Details

Time bar (total: 23.8s)

sample456.0ms

Algorithm
intervals
Results
161.0ms71×body2560valid
104.0ms136×body1280valid
99.0ms34×body5120valid
48.0ms84×body640valid
11.0ms29×body320valid
7.0ms53×body80valid
5.0ms18×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

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: 38.1b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (pow t 3.0) (tan k))
18.5b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.7b
(* (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))
19.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
12.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series923.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ k t) 2.0)
242.0ms
(* (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)))
244.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify137.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09741954
149951620
250011620

prune416.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1838191
Fresh101
Picked101
Done000
Total1858193

Merged error: 18.7b

Counts
193 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.5b
(* (pow k 2.0) (pow t 1.0))
13.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite115.0ms

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:
333.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
336.0ms
(* (pow k 2.0) (pow t 1.0))
653.0ms
(* (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 (87.0ms)

IterNodesCost
013167194
141627025
250027018

prune558.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New60210612
Fresh527
Picked101
Done000
Total60812620

Merged error: 14.0b

Counts
620 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.5b
(* (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)))

rewrite487.0ms

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))
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:
19.0ms
(pow (sin k) 2)
336.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
85.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
632.0ms
(* (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 (94.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune493.0ms

Filtered
1472 candidates to 87 candidates (5.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New146841472
Fresh2911
Picked101
Done000
Total1471131484

Merged error: 11.4b

Counts
1484 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos k) (sin k))
0.6b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.5b
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
13.5b
(* (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×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))
13.0ms
(/ 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)))
34.0ms
(* (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))
348.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
90.0ms
(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
657.0ms
(* (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))))

simplify176.0ms

Algorithm
egg-herbie
Counts
943 → 943
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0214715097
1500212259

prune669.0ms

Filtered
943 candidates to 135 candidates (14.3%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New9385943
Fresh4812
Picked011
Done000
Total94214956

Merged error: 8.9b

Counts
956 → 14

regimes368.0ms

Accuracy

42.7% (4.2b remaining)

Error of 13.4b against oracle of 9.2b and baseline of 16.5b

bsearch710.0ms

Steps
ItersRangePoint
6
7.055322399106104e-78
3.361692463022349e-77
3.330489096417523e-77
11
-2.6766715744203716e-101
-2.2769738344141557e-127
-4.0649028969036264e-114
4
-1.4501250722181258e+130
-9.551618771889815e+129
-1.4298479098591106e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06970
16970

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.4s2273×body2560valid
3.7s914×body5120valid
3.2s4050×body1280valid
1.3s2518×body640valid
382.0ms988×body320valid
278.0ms2090×body80valid
104.0ms408×body160valid