Details

Time bar (total: 20.9s)

sample386.0ms

Algorithm
intervals
Results
113.0ms68×body2560valid
94.0ms116×body1280valid
84.0ms26×body5120valid
42.0ms79×body640valid
17.0ms44×body320valid
8.0ms58×body80valid
2.0ms9×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
0534021

prune15.0ms

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: 38.6b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
5.4b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
9.0b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
28.5b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite84.0ms

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:
15.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
20.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
19.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
18.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
147.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
189.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
88.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify73.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049783531
149783531

prune318.0ms

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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New16614180
Fresh101
Picked101
Done000
Total16814182

Merged error: 15.0b

Counts
182 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (/ (cos k) (pow (sin k) 2)) l)
5.4b
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0)) 1.0))))
6.0b
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0)) 1.0))
7.3b
(* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0))

rewrite130.0ms

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
43×associate-*l*
40×add-cbrt-cube
30×unswap-sqr
29×sqr-pow
28×add-cube-cbrt *-un-lft-identity times-frac
22×cbrt-unprod
20×associate-*r*
11×pow1
5×pow-prod-down associate-*l/
4×*-commutative unpow2 add-log-exp
3×cbrt-undiv
2×associate-*r/
1×div-inv
Counts
4 → 454
Calls
4 calls:
11.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
33.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0)) 1.0))))
17.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0)) 1.0))
13.0ms
(* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0))

series368.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
134.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0)) 1.0))))
136.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0)) 1.0))
74.0ms
(* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (neg 2.0)) 1.0))

simplify111.0ms

Algorithm
egg-herbie
Counts
466 → 466
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
0521611027

prune747.0ms

Filtered
134 candidates to 466 candidates (-247.8%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New45214466
Fresh5813
Picked101
Done000
Total45822480

Merged error: 7.6b

Counts
480 → 22

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
2.4b
(* (/ (cos k) (pow (sin k) 2)) l)
5.4b
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0)) (pow (pow k (/ (neg 2.0) 2)) 1.0)) 1.0))))
6.0b
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0)) (pow (pow k (/ (neg 2.0) 2)) 1.0)) 1.0))

rewrite402.0ms

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
32×associate-*l*
28×times-frac
24×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
14×unpow-prod-down
12×pow1
9×associate-*r*
6×sqr-pow
5×associate-*l/ unpow2 unswap-sqr
4×pow-prod-down add-log-exp
3×cbrt-undiv pow-unpow *-commutative
2×associate-*r/
1×pow-pow div-inv
Counts
4 → 1440
Calls
4 calls:
3.0ms
(pow (sin k) 2)
11.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
85.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0)) (pow (pow k (/ (neg 2.0) 2)) 1.0)) 1.0))))
34.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0)) (pow (pow k (/ (neg 2.0) 2)) 1.0)) 1.0))

series301.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (sin k) 2)
23.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
128.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0)) (pow (pow k (/ (neg 2.0) 2)) 1.0)) 1.0))))
146.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (* (pow (pow t (neg 1.0)) 1.0) (pow (pow k (/ (neg 2.0) 2)) 1.0)) (pow (pow k (/ (neg 2.0) 2)) 1.0)) 1.0))

simplify412.0ms

Algorithm
egg-herbie
Counts
1452 → 1452
Iterations

Useful iterations: 0 (172.0ms)

IterNodesCost
0522044667

prune571.0ms

Filtered
90 candidates to 1452 candidates (-1513.3%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New144481452
Fresh91221
Picked101
Done000
Total1454201474

Merged error: 4.9b

Counts
1474 → 20

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0))
0.4b
(pow (sin k) 2)
5.4b
(* l (* 2.0 (* (* 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))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))
7.7b
(* 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)))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
5379×add-exp-log
5022×prod-exp
3403×pow-exp
1259×pow-to-exp
672×div-exp
63×unpow-prod-down
44×add-sqr-sqrt
42×add-cbrt-cube
26×cbrt-unprod
25×unswap-sqr sqr-pow
17×associate-*l*
14×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×pow1
5×pow-prod-down
4×associate-*r/ add-log-exp
3×pow-unpow associate-*l/ *-commutative
2×cbrt-undiv
1×pow-pow unpow2
Counts
4 → 1051
Calls
4 calls:
14.0ms
(* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0))
4.0ms
(pow (sin k) 2)
99.0ms
(* l (* 2.0 (* (* 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))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))
21.0ms
(* 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)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (pow (pow k (/ (neg 2.0) 2)) 1.0) (pow (pow t (neg 1.0)) 1.0))
4.0ms
(pow (sin k) 2)
126.0ms
(* l (* 2.0 (* (* 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))) (pow (pow (pow k (/ (neg 2.0) 2)) 1.0) 1.0))))
120.0ms
(* 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)))

simplify517.0ms

Algorithm
egg-herbie
Counts
1063 → 1063
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0547740871

prune600.0ms

Filtered
99 candidates to 1063 candidates (-973.7%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New1052111063
Fresh81119
Picked101
Done000
Total1061221083

Merged error: 4.7b

Counts
1083 → 22

regimes801.0ms

Accuracy

0% (2.7b remaining)

Error of 8.6b against oracle of 5.9b and baseline of 8.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03342
13342

end0.0ms

sample13.7s

Algorithm
intervals
Results
4.3s2217×body2560valid
3.4s897×body5120valid
3.2s4112×body1280valid
1.3s2478×body640valid
375.0ms954×body320valid
260.0ms2016×body80valid
114.0ms426×body160valid

Profiling

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