Details

Time bar (total: 23.2s)

sample184.0ms

Algorithm
intervals
Results
59.0ms55×body1280valid
46.0ms212×body80valid
38.0ms51×body640valid
13.0ms23×body320valid
10.0ms16×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
04813
116113
294413
3500212

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.8b

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.6b
(* (/ (pow t 3.0) (* l l)) (sin k))
13.0b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
14.1b
(/ (pow t 3.0) (* l l))

rewrite341.0ms

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:
35.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
281.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
5.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
316.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
239.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
616.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
179.0ms
(/ (pow t 3.0) (* l l))

simplify116.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08171679
147261405
250011405

prune543.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.4b

localize30.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.9b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
13.0b
(* (* (* (/ (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))

rewrite536.0ms

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×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:
74.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
3.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
426.0ms
(* (* (* (/ (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))

series1.5s

Counts
4 → 12
Calls
4 calls:
357.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
237.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
196.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
728.0ms
(* (* (* (/ (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))

simplify61.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013643882
150013394

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.9b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
1.7b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.0b
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
5034×add-exp-log
3200×prod-exp
1557×div-exp
709×pow-exp
424×pow-to-exp
340×add-cbrt-cube
246×cbrt-unprod
125×associate-*l/
103×frac-times
85×cbrt-undiv
61×pow1
41×pow-prod-down
40×add-sqr-sqrt
37×associate-*l*
34×times-frac
33×associate-*r/
32×tan-quot *-un-lft-identity
27×add-cube-cbrt
20×unpow-prod-down
16×flip3-+ flip-+
12×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp sqr-pow
3×distribute-lft-out
1×distribute-rgt-in distribute-lft-in div-inv
Counts
4 → 947
Calls
4 calls:
77.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
292.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
17.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.3s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt 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:
291.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k)))
365.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
226.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
686.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify261.0ms

Algorithm
egg-herbie
Counts
959 → 959
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0321427397
1500123765

prune1.6s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
1.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
4.0b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
13.0b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt 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
3634×add-exp-log
2390×prod-exp
1049×div-exp
480×pow-exp
286×pow-to-exp
249×add-cbrt-cube
185×cbrt-unprod
100×associate-*l/
98×frac-times
59×cbrt-undiv
46×associate-*r/
43×add-sqr-sqrt
41×pow1
36×associate-*l*
35×*-un-lft-identity
34×times-frac
32×tan-quot
30×add-cube-cbrt
26×unpow-prod-down pow-prod-down
16×flip3-+ flip-+
13×cbrt-prod
11×associate-*r*
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 → 702
Calls
4 calls:
2.0ms
(pow (cbrt t) 3.0)
278.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
19.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
1.2s
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt 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:
302.0ms
(pow (cbrt t) 3.0)
366.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k))
228.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
706.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify211.0ms

Algorithm
egg-herbie
Counts
714 → 714
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0319320595
1500220351

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 6.5b

regimes628.0ms

Accuracy

10.5% (7.2b remaining)

Error of 15.4b against oracle of 8.2b and baseline of 16.3b

bsearch530.0ms

Steps
ItersRangePoint
10
3.6222469794403684e-107
1.1904220505298042e-95
8.125889730343351e-96
9
-3.57416073242495e-229
-4.9091354026710725e-234
-8.409001190729996e-230

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08791
18791

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.3s2119×body1280valid
1.3s5925×body80valid
1.3s1688×body640valid
459.0ms844×body320valid
164.0ms421×body160valid