Details

Time bar (total: 51.2s)

sample256.0ms

Algorithm
intervals
Results
122.0ms68×body1280valid
47.0ms57×body640valid
34.0ms198×body80valid
19.0ms33×body320valid
4.0ms11×body160valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.0s)

IterNodesCost
01925
14825
216025
388225
4495024
done500024

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.4b

localize32.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
16.3b
(/ (pow t 3.0) (* l l))
16.5b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 152
Calls
4 calls:
138.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
53.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
23.0ms
(/ (pow t 3.0) (* l l))
874.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
517.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
430.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
301.0ms
(/ (pow t 3.0) (* l l))
968.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify2.4s

Counts
164 → 164
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02633323
17733179
235872673
done50012672

prune893.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.4b

localize65.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.0b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
16.5b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 237
Calls
4 calls:
187.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
45.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
18.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.4s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
585.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
410.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
315.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify977.0ms

Counts
249 → 249
Iterations

Useful iterations: done (968.0ms)

IterNodesCost
04377110
112676725
done50005760

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.5b

localize48.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
2.7b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
3.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.5b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
1050×add-exp-log
674×times-frac
554×prod-exp
435×div-exp
404×unpow-prod-down
381×associate-*l*
343×add-sqr-sqrt
335×*-un-lft-identity
330×add-cube-cbrt
202×cbrt-prod
151×add-cbrt-cube
145×pow-to-exp pow-exp
78×cbrt-unprod
68×sqr-pow
47×associate-*l/
37×cbrt-undiv
35×frac-times
34×pow1
20×pow-prod-down
16×tan-quot
15×associate-*r/
12×associate-*r* div-inv
8×flip3-+ flip-+
5×unswap-sqr
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in associate-/r/
Counts
4 → 718
Calls
4 calls:
255.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
408.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
44.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.7s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.6s

Counts
4 → 12
Calls
4 calls:
445.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
569.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
449.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.7s

Counts
730 → 730
Iterations

Useful iterations: done (1.6s)

IterNodesCost
081420856
1258419631
done500017266

prune5.6s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 7.9b

localize46.0ms

Local error

Found 4 expressions with local error:

2.5b
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
3.1b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.4b
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
12.9b
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
745×add-exp-log
479×prod-exp
210×div-exp
142×add-cbrt-cube
79×cbrt-unprod
75×pow-to-exp pow-exp
40×add-sqr-sqrt
36×associate-*l*
35×times-frac
32×*-un-lft-identity
30×cbrt-undiv
27×add-cube-cbrt
20×unpow-prod-down
18×associate-*l/
13×pow1
11×associate-*r/ associate-*r*
10×cbrt-prod
5×pow-prod-down associate-/l/ unswap-sqr
4×expm1-log1p-u frac-times flip3-+ flip-+ log1p-expm1-u add-log-exp sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 272
Calls
4 calls:
189.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
59.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
852.0ms
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
1.1s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.8s

Counts
4 → 12
Calls
4 calls:
386.0ms
(* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k))
380.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s
(/ (* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (cbrt t) 3.0)) (cos k)))
858.0ms
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.1s

Counts
284 → 284
Iterations

Useful iterations: done (1.1s)

IterNodesCost
040910482
112209392
done50016989

prune1.5s

Pruning

28 alts after pruning (28 fresh and 0 done)

Merged error: 7.5b

regimes1.3s

Accuracy

53.2% (3.7b remaining)

Error of 10.6b against oracle of 6.8b and baseline of 14.8b

bsearch533.0ms

Steps
ItersRangePoint
7
7.08713784555526e-61
2.3035787076265244e-59
5.664702255757937e-60
7
-0.22637101271021068
-0.008005822963963436
-0.0495663238912942

simplify20.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
059168
178168
done78168

end0.0ms

sample11.6s

Algorithm
intervals
Results
4.1s2029×body1280valid
2.7s1742×body640valid
2.4s5924×body80valid
1.4s880×body320valid
329.0ms398×body160valid