Details

Time bar (total: 14.9s)

sample129.0ms

Algorithm
intervals
Results
48.0ms67×body1280valid
25.0ms50×body640valid
24.0ms190×body80valid
11.0ms31×body320valid
4.0ms17×body160valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.2b

Counts
2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (pow t 3.0) (sin k))
3.3b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
5.0b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
27.4b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
73×times-frac
56×add-sqr-sqrt
50×div-exp
41×add-cube-cbrt *-un-lft-identity
40×prod-exp
33×associate-*l*
30×cbrt-undiv
22×cbrt-unprod
11×div-inv
10×associate-*r*
8×associate-/l*
7×unswap-sqr
6×pow1 associate-/r*
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative sqr-pow
1×frac-times associate-*r/ pow-prod-down associate-*l/ associate-/l/
Counts
4 → 184
Calls
4 calls:
5.0ms
(* (pow t 3.0) (sin k))
9.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
17.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (pow t 3.0) (sin k))
311.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
68.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
837.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify45.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010192396
150011978

prune696.0ms

Filtered
196 candidates to 138 candidates (70.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New18313196
Fresh011
Picked101
Done000
Total18414198

Merged error: 25.8b

Counts
198 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

2.6b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
2.9b
(* (pow t 3.0) (sin k))
6.8b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
18.6b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
96×add-exp-log
62×add-cbrt-cube
41×prod-exp
39×add-sqr-sqrt
32×div-exp
27×add-cube-cbrt *-un-lft-identity
25×times-frac
23×cbrt-unprod
22×associate-*l*
20×cbrt-undiv
19×associate-*r*
8×pow1
6×unswap-sqr
4×expm1-log1p-u pow-to-exp unpow-prod-down pow-exp log1p-expm1-u div-inv add-log-exp
3×associate-/r* *-commutative associate-/l*
2×pow-prod-down associate-*l/ sqr-pow
1×tan-quot frac-times frac-2neg associate-*r/ clear-num associate-/r/
Counts
4 → 148
Calls
4 calls:
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
6.0ms
(* (pow t 3.0) (sin k))
8.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
18.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
167.0ms
(* (pow t 3.0) (sin k))
335.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
848.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify113.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08631782
145291438
250011438

prune556.0ms

Filtered
160 candidates to 107 candidates (66.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1555160
Fresh6713
Picked101
Done000
Total16212174

Merged error: 25.6b

Counts
174 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
2.6b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
6.8b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
18.6b
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
436×add-exp-log
240×prod-exp
146×div-exp
100×add-cbrt-cube
48×pow-exp
40×cbrt-unprod
34×cbrt-undiv
33×add-sqr-sqrt
32×pow-to-exp
28×times-frac
26×add-cube-cbrt *-un-lft-identity
16×associate-*r*
15×associate-*l*
8×pow1
6×associate-/r*
5×div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*l/ unswap-sqr
2×tan-quot frac-2neg pow-prod-down clear-num associate-/r/ *-commutative
1×frac-times associate-*r/ associate-/l/
Counts
4 → 208
Calls
4 calls:
15.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
13.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
24.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
498.0ms
(/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k))
86.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
393.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l)
941.0ms
(* (/ (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (pow (cbrt t) 3.0) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify64.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011653923
150013194

prune661.0ms

Filtered
220 candidates to 108 candidates (49.1%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New2137220
Fresh11011
Picked101
Done000
Total21517232

Merged error: 22.0b

Counts
232 → 17

localize32.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
2.5b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
2.6b
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
18.6b
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
1780×add-exp-log
960×prod-exp
718×div-exp
196×pow-exp add-cbrt-cube
124×pow-to-exp
96×rec-exp 1-exp
84×cbrt-unprod
70×cbrt-undiv
40×times-frac
37×add-sqr-sqrt
32×add-cube-cbrt *-un-lft-identity
27×associate-*l*
14×associate-*r*
11×pow1
7×associate-*l/
6×associate-/r*
5×div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×frac-times unpow-prod-down associate-*r/ associate-/l/ sqr-pow
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative unswap-sqr
Counts
4 → 478
Calls
4 calls:
19.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
16.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
3.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
28.0ms
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.1s

Counts
4 → 12
Calls
4 calls:
481.0ms
(/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k))
583.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l))
84.0ms
(/ l (fma 2 1.0 (pow (/ k t) 2.0)))
938.0ms
(* (/ (* (/ 1 (pow (* (cbrt t) (cbrt t)) 3.0)) (* (/ 2.0 (* (pow (cbrt t) 3.0) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify109.0ms

Algorithm
egg-herbie
Counts
490 → 490
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
019609108
150017782

prune681.0ms

Filtered
490 candidates to 123 candidates (25.1%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New4828490
Fresh41216
Picked101
Done000
Total48720507

Merged error: 18.3b

Counts
507 → 20

regimes506.0ms

Accuracy

28% (2.0b remaining)

Error of 20.7b against oracle of 18.7b and baseline of 21.5b

bsearch243.0ms

Steps
ItersRangePoint
8
3.2254133426584345e-88
8.719301913697184e-85
8.6045816229314e-85
5
-3.7542262956881895e-13
-1.0508999232345835e-13
-3.6901934814442134e-13

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05466
15466

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s2058×body1280valid
876.0ms1710×body640valid
673.0ms5821×body80valid
321.0ms882×body320valid
112.0ms461×body160valid