Details

Time bar (total: 24.3s)

sample377.0ms

Algorithm
intervals
Results
116.0ms73×body2560valid
96.0ms132×body1280valid
85.0ms25×body5120valid
39.0ms86×body640valid
10.0ms46×body80valid
8.0ms26×body320valid
3.0ms12×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

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: 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)))

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)))

series906.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ k t) 2.0)
231.0ms
(* (pow t 3.0) (tan k))
365.0ms
(/ (* 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)))

simplify133.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09741954
149951620
250011620

prune414.0ms

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: 19.0b

Counts
193 → 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)))

rewrite109.0ms

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))
27.0ms
(* (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:
329.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
331.0ms
(* (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)))

simplify160.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
013167194
141627025
250027018

prune574.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New60111612
Fresh527
Picked101
Done000
Total60713620

Merged error: 15.3b

Counts
620 → 13

localize24.0ms

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)))

rewrite476.0ms

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))))
8.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
39.0ms
(* (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)
334.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
642.0ms
(* (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)))

simplify299.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune517.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New146481472
Fresh4812
Picked101
Done000
Total1469161485

Merged error: 12.4b

Counts
1485 → 16

localize24.0ms

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))))

rewrite192.0ms

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×associate-/r* 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 → 931
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))))
21.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
36.0ms
(* (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:
19.0ms
(/ (cos k) (sin k))
343.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
89.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
651.0ms
(* (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))))

simplify178.0ms

Algorithm
egg-herbie
Counts
943 → 943
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0214715097
1500212259

prune643.0ms

Filtered
943 candidates to 134 candidates (14.2%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New9385943
Fresh51015
Picked101
Done000
Total94415959

Merged error: 8.1b

Counts
959 → 15

regimes337.0ms

Accuracy

59.2% (2.8b remaining)

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

bsearch2.3s

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

sample13.0s

Algorithm
intervals
Results
4.1s2202×body2560valid
3.9s963×body5120valid
2.8s4069×body1280valid
1.1s2501×body640valid
319.0ms987×body320valid
217.0ms2020×body80valid
97.0ms426×body160valid