Details

Time bar (total: 24.7s)

sample379.0ms

Algorithm
intervals
Results
117.0ms73×body2560valid
98.0ms132×body1280valid
88.0ms25×body5120valid
41.0ms86×body640valid
8.0ms26×body320valid
5.0ms46×body80valid
3.0ms12×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
04413
114913
286912
3500111

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: 37.7b

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))
19.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.5b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite51.0ms

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×expm1-log1p-u associate-*r* log1p-expm1-u 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 → 187
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)))
11.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series904.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow (/ k t) 2.0)
237.0ms
(* (pow t 3.0) (tan k))
364.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
242.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify48.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09912005
150011672

prune477.0ms

Filtered
199 candidates to 96 candidates (48.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1927199
Fresh011
Picked101
Done000
Total1938201

Merged error: 19.0b

Counts
201 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.8b
(* (pow k 2.0) (pow t 1.0))
15.4b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite130.0ms

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×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×unpow2
2×frac-2neg clear-num *-commutative
1×pow-flip associate-*r/ inv-pow
Counts
4 → 608
Calls
4 calls:
13.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
15.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.0ms
(* (pow k 2.0) (pow t 1.0))
23.0ms
(* (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:
334.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
323.0ms
(* (pow k 2.0) (pow t 1.0))
635.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify165.0ms

Algorithm
egg-herbie
Counts
620 → 620
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
014397252
142967083
250037076

prune623.0ms

Filtered
620 candidates to 108 candidates (17.4%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New60911620
Fresh527
Picked101
Done000
Total61513628

Merged error: 15.3b

Counts
628 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
3.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.4b
(* (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)))

rewrite280.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 1468
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))))
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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin k) 2)
323.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
294.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
653.0ms
(* (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)))

simplify314.0ms

Algorithm
egg-herbie
Counts
1480 → 1480
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
0199723615
1485419182
2500217933

prune545.0ms

Filtered
1480 candidates to 94 candidates (6.4%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New147281480
Fresh4812
Picked101
Done000
Total1477161493

Merged error: 12.4b

Counts
1493 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (sin k))
0.5b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.2b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
15.4b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
3841×add-exp-log
2622×prod-exp
1370×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
99×times-frac
80×add-sqr-sqrt
65×add-cbrt-cube
59×add-cube-cbrt *-un-lft-identity
45×associate-*r*
24×associate-*l*
22×cbrt-undiv cbrt-unprod
8×div-inv
7×pow1 unpow-prod-down
6×associate-/l* unswap-sqr
5×associate-*r/
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×pow-flip pow-prod-down associate-/r/ inv-pow sqr-pow
Counts
4 → 939
Calls
4 calls:
4.0ms
(/ (cos k) (sin k))
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
26.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
32.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(/ (cos k) (sin k))
330.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
86.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
629.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify177.0ms

Algorithm
egg-herbie
Counts
951 → 951
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0240215175
1500112337

prune680.0ms

Filtered
951 candidates to 142 candidates (14.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New9465951
Fresh51015
Picked101
Done000
Total95215967

Merged error: 8.1b

Counts
967 → 15

regimes340.0ms

Accuracy

59.2% (2.8b remaining)

Error of 11.4b against oracle of 8.6b and baseline of 15.4b

bsearch2.2s

Steps
ItersRangePoint
8
3.1381575881074073e+153
4.745240176690994e+156
1.2218151027611354e+154
9
2.7413777313647e-155
9.0664153968876e-147
3.3090433695573168e-155
11
-1.637494300424913e-145
-2.849757602576434e-180
-5.157297826678039e-154
8
-3.104877055821389e+150
-1.0625869734742917e+147
-6.239143455459081e+149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06886
16886

end0.0ms

sample13.3s

Algorithm
intervals
Results
4.1s2202×body2560valid
3.9s963×body5120valid
3.0s4069×body1280valid
1.2s2501×body640valid
332.0ms987×body320valid
219.0ms2020×body80valid
100.0ms426×body160valid