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.5s

Counts
759 → 759
Iterations

Useful iterations: done (1.5s)

IterNodesCost
096022444
1278221147
done500018618

prune6.7s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 12.7b

localize47.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.4b
(/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0)))
13.9b
(* (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
677×add-exp-log
460×times-frac
352×prod-exp
275×div-exp
271×add-sqr-sqrt
238×add-cube-cbrt *-un-lft-identity
148×unpow-prod-down
127×add-cbrt-cube
112×associate-*r*
74×cbrt-prod
68×pow-to-exp pow-exp
56×cbrt-unprod
45×associate-*l*
41×cbrt-undiv
34×associate-/l*
26×sqr-pow
11×div-inv unswap-sqr
10×pow1
8×associate-*l/
7×associate-*r/
4×tan-quot expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times pow-prod-down associate-/r* associate-/r/ *-commutative
1×frac-2neg clear-num associate-/l/
Counts
4 → 500
Calls
4 calls:
188.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
39.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
41.0ms
(/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0)))
828.0ms
(* (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0))))

series2.6s

Counts
4 → 12
Calls
4 calls:
570.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
381.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
496.0ms
(/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0)))
1.1s
(* (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (/ (/ l (pow (cbrt t) 3.0)) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify1.5s

Counts
512 → 512
Iterations

Useful iterations: done (1.4s)

IterNodesCost
080117901
1224816778
done500015379

prune3.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 12.6b

regimes991.0ms

Accuracy

35.4% (1.4b remaining)

Error of 12.6b against oracle of 11.2b and baseline of 13.4b

bsearch164.0ms

Steps
ItersRangePoint
8
2.1071354199640304e-138
2.2542686958119885e-135
2.2272085936751404e-135

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03791
14691
done4691

end0.0ms

sample11.7s

Algorithm
intervals
Results
4.6s2111×body1280valid
2.3s1726×body640valid
2.2s5913×body80valid
1.6s867×body320valid
247.0ms417×body160valid