Details

Time bar (total: 27.8s)

sample535.0ms

Algorithm
intervals
Results
220.0ms90×body2560valid
115.0ms36×body5120valid
98.0ms123×body1280valid
41.0ms82×body640valid
18.0ms40×body320valid
9.0ms72×body80valid
2.0ms10×body160valid

simplify25.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (24.0ms)

IterNodesCost
04413
114713
285712
3500211

prune17.0ms

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: 38.8b

Counts
2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (pow t 3.0) (tan k))
19.1b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.0b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite49.0ms

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:
4.0ms
(pow (/ k t) 2.0)
5.0ms
(* (pow t 3.0) (tan k))
17.0ms
(/ (* 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)))

series972.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(pow (/ k t) 2.0)
236.0ms
(* (pow t 3.0) (tan k))
352.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
306.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012032050
150021724

prune641.0ms

Filtered
191 candidates to 91 candidates (47.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1838191
Fresh011
Picked101
Done000
Total1849193

Merged error: 20.8b

Counts
193 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
4.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.9b
(* (pow k 2.0) (pow t 1.0))
14.9b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
1597×add-exp-log
1095×prod-exp
882×pow-exp
668×div-exp
492×pow-to-exp
130×rec-exp 1-exp
37×add-sqr-sqrt
32×unpow-prod-down
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
19×times-frac associate-*r*
18×associate-*l*
14×sqr-pow
12×unswap-sqr
8×associate-/r*
6×cbrt-unprod
5×pow1
4×cbrt-undiv unpow2 add-log-exp
3×pow-unpow div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ clear-num associate-/l*
Counts
4 → 567
Calls
4 calls:
2.0ms
(pow (sin k) 2)
11.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.0ms
(* (pow k 2.0) (pow t 1.0))
21.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
80.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
452.0ms
(* (pow k 2.0) (pow t 1.0))
714.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify152.0ms

Algorithm
egg-herbie
Counts
579 → 579
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
012226942
144416788
250016787

prune770.0ms

Filtered
579 candidates to 100 candidates (17.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New5709579
Fresh448
Picked101
Done000
Total57513588

Merged error: 15.1b

Counts
588 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
0.4b
(pow (sin k) 2)
4.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.9b
(* (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)))

rewrite286.0ms

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:
11.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.0ms
(pow (sin k) 2)
7.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
34.0ms
(* (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:
460.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms
(pow (sin k) 2)
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
507.0ms
(* (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)))

simplify257.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0179123574
1500119144

prune717.0ms

Filtered
1472 candidates to 87 candidates (5.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New146571472
Fresh5712
Picked101
Done000
Total1471141485

Merged error: 12.5b

Counts
1485 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.7b
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
4.8b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.9b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
25023×add-exp-log
19197×prod-exp
16899×pow-exp
11140×div-exp
7959×pow-to-exp
2990×rec-exp 1-exp
51×unpow-prod-down
43×times-frac
40×associate-*l*
37×add-cbrt-cube
36×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
14×cbrt-unprod
13×associate-*r*
9×associate-/r* sqr-pow
8×cbrt-undiv
5×pow1 div-inv
4×associate-/l* add-log-exp
3×associate-*r/ unpow2 unswap-sqr
2×frac-2neg clear-num *-commutative
1×pow-flip inv-pow
Counts
4 → 5762
Calls
4 calls:
7.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
102.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
24.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
471.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
513.0ms
(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
523.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.4s

Algorithm
egg-herbie
Counts
5774 → 5774
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
04539106529
15001106355

prune1.0s

Filtered
5774 candidates to 121 candidates (2.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New577045774
Fresh11213
Picked101
Done000
Total5772165788

Merged error: 12.4b

Counts
5788 → 16

regimes934.0ms

Accuracy

54.6% (2.2b remaining)

Error of 15.6b against oracle of 13.4b and baseline of 18.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06458
16458

end0.0ms

sample14.7s

Algorithm
intervals
Results
4.5s1010×body5120valid
4.3s2157×body2560valid
3.2s4068×body1280valid
1.3s2566×body640valid
367.0ms1011×body320valid
278.0ms1997×body80valid
109.0ms439×body160valid

Profiling

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