Details

Time bar (total: 23.0s)

sample431.0ms

Algorithm
intervals
Results
129.0ms66×body2560valid
126.0ms39×body5120valid
89.0ms131×body1280valid
49.0ms97×body640valid
7.0ms67×body80valid
6.0ms21×body320valid
3.0ms14×body160valid

simplify27.0ms

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: 40.5b

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))
20.7b
(/ (* 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)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
54×associate-*l*
38×associate-*r* *-commutative
36×times-frac
14×sqr-pow
9×associate-/r*
8×div-inv
7×unpow-prod-down
5×associate-*r/
4×associate-/l*
3×tan-quot
1×pow-to-exp frac-2neg associate-*l/ clear-num associate-/r/
Counts
4 → 66
Calls
4 calls:
2.0ms
(pow (/ k t) 2.0)
4.0ms
(* (pow t 3.0) (tan k))
12.0ms
(/ (* 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)))

series905.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(pow (/ k t) 2.0)
236.0ms
(* (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)))
240.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify45.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0476691
11912679
25002679

prune304.0ms

Filtered
78 candidates to 63 candidates (80.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New681078
Fresh011
Picked101
Done000
Total691180

Merged error: 13.6b

Counts
80 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.5b
(* (pow k 2.0) (pow t 1.0))
15.5b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×sqr-pow
23×associate-*r*
16×times-frac unpow2
9×associate-*r/ associate-/r* *-commutative
8×associate-/l*
4×pow-to-exp associate-*l* clear-num div-inv
3×frac-2neg
2×prod-exp unswap-sqr
1×unpow-prod-down rec-exp un-div-inv inv-pow
Counts
4 → 54
Calls
4 calls:
6.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.0ms
(* (pow k 2.0) (pow t 1.0))
12.0ms
(* (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:
339.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
90.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
333.0ms
(* (pow k 2.0) (pow t 1.0))
649.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify37.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0493550
11207548
25002548

prune347.0ms

Filtered
66 candidates to 51 candidates (77.3%)
Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New57966
Fresh2810
Picked011
Done000
Total591877

Merged error: 9.8b

Counts
77 → 18

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.9b
(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
7.2b
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)
8.5b
(* (pow k 2.0) (pow t 1.0))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-/l*
45×frac-times associate-*l*
37×sqr-pow
18×clear-num
17×frac-2neg *-commutative
15×associate-/r*
10×div-inv
9×associate-*l/
7×unpow-prod-down
5×associate-*r/
4×pow-to-exp associate-*r*
2×prod-exp unswap-sqr
1×rec-exp times-frac un-div-inv inv-pow
Counts
4 → 84
Calls
4 calls:
5.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms
(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
9.0ms
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)
4.0ms
(* (pow k 2.0) (pow t 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
347.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
657.0ms
(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
385.0ms
(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)
339.0ms
(* (pow k 2.0) (pow t 1.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07641177
133851061
250021061

prune480.0ms

Filtered
96 candidates to 74 candidates (77.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New90696
Fresh61016
Picked101
Done101
Total9816114

Merged error: 6.2b

Counts
114 → 16

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2)))
0.5b
(/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k))
3.9b
(* (/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
7.2b
(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
137×associate-*l*
93×associate-/l*
76×sqr-pow
70×frac-times
52×div-inv
48×unpow-prod-down
42×times-frac
25×*-commutative
24×clear-num
23×frac-2neg
16×associate-/r*
14×associate-*l/
10×associate-*r*
8×unswap-sqr
5×associate-*r/
2×pow-to-exp
1×div-exp un-div-inv
Counts
4 → 125
Calls
4 calls:
4.0ms
(/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2)))
17.0ms
(/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k))
22.0ms
(* (/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
13.0ms
(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

series1.6s

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2)))
486.0ms
(/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k))
687.0ms
(* (/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ (pow l (/ 2 2)) (pow (sin k) (/ 2 2))))
377.0ms
(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

simplify157.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08122127
149061718
250011718

prune896.0ms

Filtered
137 candidates to 121 candidates (88.3%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New12116137
Fresh11415
Picked101
Done000
Total13320153

Merged error: 1.4b

Counts
153 → 20

regimes440.0ms

Accuracy

41.9% (1.8b remaining)

Error of 3.2b against oracle of 1.5b and baseline of 4.5b

bsearch211.0ms

Steps
ItersRangePoint
7
1.1062005517729752e-72
3.988512999708643e-71
9.695058772041076e-72

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05044
15044

end0.0ms

sample13.6s

Algorithm
intervals
Results
4.3s970×body5120valid
4.1s2217×body2560valid
3.0s4155×body1280valid
1.1s2453×body640valid
353.0ms1027×body320valid
230.0ms2079×body80valid
99.0ms411×body160valid