Details

Time bar (total: 25.6s)

sample464.0ms

Algorithm
intervals
Results
162.0ms35×body5120valid
122.0ms67×body2560valid
95.0ms134×body1280valid
36.0ms83×body640valid
11.0ms60×body80valid
11.0ms35×body320valid
3.0ms15×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114713
285712
3500211

prune13.0ms

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: 38.5b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
20.5b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
29.2b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite56.0ms

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))
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)))

series896.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ k t) 2.0)
232.0ms
(* (pow t 3.0) (tan k))
357.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
243.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify133.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09741954
149951620
250011620

prune428.0ms

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: 21.1b

Counts
193 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.6b
(* (pow k 2.0) (pow t 1.0))
15.7b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite105.0ms

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))
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:
341.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
336.0ms
(* (pow k 2.0) (pow t 1.0))
648.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify161.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
013167194
141627025
250027018

prune593.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New60012612
Fresh527
Picked101
Done000
Total60614620

Merged error: 16.8b

Counts
620 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.7b
(* (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)))

rewrite271.0ms

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)
12.0ms
(/ 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))
41.0ms
(* (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)
335.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
648.0ms
(* (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)))

simplify303.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune739.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New146571472
Fresh5813
Picked101
Done000
Total1471151486

Merged error: 13.8b

Counts
1486 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.5b
(* (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))))
5.0b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.4b
(* (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)))
104.0ms
(* (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))
22.0ms
(* (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:
333.0ms
(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
647.0ms
(* (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))))
82.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
639.0ms
(* (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 (67.0ms)

IterNodesCost
04423106447
15002106273

prune765.0ms

Filtered
5774 candidates to 118 candidates (2.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New577045774
Fresh21214
Picked101
Done000
Total5773165789

Merged error: 13.3b

Counts
5789 → 16

regimes422.0ms

Accuracy

43.6% (2.7b remaining)

Error of 15.8b against oracle of 13.1b and baseline of 17.9b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05043
15043

end0.0ms

sample13.6s

Algorithm
intervals
Results
4.2s2171×body2560valid
4.1s960×body5120valid
2.9s4080×body1280valid
1.2s2541×body640valid
346.0ms1021×body320valid
221.0ms2012×body80valid
108.0ms455×body160valid