Details

Time bar (total: 3.9s)

analyze103.0ms

Algorithm
search

sample24.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify72.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04414
116514
282614
3386714
4500214

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* v v))
0.3b
(* PI t)
0.4b
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
0.5b
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
18×associate-*r/
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- sqrt-div associate-*r* associate-/r/ flip--
7×associate-*l* pow-prod-down
4×cbrt-undiv frac-times div-exp add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 94
Calls
4 calls:
5.0ms
(* 3.0 (* v v))
3.0ms
(* PI t)
8.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
14.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))

series67.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 3.0 (* v v))
2.0ms
(* PI t)
20.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
42.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))

simplify106.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07701153
143251002
250021002

prune192.0ms

Filtered
72 candidates to 106 candidates (-47.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1006106
Fresh000
Picked011
Done000
Total1007107

Merged error: 0.3b

Counts
107 → 7

localize37.0ms

Local error

Found 4 expressions with local error:

4.2b
(/ (pow v 4) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
4.2b
(/ (* (pow v 4) (sqrt 1.0)) (* t (* (sqrt 2.0) PI)))
7.8b
(/ (pow v 2) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
7.8b
(/ (* (pow v 2) (sqrt 1.0)) (* t (* (sqrt 2.0) PI)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
164×add-exp-log
78×prod-exp
74×add-cbrt-cube
48×div-exp
30×cbrt-unprod
20×cbrt-undiv
17×times-frac associate-/l*
14×pow-to-exp pow-exp
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
4×pow1 frac-2neg clear-num associate-/r* div-inv add-log-exp sqr-pow
2×unpow2
Counts
4 → 146
Calls
4 calls:
12.0ms
(/ (pow v 4) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
11.0ms
(/ (* (pow v 4) (sqrt 1.0)) (* t (* (sqrt 2.0) PI)))
13.0ms
(/ (pow v 2) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
11.0ms
(/ (* (pow v 2) (sqrt 1.0)) (* t (* (sqrt 2.0) PI)))

series56.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (pow v 4) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
12.0ms
(/ (* (pow v 4) (sqrt 1.0)) (* t (* (sqrt 2.0) PI)))
14.0ms
(/ (pow v 2) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
13.0ms
(/ (* (pow v 2) (sqrt 1.0)) (* t (* (sqrt 2.0) PI)))

simplify110.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07451463
144481240
250011240

prune631.0ms

Filtered
71 candidates to 158 candidates (-122.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1580158
Fresh055
Picked011
Done011
Total1587165

Merged error: 0.3b

Counts
165 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* v v))
0.4b
(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.5b
(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
0.5b
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log associate-*r/ add-cbrt-cube
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity sqrt-div
9×flip3-- associate-*l* flip--
8×associate-/r/
7×pow-prod-down
6×associate-*r*
4×cbrt-undiv frac-times div-exp add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 96
Calls
4 calls:
6.0ms
(* 3.0 (* v v))
8.0ms
(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
7.0ms
(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
17.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))

series83.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 3.0 (* v v))
19.0ms
(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
21.0ms
(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))
39.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))

simplify102.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07951295
142451138
250011138

prune177.0ms

Filtered
75 candidates to 108 candidates (-44.0%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1062108
Fresh224
Picked011
Done022
Total1087115

Merged error: 0.3b

Counts
115 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI t)
0.3b
(* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b
(* (* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.5b
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
100×sqrt-div
86×associate-*r/
40×add-exp-log add-cbrt-cube
35×flip3-- flip--
32×frac-times
26×associate-/r/
20×pow1 prod-exp cbrt-unprod
17×associate-*r*
16×associate-*l/
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
10×pow-prod-down sqrt-prod
5×cbrt-undiv div-exp associate-*l*
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-/l/
1×frac-2neg div-sub clear-num associate-/r* div-inv unswap-sqr
Counts
4 → 131
Calls
4 calls:
3.0ms
(* PI t)
10.0ms
(* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
17.0ms
(* (* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
25.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* PI t)
39.0ms
(* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
20.0ms
(* (* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
44.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* (* PI t) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (sqrt (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))

simplify52.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011122689
150012386

prune380.0ms

Filtered
102 candidates to 143 candidates (-40.2%)
Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New1403143
Fresh033
Picked011
Done033
Total14010150

Merged error: 0.3b

Counts
150 → 10

regimes558.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06151
16151

end0.0ms

analyze106.0ms

Algorithm
search

sample650.0ms

Algorithm
intervals
Results
518.0ms8000×body80valid
1.0ms13×body80nan

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