Details

Time bar (total: 1.3m)

sample435.0ms

Algorithm
intervals
Results
138.0ms29×body5120valid
116.0ms66×body2560valid
98.0ms129×body1280valid
39.0ms79×body640valid
12.0ms34×body320valid
9.0ms74×body80valid
2.0ms10×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

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: 42.6b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
0.6b
(* (pow t 3.0) (tan k))
25.4b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.8b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
392×add-exp-log
265×prod-exp
74×div-exp add-cbrt-cube
61×pow-exp
41×pow-to-exp
40×cbrt-unprod
25×associate-*l*
21×add-sqr-sqrt
17×unpow-prod-down
16×add-cube-cbrt *-un-lft-identity
12×cbrt-undiv
10×times-frac
7×associate-*r/ associate-*r*
6×pow1
4×tan-quot add-log-exp
3×*-commutative unswap-sqr sqr-pow
2×associate-*l/ div-inv
1×frac-2neg pow-prod-down clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 185
Calls
4 calls:
15.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
6.0ms
(* (pow t 3.0) (tan k))
18.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
12.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.1s

Counts
4 → 12
Calls
4 calls:
273.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
243.0ms
(* (pow t 3.0) (tan k))
361.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
240.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify130.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09082174
147741790
250021790

prune366.0ms

Filtered
197 candidates to 80 candidates (40.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1916197
Fresh101
Picked101
Done000
Total1936199

Merged error: 25.6b

Counts
199 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.3b
(* (pow k 2.0) (pow t 1.0))
20.6b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
1645×add-exp-log
1122×prod-exp
899×pow-exp
688×div-exp
509×pow-to-exp
140×rec-exp 1-exp
37×add-sqr-sqrt
29×unpow-prod-down
25×add-cbrt-cube
22×times-frac
20×add-cube-cbrt *-un-lft-identity
19×associate-*r*
18×associate-*l*
13×sqr-pow
12×unswap-sqr
9×associate-/r*
7×cbrt-unprod
6×cbrt-undiv
5×pow1
4×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
7.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.0ms
(* (pow k 2.0) (pow t 1.0))
22.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts
4 → 12
Calls
4 calls:
331.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
331.0ms
(* (pow k 2.0) (pow t 1.0))
641.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify162.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
013167194
141627025
250027018

prune555.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New6048612
Fresh235
Picked101
Done000
Total60711618

Merged error: 20.8b

Counts
618 → 11

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
20.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
5603×add-exp-log
4515×prod-exp
3078×pow-exp
2032×div-exp
1869×pow-to-exp
434×rec-exp 1-exp
27×add-cbrt-cube
23×add-sqr-sqrt
22×times-frac
20×unpow-prod-down
18×add-cube-cbrt *-un-lft-identity
12×associate-*r*
11×associate-*l*
9×associate-/r*
8×cbrt-unprod
7×cbrt-undiv
6×pow1 sqr-pow
4×div-inv associate-/l* unpow2 add-log-exp
3×pow-unpow unswap-sqr
2×frac-2neg clear-num
1×pow-flip pow-pow associate-*r/ *-commutative inv-pow
Counts
4 → 1460
Calls
4 calls:
3.0ms
(pow (sin k) 2)
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
42.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
330.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
80.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
835.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify299.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune504.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New146571472
Fresh2810
Picked101
Done000
Total1468151483

Merged error: 15.6b

Counts
1483 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.9b
(pow (cbrt (sin k)) 4)
2.0b
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
20.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
28004×times-frac
11423×add-sqr-sqrt
10970×add-cube-cbrt *-un-lft-identity
10470×add-exp-log
7729×unpow-prod-down
6478×div-exp
5244×prod-exp
4340×pow-exp
3843×cbrt-prod
3557×associate-*r*
2573×pow-to-exp
1342×sqr-pow
668×unpow2
620×rec-exp 1-exp
326×associate-/l*
303×div-inv
108×unswap-sqr
47×add-cbrt-cube
23×cbrt-undiv associate-/r/
12×associate-/r*
11×associate-*l*
8×cbrt-unprod
6×pow1
4×add-log-exp
3×pow-unpow
2×pow-pow frac-2neg clear-num
1×pow-flip pow1/3 associate-*r/ *-commutative associate-/l/ inv-pow
Counts
4 → 9570
Calls
4 calls:
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.0ms
(pow (cbrt (sin k)) 4)
151.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
1.1s
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
338.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
128.0ms
(pow (cbrt (sin k)) 4)
87.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
951.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.4s

Algorithm
egg-herbie
Counts
9582 → 9582
Iterations

Useful iterations: 0 (136.0ms)

IterNodesCost
010771265606

prune49.7s

Filtered
9582 candidates to 6614 candidates (69.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New9562209582
Fresh8614
Picked101
Done000
Total9571269597

Merged error: 10.0b

Counts
9597 → 26

regimes854.0ms

Accuracy

28.2% (3.3b remaining)

Error of 10.9b against oracle of 7.6b and baseline of 12.2b

bsearch1.3s

Steps
ItersRangePoint
11
2.512579933221449e+133
2.539474402547936e+158
3.8000753786438794e+149
8
3.0514006174485665e-162
2.414262268045163e-158
2.368195771051515e-158
5
-9.966042788984376e-183
-2.7615416047363757e-183
-3.580792123892542e-183
8
-1.8783855919608248e+153
-1.3968704931933265e+149
-1.283431163841487e+152

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0106145
1106145

end0.0ms

sample14.4s

Algorithm
intervals
Results
4.6s2329×body2560valid
4.1s954×body5120valid
3.2s3997×body1280valid
1.3s2503×body640valid
386.0ms1042×body320valid
250.0ms2009×body80valid
119.0ms483×body160valid