Details

Time bar (total: 44.6s)

sample265.0ms

Algorithm
intervals
Results
79.0ms199×body80valid
74.0ms56×body1280valid
54.0ms64×body640valid
14.0ms24×body320valid
12.0ms21×body160valid

simplify3.0s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.9b

localize25.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
17.1b
(/ (pow t 3.0) (* l l))
17.6b
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite273.0ms

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:
33.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
95.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
20.0ms
(/ (pow t 3.0) (* l l))
118.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

series2.1s

Counts
4 → 12
Calls
4 calls:
415.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
595.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
203.0ms
(/ (pow t 3.0) (* l l))
874.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.9s

Counts
190 → 190
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03714464
19314301
233223731
done50003730

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 25.1b

localize58.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
7.8b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
17.6b
(/ (/ 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)))

rewrite573.0ms

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:
44.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
214.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
20.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
273.0ms
(/ (/ 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)))

series2.2s

Counts
4 → 12
Calls
4 calls:
334.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
484.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
299.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.0s
(/ (/ 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 (3.1s)

IterNodesCost
05638511
114168094
248297039
done50017038

prune2.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 18.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.6b
(/ (/ 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)))

rewrite950.0ms

Algorithm
rewrite-expression-head
Rules
842×add-exp-log
426×div-exp
370×prod-exp
128×add-cbrt-cube
98×pow-to-exp pow-exp
88×times-frac
65×add-sqr-sqrt
52×add-cube-cbrt *-un-lft-identity cbrt-unprod
48×cbrt-undiv
46×associate-*l/
35×associate-*l*
28×associate-/r/
26×unpow-prod-down
25×frac-times
20×tan-quot
16×pow1
15×associate-*r/
14×associate-/l*
13×cbrt-prod
7×pow-prod-down
6×associate-*r* div-inv
5×unswap-sqr sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r*
2×pow-pow *-commutative
1×frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 335
Calls
4 calls:
8.0ms
(pow (cbrt t) 3.0)
39.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
430.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
442.0ms
(/ (/ 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)))

series2.6s

Counts
4 → 12
Calls
4 calls:
483.0ms
(pow (cbrt t) 3.0)
381.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
596.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan 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)))

simplify3.7s

Counts
347 → 347
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
061111955
1160610956
249857663
done50007663

prune1.8s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 15.9b

localize56.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
2.9b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.9b
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
17.1b
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k))))

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
870×add-exp-log
428×div-exp
381×prod-exp
176×add-cbrt-cube
155×times-frac
78×cbrt-undiv
77×add-sqr-sqrt
76×pow-to-exp pow-exp
64×add-cube-cbrt *-un-lft-identity
61×cbrt-unprod
35×associate-*l*
31×associate-*l/
21×div-inv
20×unpow-prod-down associate-/r/
11×associate-/l*
10×cbrt-prod associate-*r/
9×associate-/r*
8×pow1
6×associate-*r*
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
2×frac-2neg pow-prod-down clear-num *-commutative
1×associate-/l/
Counts
4 → 350
Calls
4 calls:
204.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
57.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
17.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
257.0ms
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k))))

series2.4s

Counts
4 → 12
Calls
4 calls:
376.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
358.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
614.0ms
(/ (fma 2 1.0 (pow (/ k t) 2.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
1.1s
(/ (/ 2.0 (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k))))

simplify1.3s

Counts
362 → 362
Iterations

Useful iterations: done (1.2s)

IterNodesCost
061615445
1169714150
done500010529

prune2.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 14.4b

regimes1.1s

Accuracy

44.7% (1.2b remaining)

Error of 12.8b against oracle of 11.6b and baseline of 13.8b

bsearch723.0ms

Steps
ItersRangePoint
8
7.194482888246986e-189
2.1090834793542313e-185
9.430149747819988e-188
10
-7.576468862602086e-193
-5.443375548944992e-203
-2.6732218473581146e-199

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
044132
15793
done5793

end0.0ms

sample10.8s

Algorithm
intervals
Results
4.7s2063×body1280valid
2.6s1706×body640valid
1.6s5870×body80valid
1.1s872×body320valid
219.0ms481×body160valid