Details

Time bar (total: 48.9s)

sample283.0ms

Algorithm
intervals
Results
105.0ms74×body1280valid
75.0ms48×body640valid
40.0ms196×body80valid
21.0ms31×body320valid
10.0ms20×body160valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01925
17625
2324525
done500125

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize49.0ms

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))
12.0b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.6b
(/ (pow t 3.0) (* l l))

rewrite954.0ms

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×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:
65.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
123.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
736.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
19.0ms
(/ (pow t 3.0) (* l l))

series2.0s

Counts
4 → 12
Calls
4 calls:
352.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
509.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
899.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
263.0ms
(/ (pow t 3.0) (* l l))

simplify3.4s

Counts
164 → 164
Iterations

Useful iterations: done (3.4s)

IterNodesCost
02633323
130473163
done50002681

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.9b

localize62.0ms

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)
12.0b
(* (* (* (/ (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))

rewrite1.5s

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:
235.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
62.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
19.0ms
(/ (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))

series2.3s

Counts
4 → 12
Calls
4 calls:
529.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
357.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
268.0ms
(/ (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))

simplify666.0ms

Counts
249 → 249
Iterations

Useful iterations: done (656.0ms)

IterNodesCost
04377110
done50016803

prune1.9s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.3b

localize52.0ms

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))
12.0b
(* (* (* (/ (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))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
791×prod-exp
489×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
63×cbrt-unprod
44×associate-*l/
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×frac-times times-frac
30×pow1 add-cube-cbrt
26×unpow-prod-down
25×cbrt-undiv
17×pow-prod-down
16×tan-quot
14×associate-*r/
13×cbrt-prod
11×associate-*r*
8×flip3-+ flip-+
5×unswap-sqr sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 div-inv
Counts
4 → 386
Calls
4 calls:
7.0ms
(pow (cbrt t) 3.0)
328.0ms
(* (* (/ (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))
1.5s
(* (* (* (/ (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))

series3.0s

Counts
4 → 12
Calls
4 calls:
519.0ms
(pow (cbrt t) 3.0)
503.0ms
(* (* (/ (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))
327.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin 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))

simplify1.2s

Counts
398 → 398
Iterations

Useful iterations: done (1.2s)

IterNodesCost
055316779
done500015197

prune1.9s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 5.7b

localize103.0ms

Local error

Found 4 expressions with local error:

3.9b
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.2b
(/ (* (* (* (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))))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.9b
(* (* (* (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))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
966×add-exp-log
593×prod-exp
294×div-exp
145×pow-exp
103×add-cbrt-cube
87×pow-to-exp
83×times-frac
58×add-sqr-sqrt
53×cbrt-unprod
50×*-un-lft-identity
45×add-cube-cbrt
36×associate-*l*
28×associate-*l/
26×unpow-prod-down
25×associate-*r/
23×cbrt-undiv
19×frac-times associate-/r*
14×tan-quot
13×pow1
11×associate-*r* associate-/l/
10×cbrt-prod sqr-pow
8×flip3-+ flip-+
5×pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×*-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/ associate-/l*
Counts
4 → 351
Calls
4 calls:
251.0ms
(* (* (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)) (* (/ (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))))
36.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.1s
(* (* (* (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))

series3.4s

Counts
4 → 12
Calls
4 calls:
558.0ms
(* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
1.1s
(/ (* (* (* (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))))
426.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.3s
(* (* (* (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))

simplify846.0ms

Counts
363 → 363
Iterations

Useful iterations: done (829.0ms)

IterNodesCost
055215366
done500014335

prune2.0s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 5.3b

regimes1.2s

Accuracy

32.6% (4.8b remaining)

Error of 12.2b against oracle of 7.4b and baseline of 14.6b

bsearch647.0ms

Steps
ItersRangePoint
5
5.381305634170913e-91
1.1998745633530718e-90
1.009878416081778e-90
9
-9.398525281878855e-168
-3.8693183758173566e-176
-1.2086640029117327e-168

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
063174
181174
done81174

end0.0ms

sample11.6s

Algorithm
intervals
Results
4.7s2072×body1280valid
3.7s1746×body640valid
1.7s5903×body80valid
675.0ms832×body320valid
211.0ms413×body160valid