Details

Time bar (total: 41.4s)

sample350.0ms

Algorithm
intervals
Results
174.0ms74×body1280valid
49.0ms48×body640valid
47.0ms196×body80valid
31.0ms31×body320valid
10.0ms20×body160valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.7b

localize38.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (/ (pow t 3.0) (* l l)) (sin k))
2.1b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.4b
(/ (/ 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))

rewrite334.0ms

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:
49.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
105.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
131.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
23.0ms
(/ (pow t 3.0) (* l l))

series2.0s

Counts
4 → 12
Calls
4 calls:
355.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
461.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
946.0ms
(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))
256.0ms
(/ (pow t 3.0) (* l l))

simplify1.8s

Counts
190 → 190
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03714464
19304301
233093731
done50013730

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.0b

localize75.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.2b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.4b
(/ (/ 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)))

rewrite581.0ms

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:
245.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
30.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
17.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
264.0ms
(/ (/ 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)))

series2.3s

Counts
4 → 12
Calls
4 calls:
566.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
367.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
318.0ms
(/ (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)))

simplify3.3s

Counts
278 → 278
Iterations

Useful iterations: done (3.2s)

IterNodesCost
05638511
114168094
248247039
done50007038

prune2.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 13.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.1b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.4b
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite858.0ms

Algorithm
rewrite-expression-head
Rules
1478×add-exp-log
704×div-exp
684×prod-exp
224×pow-exp
134×pow-to-exp
128×add-cbrt-cube
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 → 415
Calls
4 calls:
4.0ms
(pow (cbrt t) 3.0)
300.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
65.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
427.0ms
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (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:
526.0ms
(pow (cbrt t) 3.0)
502.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
378.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.0s
(/ (/ 2.0 (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.2s

Counts
427 → 427
Iterations

Useful iterations: done (1.2s)

IterNodesCost
072218777
1174017144
done500012824

prune2.0s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.7b

localize116.0ms

Local error

Found 4 expressions with local error:

11.0b
(/ (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (* (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt (fma 2 1.0 (pow (/ k t) 2.0)))))
19.3b
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
19.3b
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
19.3b
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

rewrite370.0ms

Algorithm
rewrite-expression-head
Rules
293×add-exp-log
147×prod-exp
114×div-exp
52×add-cbrt-cube
28×pow-exp
24×cbrt-undiv cbrt-unprod
18×pow-to-exp
16×times-frac
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×associate-/l*
9×cbrt-prod
6×associate-*r/ associate-*l/ associate-/r/
4×tan-quot pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 div-inv
2×frac-times
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 131
Calls
4 calls:
356.0ms
(/ (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (* (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt (fma 2 1.0 (pow (/ k t) 2.0)))))
2.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
2.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
2.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.2s
(/ (/ 2.0 (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))) (* (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt (fma 2 1.0 (pow (/ k t) 2.0)))))
238.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
221.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))
173.0ms
(cbrt (fma 2 1.0 (pow (/ k t) 2.0)))

simplify1.6s

Counts
143 → 143
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03146088
18125378
228154504
done50004293

prune782.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 9.7b

regimes1.2s

Accuracy

29.2% (2.4b remaining)

Error of 13.4b against oracle of 11.1b and baseline of 14.4b

bsearch250.0ms

Steps
ItersRangePoint
1
6.362968132230824e-21
6.637760941833341e-21
6.431666334631453e-21
6
-4.098763797904608e+28
-9.26603679748231e+27
-9.349729753898897e+27

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
051212
161212
done61212

end0.0ms

sample11.3s

Algorithm
intervals
Results
4.3s2072×body1280valid
2.7s5903×body80valid
2.3s1746×body640valid
1.1s832×body320valid
252.0ms413×body160valid