Details

Time bar (total: 1.6m)

sample442.0ms

Algorithm
intervals
Results
138.0ms29×body5120valid
112.0ms66×body2560valid
100.0ms129×body1280valid
47.0ms79×body640valid
13.0ms34×body320valid
9.0ms74×body80valid
3.0ms10×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

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: 42.6b

Counts
2 → 2

localize18.0ms

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 expm1-log1p-u log1p-expm1-u 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 → 193
Calls
4 calls:
13.0ms
(* (* (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)))
15.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.1s

Counts
4 → 12
Calls
4 calls:
267.0ms
(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
232.0ms
(* (pow t 3.0) (tan k))
369.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
245.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify135.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09252237
148051854
250011854

prune417.0ms

Filtered
205 candidates to 88 candidates (42.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1996205
Fresh101
Picked101
Done000
Total2016207

Merged error: 25.6b

Counts
207 → 6

localize22.0ms

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)))

rewrite112.0ms

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×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
10.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms
(* (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:
336.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
323.0ms
(* (pow k 2.0) (pow t 1.0))
637.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify164.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
014397252
142967083
250037076

prune618.0ms

Filtered
620 candidates to 108 candidates (17.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New6128620
Fresh235
Picked101
Done000
Total61511626

Merged error: 20.8b

Counts
626 → 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)))

rewrite280.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 1468
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))
40.0ms
(* (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:
19.0ms
(pow (sin k) 2)
326.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
845.0ms
(* (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)))

simplify303.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune570.0ms

Filtered
1480 candidates to 94 candidates (6.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New147371480
Fresh2810
Picked101
Done000
Total1476151491

Merged error: 15.6b

Counts
1491 → 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)))

rewrite2.8s

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×expm1-log1p-u log1p-expm1-u 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 → 9578
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)
146.0ms
(/ (/ (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:
331.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
430.0ms
(pow (cbrt (sin k)) 4)
87.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
660.0ms
(* (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
9590 → 9590
Iterations

Useful iterations: 0 (149.0ms)

IterNodesCost
010779269614

prune1.0m

Filtered
9590 candidates to 8073 candidates (84.2%)
Pruning

27 alts after pruning (27 fresh and 0 done)

PrunedKeptTotal
New9569219590
Fresh8614
Picked101
Done000
Total9578279605

Merged error: 10.0b

Counts
9605 → 27

regimes965.0ms

Accuracy

30.7% (3.2b remaining)

Error of 10.8b against oracle of 7.6b and baseline of 12.2b

bsearch1.3s

Steps
ItersRangePoint
11
2.512579933221449e+133
2.539474402547936e+158
5.359847357268255e+152
8
3.0514006174485665e-162
2.414262268045163e-158
2.368195771051515e-158
3
-2.7615416047363757e-183
-1.8692576841174017e-183
-2.0255984982069005e-183
8
-1.8783855919608248e+153
-1.3968704931933265e+149
-1.283431163841487e+152

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0107157
1107157

end0.0ms

sample14.5s

Algorithm
intervals
Results
4.7s2329×body2560valid
4.1s954×body5120valid
3.2s3997×body1280valid
1.3s2503×body640valid
413.0ms1042×body320valid
259.0ms2009×body80valid
125.0ms483×body160valid