Details

Time bar (total: 27.4s)

sample424.0ms

Algorithm
intervals
Results
139.0ms67×body2560valid
113.0ms148×body1280valid
88.0ms28×body5120valid
42.0ms81×body640valid
11.0ms29×body320valid
8.0ms61×body80valid
3.0ms11×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211

prune12.0ms

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: 41.6b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.4b
(* (pow t 3.0) (tan k))
22.5b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.3b
(* (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:
4.0ms
(pow (/ k t) 2.0)
6.0ms
(* (pow t 3.0) (tan k))
18.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
16.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series922.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(pow (/ k t) 2.0)
238.0ms
(* (pow t 3.0) (tan k))
371.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
245.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify136.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09741954
149951620
250011620

prune435.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1829191
Fresh011
Picked101
Done000
Total18310193

Merged error: 24.9b

Counts
193 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
9.5b
(* (pow k 2.0) (pow t 1.0))
19.1b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite116.0ms

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)))
9.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms
(* (pow k 2.0) (pow t 1.0))
22.0ms
(* (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:
336.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms
(* (pow k 2.0) (pow t 1.0))
642.0ms
(* (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
013167192
141627023
250027016

prune565.0ms

Filtered
612 candidates to 99 candidates (16.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New6057612
Fresh729
Picked101
Done000
Total6139622

Merged error: 20.1b

Counts
622 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.9b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
19.1b
(* (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)))

rewrite285.0ms

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:
2.0ms
(pow (sin k) 2)
15.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
37.0ms
(* (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:
18.0ms
(pow (sin k) 2)
339.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
657.0ms
(* (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)))

simplify319.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
0174223541
1457419109
2500217856

prune508.0ms

Filtered
1472 candidates to 85 candidates (5.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New146571472
Fresh358
Picked011
Done000
Total1468131481

Merged error: 15.3b

Counts
1481 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.1b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.4b
(* (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))))
13.6b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.4s

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)))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
98.0ms
(* (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))))
26.0ms
(* (pow (/ 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:
331.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
630.0ms
(* (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))))
635.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Algorithm
egg-herbie
Counts
5774 → 5774
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
04423106445
15002106271

prune724.0ms

Filtered
5774 candidates to 117 candidates (2.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New576955774
Fresh3811
Picked101
Done101
Total5774135787

Merged error: 15.3b

Counts
5787 → 13

regimes485.0ms

Accuracy

47.1% (2.6b remaining)

Error of 16.7b against oracle of 14.1b and baseline of 19.0b

bsearch516.0ms

Steps
ItersRangePoint
8
9.957219710147508e-81
9.076168226220815e-77
1.732470088274872e-80
7
-2.547541755723421e-123
-4.6257640398473067e-125
-3.400217259796094e-124

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06365
16365

end0.0ms

sample14.9s

Algorithm
intervals
Results
4.5s2239×body2560valid
4.5s1012×body5120valid
3.3s4068×body1280valid
1.4s2502×body640valid
381.0ms994×body320valid
275.0ms2050×body80valid
121.0ms472×body160valid

Profiling

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