Details

Time bar (total: 45.5s)

sample276.0ms

Algorithm
intervals
Results
99.0ms67×body1280valid
71.0ms221×body80valid
50.0ms51×body640valid
15.0ms23×body320valid
6.0ms11×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5000
3903
2161
148
019

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.1b

localize58.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.6b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.9b
(/ (pow t 3.0) (* l l))

rewrite678.0ms

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×pow-to-exp cbrt-undiv pow-exp tan-quot
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 clear-num associate-/r* frac-2neg distribute-lft-in
Counts
4 → 152
Calls
4 calls:
74.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
27.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
545.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
18.0ms
(/ (pow t 3.0) (* l l))

series2.0s

Counts
4 → 12
Calls
4 calls:
464.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
336.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
960.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
235.0ms
(/ (pow t 3.0) (* l l))

simplify499.0ms

Counts
164 → 164
Iterations
IterNodes
done5000
1839
0262

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.3b

localize93.0ms

Local error

Found 4 expressions with local error:

3.2b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.2b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b
(* (* (* (/ (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))

rewrite1.1s

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 clear-num frac-2neg distribute-lft-in
Counts
4 → 237
Calls
4 calls:
159.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
32.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
909.0ms
(* (* (* (/ (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))

series2.1s

Counts
4 → 12
Calls
4 calls:
521.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
276.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
283.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s
(* (* (* (/ (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))

simplify562.0ms

Counts
249 → 249
Iterations
IterNodes
done5001
11394
0440

prune2.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.5b

localize78.0ms

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)))
3.2b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b
(* (* (* (/ (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))

rewrite2.1s

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:
195.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
273.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
27.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.5s
(* (* (* (/ (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))

series2.8s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
853.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
404.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s
(* (* (* (/ (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))

simplify1.2s

Counts
730 → 730
Iterations
IterNodes
done5001
12756
0817

prune7.0s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 7.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt t) 3.0)
1.3b
(/ (* (pow (cbrt t) 3.0) (sin k)) l)
6.4b
(/ (* (* (/ (* (pow (cbrt t) 3.0) (sin k)) l) (pow (cbrt t) 3.0)) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (cbrt t) 3.0)))
13.1b
(* (* (/ (* (pow (cbrt t) 3.0) (sin k)) l) (pow (cbrt t) 3.0)) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
897×add-exp-log
483×prod-exp
355×div-exp
134×add-cbrt-cube
115×pow-to-exp pow-exp
97×times-frac
61×cbrt-unprod
49×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
42×unpow-prod-down
41×cbrt-undiv
37×associate-/r*
21×cbrt-prod
18×frac-times associate-*l/ associate-*r/
12×tan-quot
11×associate-/l/
10×pow1
8×flip3-+ flip-+
7×sqr-pow
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u div-inv add-log-exp
3×pow-unpow pow-prod-down
2×clear-num pow-pow frac-2neg associate-/l*
1×pow1/3 associate-*r* associate-*l* associate-/r/ *-commutative
Counts
4 → 360
Calls
4 calls:
7.0ms
(pow (cbrt t) 3.0)
24.0ms
(/ (* (pow (cbrt t) 3.0) (sin k)) l)
507.0ms
(/ (* (* (/ (* (pow (cbrt t) 3.0) (sin k)) l) (pow (cbrt t) 3.0)) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (cbrt t) 3.0)))
457.0ms
(* (* (/ (* (pow (cbrt t) 3.0) (sin k)) l) (pow (cbrt t) 3.0)) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series2.4s

Counts
4 → 12
Calls
4 calls:
427.0ms
(pow (cbrt t) 3.0)
387.0ms
(/ (* (pow (cbrt t) 3.0) (sin k)) l)
839.0ms
(/ (* (* (/ (* (pow (cbrt t) 3.0) (sin k)) l) (pow (cbrt t) 3.0)) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))) (/ l (pow (cbrt t) 3.0)))
769.0ms
(* (* (/ (* (pow (cbrt t) 3.0) (sin k)) l) (pow (cbrt t) 3.0)) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify910.0ms

Counts
372 → 372
Iterations
IterNodes
done5001
12043
0559

prune2.1s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 4.9b

regimes1.7s

Accuracy

60.6% (3.8b remaining)

Error of 8.7b against oracle of 4.9b and baseline of 14.5b

bsearch505.0ms

Steps
ItersRangePoint
10
1.2276075427297e-12
27750.67288899747
1.6765330329368327e-05
5
-8017959488307491.0
-3813544086202141.0
-6870817860977717.0

simplify11.0ms

Iterations
IterNodes
done59
159
046

end0.0ms

sample11.5s

Algorithm
intervals
Results
4.3s1999×body1280valid
3.5s1723×body640valid
2.0s5994×body80valid
641.0ms851×body320valid
287.0ms458×body160valid