Details

Time bar (total: 23.5s)

sample412.0ms

Algorithm
intervals
Results
135.0ms26×body5120valid
99.0ms56×body2560valid
95.0ms126×body1280valid
42.0ms88×body640valid
10.0ms32×body320valid
6.0ms58×body80valid
4.0ms16×body160valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

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: 38.6b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.6b
(* (pow t 3.0) (tan k))
20.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite57.0ms

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))
23.0ms
(/ (* 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)))

series940.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(pow (/ k t) 2.0)
243.0ms
(* (pow t 3.0) (tan k))
379.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
252.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify131.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09741954
149951620
250011620

prune461.0ms

Filtered
191 candidates to 88 candidates (46.1%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1856191
Fresh101
Picked101
Done000
Total1876193

Merged error: 19.8b

Counts
193 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.7b
(* (pow k 2.0) (pow t 1.0))
15.3b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite119.0ms

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:
11.0ms
(/ 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))
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:
349.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
83.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
341.0ms
(* (pow k 2.0) (pow t 1.0))
661.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify150.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
013167194
141627025
250027018

prune619.0ms

Filtered
612 candidates to 100 candidates (16.3%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New60210612
Fresh145
Picked101
Done000
Total60414618

Merged error: 15.7b

Counts
618 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
0.9b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.5b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
15.3b
(* (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)))

rewrite492.0ms

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))
38.0ms
(* (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:
20.0ms
(pow (sin k) 2)
352.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
651.0ms
(* (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)))

simplify286.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
0174223543
1457419111
2500217858

prune580.0ms

Filtered
1472 candidates to 86 candidates (5.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New146391472
Fresh9413
Picked101
Done000
Total1473131486

Merged error: 13.1b

Counts
1486 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos k) (fabs (sin k)))
0.9b
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.9b
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
15.3b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

rewrite222.0ms

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) (fabs (sin k)))
12.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
22.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (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) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

series1.1s

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (cos k) (fabs (sin k)))
350.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
78.0ms
(* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l)))
644.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (fabs (sin k))) (/ l (/ (fabs (sin k)) l))))

simplify169.0ms

Algorithm
egg-herbie
Counts
943 → 943
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0215016793
1500113902

prune813.0ms

Filtered
943 candidates to 135 candidates (14.3%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New93211943
Fresh6612
Picked101
Done000
Total93917956

Merged error: 8.0b

Counts
956 → 17

regimes454.0ms

Accuracy

49.7% (3.6b remaining)

Error of 12.2b against oracle of 8.5b and baseline of 15.7b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06056
16056

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.3s2235×body2560valid
4.2s1008×body5120valid
3.0s4014×body1280valid
1.2s2572×body640valid
328.0ms955×body320valid
242.0ms2081×body80valid
105.0ms454×body160valid