Details

Time bar (total: 15.1s)

sample129.0ms

Algorithm
intervals
Results
47.0ms65×body1280valid
27.0ms54×body640valid
25.0ms196×body80valid
9.0ms24×body320valid
3.0ms12×body160valid

simplify31.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ (pow t 3.0) (* l l)) (sin k))
3.1b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
12.5b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.0b
(/ (pow t 3.0) (* l l))

rewrite58.0ms

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:
9.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
23.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
7.0ms
(/ (pow t 3.0) (* l l))

series1.4s

Counts
4 → 12
Calls
4 calls:
243.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
321.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
634.0ms
(* (* (* (/ (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))

simplify124.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08171679
147261405
250011405

prune550.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.0b

localize28.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
3.1b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
8.2b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.5b
(* (* (* (* (/ (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))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
346×add-exp-log
203×prod-exp
97×div-exp
82×add-cbrt-cube
55×associate-*l/
46×cbrt-unprod
41×pow-exp
35×frac-times
32×pow1
28×pow-to-exp
22×*-un-lft-identity
19×pow-prod-down
17×add-sqr-sqrt add-cube-cbrt
16×tan-quot
15×times-frac associate-*r/
13×cbrt-undiv
11×associate-*r*
8×flip3-+ flip-+
5×associate-/l*
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp sqr-pow
3×associate-*l* associate-/r* *-commutative distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv
Counts
4 → 212
Calls
4 calls:
14.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
20.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
32.0ms
(* (* (* (* (/ (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:
293.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
367.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
201.0ms
(/ (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))

simplify65.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011963855
150013336

prune805.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
1.5b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k))
3.1b
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
12.5b
(* (* (* (* (/ (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))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
891×add-exp-log
478×prod-exp
369×div-exp
124×pow-to-exp pow-exp
119×add-cbrt-cube
64×cbrt-unprod
55×associate-*l/
35×frac-times
33×pow1
27×cbrt-undiv
19×pow-prod-down
16×tan-quot
15×*-un-lft-identity associate-*r/
11×associate-*r*
10×add-sqr-sqrt add-cube-cbrt
8×flip3-+ flip-+
6×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod pow-unpow associate-*l* *-commutative distribute-lft-out
2×pow-pow
1×distribute-rgt-in distribute-lft-in pow1/3 sqr-pow
Counts
4 → 297
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
40.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k))
49.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
65.0ms
(* (* (* (* (/ (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))

series1.7s

Counts
4 → 12
Calls
4 calls:
312.0ms
(pow (cbrt t) 3.0)
294.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k))
375.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
758.0ms
(* (* (* (* (/ (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))

simplify75.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013985480
150024437

prune852.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
3.1b
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
5.4b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.5b
(* (* (* (/ (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))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
773×add-exp-log
437×prod-exp
291×div-exp
115×add-cbrt-cube
98×pow-to-exp pow-exp
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 → 306
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
48.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
11.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
63.0ms
(* (* (* (/ (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))

series1.7s

Counts
4 → 12
Calls
4 calls:
305.0ms
(pow (cbrt t) 3.0)
365.0ms
(* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
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))

simplify72.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015705422
150014782

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.0b

regimes572.0ms

Accuracy

-9.3% (6.3b remaining)

Error of 15.0b against oracle of 8.7b and baseline of 14.5b

bsearch4.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08277
18277

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s2002×body1280valid
893.0ms1740×body640valid
708.0ms6031×body80valid
294.0ms826×body320valid
111.0ms438×body160valid