Details

Time bar (total: 14.2s)

analyze2.2s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14

sample174.0ms

Algorithm
intervals
Results
53.0ms66×body1280valid
28.0ms53×body640valid
13.0ms107×body80valid
7.0ms18×body320valid
3.0ms12×body160valid

simplify24.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0508625

prune17.0ms

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: 27.6b

Counts
2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
5.9b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
6.4b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
20.8b
(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
170×add-exp-log
106×prod-exp
74×add-cbrt-cube
40×cbrt-unprod
37×associate-*r/
30×div-exp
22×associate-*l*
14×add-sqr-sqrt
12×cbrt-undiv distribute-rgt-in pow-to-exp add-cube-cbrt *-un-lft-identity distribute-lft-in pow-exp
11×pow1
10×associate-/r/
9×tan-quot
6×frac-times flip3-+ times-frac flip-+
5×associate-*r* associate-*l/
4×pow-prod-down add-log-exp
3×unpow-prod-down *-commutative associate-/l*
2×div-inv
1×frac-2neg clear-num associate-/r* unswap-sqr sqr-pow
Counts
4 → 152
Calls
4 calls:
19.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
28.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
23.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
19.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

series512.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
116.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
179.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
100.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

simplify53.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
050683715

prune297.0ms

Filtered
92 candidates to 164 candidates (-78.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15410164
Fresh011
Picked101
Done000
Total15511166

Merged error: 19.6b

Counts
166 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

2.1b
(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
5.9b
(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
6.4b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
13.6b
(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
551×add-exp-log
424×prod-exp
85×add-cbrt-cube
74×pow-exp
66×div-exp
52×cbrt-unprod
50×pow-to-exp
27×associate-*r/
21×associate-*l*
20×associate-*l/
15×associate-*r*
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
10×cbrt-undiv
9×tan-quot
7×unpow-prod-down
6×frac-times flip3-+ flip-+
5×associate-/r/
4×pow-prod-down *-commutative add-log-exp
3×cbrt-prod times-frac
2×sqr-pow
1×div-inv unswap-sqr
Counts
4 → 210
Calls
4 calls:
21.0ms
(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
30.0ms
(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
29.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
26.0ms
(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
128.0ms
(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
200.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
111.0ms
(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

simplify85.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050336560

prune355.0ms

Filtered
90 candidates to 222 candidates (-146.7%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New2139222
Fresh2810
Picked101
Done000
Total21617233

Merged error: 16.8b

Counts
233 → 17

localize41.0ms

Local error

Found 4 expressions with local error:

4.3b
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
4.9b
(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
5.9b
(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
6.4b
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
1830×add-exp-log
1542×prod-exp
314×pow-exp
183×pow-to-exp
178×div-exp
112×add-cbrt-cube
73×cbrt-unprod
32×associate-*l/
27×associate-*r/
21×associate-*l*
12×cbrt-undiv add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity associate-*r*
9×tan-quot
6×frac-times flip3-+ flip-+
5×associate-/r/
4×pow-prod-down *-commutative add-log-exp
3×times-frac
2×unpow-prod-down sqr-pow
1×div-inv unswap-sqr
Counts
4 → 391
Calls
4 calls:
28.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
21.0ms
(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
43.0ms
(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
36.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

series508.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
67.0ms
(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
128.0ms
(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
205.0ms
(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

simplify139.0ms

Algorithm
egg-herbie
Counts
403 → 403
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
0502214013

prune401.0ms

Filtered
86 candidates to 403 candidates (-368.6%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New3976403
Fresh21416
Picked101
Done000
Total40020420

Merged error: 12.5b

Counts
420 → 20

localize43.0ms

Local error

Found 4 expressions with local error:

5.6b
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
5.9b
(* l (* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
6.1b
(* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))
6.2b
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))

rewrite508.0ms

Algorithm
rewrite-expression-head
Rules
5308×add-exp-log
4102×prod-exp
1107×div-exp
772×pow-exp
442×pow-to-exp
216×rec-exp 1-exp
215×add-cbrt-cube
133×cbrt-unprod
39×cbrt-undiv
34×associate-*r/
30×associate-*l*
20×pow1 add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity times-frac
15×associate-*r*
12×associate-*l/
10×pow-prod-down
6×tan-quot frac-times
5×associate-/r/
4×unpow-prod-down flip3-+ *-commutative flip-+ add-log-exp sqr-pow
2×div-inv
1×unswap-sqr
Counts
4 → 888
Calls
4 calls:
38.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
52.0ms
(* l (* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
29.0ms
(* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))
24.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))

series549.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
126.0ms
(* l (* (/ 1 (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
139.0ms
(* l (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))
109.0ms
(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))

simplify252.0ms

Algorithm
egg-herbie
Counts
900 → 900
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
0558433275

prune403.0ms

Filtered
99 candidates to 900 candidates (-809.1%)
Pruning

22 alts after pruning (22 fresh and 0 done)

PrunedKeptTotal
New8919900
Fresh61319
Picked101
Done000
Total89822920

Merged error: 11.9b

Counts
920 → 22

regimes1.1s

Accuracy

18.4% (5.3b remaining)

Error of 17.7b against oracle of 12.5b and baseline of 18.9b

bsearch170.0ms

Steps
ItersRangePoint
6
4.0492169138280456e+136
4.467953641622969e+137
4.363544639733127e+136
7
-1.3509256827506928e-303
-7.226005228927007e-305
-7.301962593525272e-305

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089186
189186

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.6s2023×body1280valid
850.0ms1546×body640valid
441.0ms3336×body80valid
289.0ms731×body320valid
100.0ms364×body160valid

Profiling

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