Details

Time bar (total: 25.0s)

sample131.0ms

Algorithm
intervals
Results
47.0ms61×body1280valid
32.0ms63×body640valid
19.0ms189×body80valid
10.0ms30×body320valid
3.0ms12×body160valid

simplify28.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113
done500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.2b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.3b
(/ (pow t 3.0) (* l l))

rewrite652.0ms

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×flip3-+ flip-+ 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 → 144
Calls
4 calls:
33.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
80.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
521.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
12.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
253.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
328.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
649.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
183.0ms
(/ (pow t 3.0) (* l l))

simplify116.0ms

Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08011619
146461348
250021348
done50021348

prune484.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.9b

localize26.0ms

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))
3.9b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
6.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.2b
(* (* (* (* (/ (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))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
203×prod-exp
97×div-exp
82×add-cbrt-cube
55×associate-*l/
46×cbrt-unprod
41×pow-exp
35×frac-times
32×pow1
28×pow-to-exp
22×*-un-lft-identity
19×pow-prod-down
17×add-sqr-sqrt add-cube-cbrt
16×tan-quot
15×times-frac associate-*r/
13×cbrt-undiv
11×associate-*r*
8×flip3-+ flip-+
5×associate-/l*
4×unpow-prod-down add-log-exp sqr-pow
3×associate-*l* associate-/r* *-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv
Counts
4 → 204
Calls
4 calls:
57.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
195.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
10.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
966.0ms
(* (* (* (* (/ (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))

series1.6s

Counts
4 → 12
Calls
4 calls:
288.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
381.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
197.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
734.0ms
(* (* (* (* (/ (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))

simplify58.0ms

Counts
216 → 216
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011793756
150013242
done50013242

prune742.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
2.7b
(* (* (/ (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))
3.9b
(* (* (* (/ (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))
13.2b
(* (* (* (* (/ (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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite3.6s

Algorithm
rewrite-expression-head
Rules
2290×add-exp-log
1252×prod-exp
916×div-exp
372×pow-exp
228×pow-to-exp
178×add-cbrt-cube
95×associate-*l/
94×cbrt-unprod
64×frac-times
46×cbrt-undiv
32×pow1
28×tan-quot
26×associate-*r/
23×associate-/r/
19×pow-prod-down
16×flip3-+ flip-+
14×*-un-lft-identity
11×associate-*r*
9×add-sqr-sqrt add-cube-cbrt
4×add-log-exp
3×times-frac associate-*l* *-commutative distribute-lft-out associate-/l*
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* div-inv
Counts
4 → 502
Calls
4 calls:
1.4s
(/ 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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
99.0ms
(* (* (/ (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))
358.0ms
(* (* (* (/ (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))
1.6s
(* (* (* (* (/ (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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
699.0ms
(/ 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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
292.0ms
(* (* (/ (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))
362.0ms
(* (* (* (/ (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))
968.0ms
(* (* (* (* (/ (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)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify132.0ms

Counts
514 → 514
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0202813603
1500212330
done500212330

prune895.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.0b

localize38.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
5.1b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k))
6.7b
(* (/ 2.0 (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
12.0b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite3.5s

Algorithm
rewrite-expression-head
Rules
1020×add-exp-log
662×prod-exp
280×div-exp
138×pow-exp
124×add-cbrt-cube
85×pow-to-exp
70×cbrt-unprod
30×associate-*r*
29×associate-*l/
27×add-sqr-sqrt associate-*r/
24×cbrt-undiv
23×*-un-lft-identity
22×pow1
21×times-frac associate-*l*
20×frac-times
18×add-cube-cbrt
14×tan-quot
11×pow-prod-down associate-/r/
8×flip3-+ flip-+
4×unpow-prod-down *-commutative add-log-exp unswap-sqr sqr-pow
3×distribute-lft-out
2×div-inv
1×distribute-rgt-in distribute-lft-in
Counts
4 → 299
Calls
4 calls:
171.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
56.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k))
2.4s
(* (/ 2.0 (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
807.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.1s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
259.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k))
688.0ms
(* (/ 2.0 (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))))
837.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify90.0ms

Counts
311 → 311
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
016217820
150026935
done50026935

prune789.0ms

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 6.9b

regimes709.0ms

Accuracy

20.6% (5.8b remaining)

Error of 13.7b against oracle of 7.8b and baseline of 15.2b

bsearch167.0ms

Steps
ItersRangePoint
2
2.0510443546601508e-05
2.3761734392231562e-05
2.1729677613712775e-05
6
-4.02997273420241e-37
-4.638699354804609e-38
-4.695605514262814e-38

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07761
17761
done7761

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2074×body1280valid
904.0ms1732×body640valid
656.0ms5979×body80valid
307.0ms842×body320valid
98.0ms411×body160valid