Details

Time bar (total: 21.9s)

sample159.0ms

Algorithm
intervals
Results
75.0ms83×body1280valid
23.0ms197×body80valid
22.0ms39×body640valid
9.0ms24×body320valid
3.0ms10×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04813
116113
294413
3500212

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
3.7b
(* (/ (pow t 3.0) (* l l)) (sin k))
12.9b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
16.4b
(/ (pow t 3.0) (* l l))

rewrite604.0ms

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:
73.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
32.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
483.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
11.0ms
(/ (pow t 3.0) (* l l))

series1.3s

Counts
4 → 12
Calls
4 calls:
301.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
227.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
605.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
174.0ms
(/ (pow t 3.0) (* l l))

simplify124.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08171679
147261405
250011405

prune533.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize31.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
8.0b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
12.9b
(* (* (* (/ (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))

rewrite879.0ms

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:
138.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
28.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
9.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
691.0ms
(* (* (* (/ (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:
344.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
225.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
186.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
698.0ms
(* (* (* (/ (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))

simplify62.0ms

Algorithm
egg-herbie
Counts
249 → 249
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013643882
150013394

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
2.7b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
12.9b
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
2085×add-exp-log
1365×prod-exp
627×div-exp
253×add-cbrt-cube
210×pow-to-exp pow-exp
187×cbrt-unprod
116×associate-*l/
98×frac-times
57×cbrt-undiv
50×pow1
43×add-sqr-sqrt
36×associate-*l*
35×*-un-lft-identity
34×times-frac
33×pow-prod-down
32×tan-quot
30×add-cube-cbrt associate-*r/
26×unpow-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 → 526
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
566.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
28.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
2.4s
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
273.0ms
(pow (cbrt t) 3.0)
344.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
459.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
681.0ms
(* (* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify148.0ms

Algorithm
egg-herbie
Counts
538 → 538
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0259312507
1500111873

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
0.7b
(pow (cbrt t) 3.0)
4.7b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.3b
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite913.0ms

Algorithm
rewrite-expression-head
Rules
2084×add-exp-log
1364×prod-exp
627×div-exp
251×add-cbrt-cube
211×pow-to-exp pow-exp
186×cbrt-unprod
81×frac-times
70×associate-*l/
57×cbrt-undiv
49×pow1
44×add-sqr-sqrt
39×associate-*r/
35×associate-*l*
34×times-frac
32×unpow-prod-down pow-prod-down
31×add-cube-cbrt *-un-lft-identity
24×tan-quot
16×cbrt-prod flip3-+ flip-+
6×pow-unpow sqr-pow
5×unswap-sqr
4×distribute-rgt-in expm1-log1p-u pow-pow distribute-lft-in associate-*r* log1p-expm1-u add-log-exp
2×pow1/3 *-commutative
1×div-inv
Counts
4 → 515
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
3.0ms
(pow (cbrt t) 3.0)
28.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
820.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt 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:
291.0ms
(pow (cbrt t) 3.0)
296.0ms
(pow (cbrt t) 3.0)
219.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
681.0ms
(* (* (* (/ (pow (cbrt t) 3.0) (* (cbrt l) (cbrt l))) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify152.0ms

Algorithm
egg-herbie
Counts
527 → 527
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0249813026
1500112892

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.8b

regimes628.0ms

Accuracy

15.7% (7.0b remaining)

Error of 17.5b against oracle of 10.5b and baseline of 18.8b

bsearch381.0ms

Steps
ItersRangePoint
7
6.477526161048875e-111
7.387063241046734e-109
6.565726687888966e-111
9
-8.398173019220788e-261
-1.4529523301294986e-269
-5.4815075938618785e-263

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08757
110057
210757
311557
412757
513257
613257

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s2092×body1280valid
915.0ms1661×body640valid
673.0ms5990×body80valid
340.0ms885×body320valid
113.0ms433×body160valid