Details

Time bar (total: 24.2s)

sample428.0ms

Algorithm
intervals
Results
132.0ms34×body5120valid
118.0ms71×body2560valid
93.0ms129×body1280valid
41.0ms92×body640valid
11.0ms35×body320valid
7.0ms64×body80valid
3.0ms13×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211

prune11.0ms

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: 39.0b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
20.1b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
337×add-exp-log
220×prod-exp
71×div-exp
65×add-cbrt-cube
51×pow-exp
34×pow-to-exp cbrt-unprod
30×unpow-prod-down
28×add-sqr-sqrt
24×associate-*l*
23×add-cube-cbrt *-un-lft-identity
19×times-frac
12×cbrt-undiv
5×pow1 associate-*r/
4×associate-*r* add-log-exp sqr-pow
3×tan-quot pow-unpow div-inv unswap-sqr
2×*-commutative
1×pow-pow frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 179
Calls
4 calls:
5.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
22.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series920.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ k t) 2.0)
236.0ms
(* (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)))
248.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify139.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09741954
149951620
250011620

prune453.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1847191
Fresh011
Picked101
Done000
Total1858193

Merged error: 21.7b

Counts
193 → 8

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))
6.6b
(* (pow k 2.0) (pow t 1.0))
16.1b
(* (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×div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 600
Calls
4 calls:
7.0ms
(/ 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))
28.0ms
(* (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:
333.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
334.0ms
(* (pow k 2.0) (pow t 1.0))
645.0ms
(* (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
612 → 612
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
013167194
141627025
250027018

prune627.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New60111612
Fresh347
Picked101
Done000
Total60515620

Merged error: 16.8b

Counts
620 → 15

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))
16.1b
(* (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)))

rewrite270.0ms

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×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 → 1460
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))))
13.0ms
(/ (* (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
19.0ms
(pow (sin k) 2)
341.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
662.0ms
(* (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)))

simplify312.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune554.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New146481472
Fresh9514
Picked101
Done000
Total1474131487

Merged error: 13.5b

Counts
1487 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.6b
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
5.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0b
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite607.0ms

Algorithm
rewrite-expression-head
Rules
9372×add-exp-log
6088×prod-exp
4663×pow-exp
3902×div-exp
2343×pow-to-exp
35×times-frac add-cbrt-cube
34×unpow-prod-down
29×associate-*l*
28×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×cbrt-prod associate-/r*
8×cbrt-undiv
7×associate-/l* sqr-pow
5×div-inv
4×pow1 add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
Counts
4 → 1845
Calls
4 calls:
7.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
51.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
9.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
20.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts
4 → 12
Calls
4 calls:
339.0ms
(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
636.0ms
(* (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
645.0ms
(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify404.0ms

Algorithm
egg-herbie
Counts
1857 → 1857
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0200640014
1500139675

prune742.0ms

Filtered
1857 candidates to 109 candidates (5.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New184981857
Fresh7512
Picked101
Done000
Total1857131870

Merged error: 13.2b

Counts
1870 → 13

regimes257.0ms

Accuracy

0% (3.5b remaining)

Error of 16.1b against oracle of 12.6b and baseline of 16.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03628
13628

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.3s952×body5120valid
4.2s2264×body2560valid
2.9s4101×body1280valid
1.2s2475×body640valid
351.0ms1013×body320valid
229.0ms2086×body80valid
96.0ms432×body160valid