Details

Time bar (total: 15.9s)

sample126.0ms

Algorithm
intervals
Results
49.0ms66×body1280valid
28.0ms60×body640valid
20.0ms196×body80valid
9.0ms26×body320valid
3.0ms11×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.3b

localize21.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.0b
(* (/ (pow t 3.0) (* l l)) (sin k))
11.1b
(* (* (* (/ (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))

rewrite59.0ms

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:
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
26.0ms
(* (* (* (/ (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:
316.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
248.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
626.0ms
(* (* (* (/ (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))

simplify122.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08171679
147261405
250011405

prune542.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.7b

localize31.0ms

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))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.4b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
11.1b
(* (* (* (/ (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))

rewrite82.0ms

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:
17.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
31.0ms
(* (* (* (/ (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:
361.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
239.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
195.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
733.0ms
(* (* (* (/ (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 (31.0ms)

IterNodesCost
013643882
150013394

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.9b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
11.1b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
1369×add-exp-log
991×prod-exp
289×div-exp
224×pow-exp
134×pow-to-exp
115×add-cbrt-cube
75×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 associate-*r/
26×unpow-prod-down
17×pow-prod-down
16×tan-quot
13×cbrt-undiv 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:
3.0ms
(pow (cbrt t) 3.0)
25.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
12.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
45.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
302.0ms
(pow (cbrt t) 3.0)
367.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
243.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
742.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify106.0ms

Algorithm
egg-herbie
Counts
398 → 398
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
018618687
150016760

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.1b

localize42.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))
2.9b
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
3.4b
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
11.1b
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
3309×add-exp-log
2549×prod-exp
584×div-exp
448×pow-exp
268×pow-to-exp
214×add-cbrt-cube
201×cbrt-unprod
65×pow1
62×associate-*l/
45×pow-prod-down
37×associate-*l*
36×add-sqr-sqrt
34×frac-times times-frac
33×*-un-lft-identity
30×associate-*r/
28×cbrt-undiv add-cube-cbrt
20×unpow-prod-down
16×tan-quot
15×associate-*r*
13×cbrt-prod
8×flip3-+ flip-+
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 → 635
Calls
4 calls:
17.0ms
(* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))
40.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
15.0ms
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
65.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))
359.0ms
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k))
289.0ms
(* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k))))
731.0ms
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (* (/ (pow (cbrt t) 3.0) l) (* (cbrt (sin k)) (cbrt (sin k)))) (cbrt (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify186.0ms

Algorithm
egg-herbie
Counts
647 → 647
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0274819545
1500117016

prune1.2s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.1b

regimes672.0ms

Accuracy

16.1% (6.2b remaining)

Error of 16.7b against oracle of 10.4b and baseline of 17.9b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06988
16988

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2041×body1280valid
852.0ms1752×body640valid
612.0ms5890×body80valid
299.0ms868×body320valid
105.0ms470×body160valid