Details

Time bar (total: 27.5s)

sample140.0ms

Algorithm
intervals
Results
53.0ms65×body1280valid
31.0ms50×body640valid
20.0ms178×body80valid
12.0ms33×body320valid
6.0ms24×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01925
14725
215325
375925
4375425
done500125

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (/ (pow t 3.0) (* l l)) (sin k))
2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.6b
(/ (pow t 3.0) (* l l))

rewrite393.0ms

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:
16.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
39.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
326.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
262.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
334.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
660.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
191.0ms
(/ (pow t 3.0) (* l l))

simplify1.4s

Counts
156 → 156
Iterations

Useful iterations: 2 (631.0ms)

IterNodesCost
02553209
17863070
237332565
done50002565

prune524.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.3b

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (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))
7.5b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.9b
(* (* (* (/ (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))

rewrite628.0ms

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×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 → 229
Calls
4 calls:
86.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
501.0ms
(* (* (* (/ (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:
372.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
198.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
744.0ms
(* (* (* (/ (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))

simplify509.0ms

Counts
241 → 241
Iterations

Useful iterations: done (499.0ms)

IterNodesCost
04296958
113456583
done50016450

prune924.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.4b

localize26.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 2.0 (* (* (* (/ (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)))
2.9b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.9b
(* (* (* (/ (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))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
1254×add-exp-log
687×prod-exp
503×div-exp
187×add-cbrt-cube
145×pow-to-exp pow-exp
99×cbrt-unprod
78×associate-*l/
63×frac-times
49×cbrt-undiv
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
29×pow1 add-cube-cbrt
28×tan-quot
25×associate-*r/
23×associate-/r/
20×unpow-prod-down
17×pow-prod-down
16×flip3-+ flip-+
11×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×add-log-exp sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 397
Calls
4 calls:
790.0ms
(/ 2.0 (* (* (* (/ (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)))
196.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
21.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
920.0ms
(* (* (* (/ (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))

series2.0s

Counts
4 → 12
Calls
4 calls:
667.0ms
(/ 2.0 (* (* (* (/ (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)))
361.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
241.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
764.0ms
(* (* (* (/ (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))

simplify610.0ms

Counts
409 → 409
Iterations

Useful iterations: done (586.0ms)

IterNodesCost
053815946
1186714498
done500013311

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.9b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.1b
(/ 2.0 (* (* (/ (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))))
4.8b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
16.2b
(* (* (/ (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)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
1938×add-exp-log
985×prod-exp
856×div-exp
677×times-frac
404×unpow-prod-down
380×associate-*l*
343×add-sqr-sqrt
330×add-cube-cbrt *-un-lft-identity
275×add-cbrt-cube
241×pow-to-exp pow-exp
202×cbrt-prod
137×cbrt-unprod
82×cbrt-undiv
68×sqr-pow
59×frac-times
54×associate-*l/
39×associate-*r/
32×pow1
24×tan-quot associate-/r/
19×pow-prod-down
16×flip3-+ flip-+
13×div-inv
5×associate-*r* unswap-sqr
4×distribute-rgt-in distribute-lft-in add-log-exp
3×*-commutative associate-/l*
1×frac-2neg clear-num associate-/r*
Counts
4 → 880
Calls
4 calls:
140.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
357.0ms
(/ 2.0 (* (* (/ (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))))
20.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
381.0ms
(* (* (/ (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)))

series2.0s

Counts
4 → 12
Calls
4 calls:
296.0ms
(* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
666.0ms
(/ 2.0 (* (* (/ (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))))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
749.0ms
(* (* (/ (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)))

simplify805.0ms

Counts
892 → 892
Iterations

Useful iterations: done (762.0ms)

IterNodesCost
093530587
1322328415
done500028271

prune3.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.6b

regimes497.0ms

Accuracy

7.9% (5.7b remaining)

Error of 13.7b against oracle of 8.0b and baseline of 14.2b

bsearch352.0ms

Steps
ItersRangePoint
8
2.0525398386665953e-258
2.984272116100817e-254
3.6480188607512227e-258
10
-1.596688388201961e-102
-1.3766878582811875e-112
-8.986457495608877e-105

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
044117
16082
done6082

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s2072×body1280valid
951.0ms1742×body640valid
680.0ms5877×body80valid
330.0ms868×body320valid
114.0ms441×body160valid