Details

Time bar (total: 22.5s)

sample468.0ms

Algorithm
intervals
Results
173.0ms77×body2560valid
103.0ms29×body5120valid
101.0ms131×body1280valid
43.0ms81×body640valid
13.0ms34×body320valid
6.0ms49×body80valid
3.0ms13×body160valid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0534021

prune18.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.3b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
5.7b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
8.0b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
29.0b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
356×add-exp-log
241×prod-exp
74×add-cbrt-cube
69×div-exp
48×pow-exp
40×cbrt-unprod
36×pow-to-exp
18×associate-*l*
14×add-sqr-sqrt
12×cbrt-undiv add-cube-cbrt *-un-lft-identity
11×pow1
7×associate-*r/
6×times-frac
5×associate-*r* associate-*l/
4×pow-prod-down add-log-exp
3×tan-quot unpow-prod-down *-commutative associate-/l*
2×associate-/r/ div-inv
1×frac-2neg clear-num associate-/r* unswap-sqr sqr-pow
Counts
4 → 168
Calls
4 calls:
13.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
17.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
15.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
13.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series466.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
126.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
162.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
72.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify72.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049733531
149733531

prune262.0ms

Filtered
82 candidates to 180 candidates (-119.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1719180
Fresh011
Picked101
Done000
Total17210182

Merged error: 15.3b

Counts
182 → 10

localize26.0ms

Local error

Found 4 expressions with local error:

2.0b
(* (/ (cos k) (pow (sin k) 2)) l)
5.7b
(* l (* 2.0 (* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
5.9b
(* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
7.3b
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
1265×add-exp-log
1066×prod-exp
757×pow-exp
287×pow-to-exp
171×div-exp
71×unpow-prod-down
70×add-sqr-sqrt
47×associate-*l*
40×add-cbrt-cube
30×unswap-sqr
29×sqr-pow
28×add-cube-cbrt *-un-lft-identity times-frac
22×cbrt-unprod
16×associate-*r*
11×pow1
5×pow-prod-down
4×associate-*r/ *-commutative unpow2 add-log-exp
3×cbrt-undiv associate-*l/
1×div-inv
Counts
4 → 454
Calls
4 calls:
9.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
29.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
15.0ms
(* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
12.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

series343.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
112.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
148.0ms
(* (pow (* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))
64.0ms
(* (pow (pow k (neg 2.0)) 1.0) (pow (pow t (neg 1.0)) 1.0))

simplify101.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
0547211034

prune664.0ms

Filtered
135 candidates to 466 candidates (-245.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New45412466
Fresh369
Picked101
Done000
Total45818476

Merged error: 9.0b

Counts
476 → 18

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
2.0b
(* (/ (cos k) (pow (sin k) 2)) l)
5.7b
(* l (* 2.0 (* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
5.9b
(* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
6626×add-exp-log
6281×prod-exp
4618×pow-exp
1798×pow-to-exp
801×div-exp
38×add-cbrt-cube
36×add-sqr-sqrt associate-*l*
28×times-frac
24×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
14×unpow-prod-down
12×pow1
6×sqr-pow
5×associate-*r* unpow2 unswap-sqr
4×associate-*r/ pow-prod-down add-log-exp
3×cbrt-undiv pow-unpow associate-*l/ *-commutative
1×pow-pow div-inv
Counts
4 → 1440
Calls
4 calls:
2.0ms
(pow (sin k) 2)
9.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
75.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
28.0ms
(* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))

series275.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin k) 2)
21.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
107.0ms
(* l (* 2.0 (* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))))
145.0ms
(* (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0))) 1.0) (* (/ (cos k) (pow (sin k) 2)) l))

simplify360.0ms

Algorithm
egg-herbie
Counts
1452 → 1452
Iterations

Useful iterations: 0 (135.0ms)

IterNodesCost
0617444672

prune489.0ms

Filtered
91 candidates to 1452 candidates (-1495.6%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New144571452
Fresh61117
Picked101
Done000
Total1452181470

Merged error: 5.6b

Counts
1470 → 18

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.0b
(* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))
5.7b
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))))))
7.1b
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0)))

rewrite314.0ms

Algorithm
rewrite-expression-head
Rules
5645×add-exp-log
5209×prod-exp
3655×pow-exp
1351×pow-to-exp
756×div-exp
45×add-cbrt-cube
43×add-sqr-sqrt
34×associate-*l*
32×times-frac
27×cbrt-unprod
24×add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
12×pow1 sqr-pow
10×unswap-sqr
7×associate-*r*
6×unpow2
5×associate-*r/
4×pow-prod-down add-log-exp
3×cbrt-undiv pow-unpow associate-*l/ *-commutative
1×pow-pow div-inv
Counts
4 → 1135
Calls
4 calls:
2.0ms
(pow (sin k) 2)
16.0ms
(* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))
89.0ms
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))))))
18.0ms
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin k) 2)
85.0ms
(* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))
107.0ms
(* l (* 2.0 (* (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0) (* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0))))))
111.0ms
(* l (* (/ (cos k) (pow (sin k) 2)) (pow (* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0)) 1.0)))

simplify317.0ms

Algorithm
egg-herbie
Counts
1147 → 1147
Iterations

Useful iterations: 0 (114.0ms)

IterNodesCost
0604541178

prune463.0ms

Filtered
91 candidates to 1147 candidates (-1160.4%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1136111147
Fresh9817
Picked101
Done000
Total1146191165

Merged error: 4.6b

Counts
1165 → 19

regimes1.0s

Accuracy

23% (2.2b remaining)

Error of 7.6b against oracle of 5.4b and baseline of 8.3b

bsearch650.0ms

Steps
ItersRangePoint
8
8.222127626796667e-107
3.196970793254423e-102
3.2285213753541727e-105
9
-1.845808290784583e-115
-1.154298382586904e-121
-6.6368440463434e-116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
059101
159101

end0.0ms

sample15.2s

Algorithm
intervals
Results
4.6s2191×body2560valid
4.4s990×body5120valid
3.4s4148×body1280valid
1.4s2594×body640valid
377.0ms968×body320valid
258.0ms1937×body80valid
125.0ms452×body160valid

Profiling

Loading profile data...