Details

Time bar (total: 2.5m)

sample443.0ms

Algorithm
intervals
Results
135.0ms34×body5120valid
122.0ms67×body2560valid
101.0ms138×body1280valid
33.0ms65×body640valid
12.0ms33×body320valid
7.0ms55×body80valid
4.0ms18×body160valid

simplify26.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (25.0ms)

IterNodesCost
04413
114713
285712
3500211

prune18.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.7b

Counts
2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
1.0b
(* (pow t 3.0) (tan k))
23.0b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
31.6b
(* (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×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))
20.0ms
(/ (* 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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (/ k t) 2.0)
278.0ms
(* (pow t 3.0) (tan k))
419.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
283.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify129.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09741954
149951620
250011620

prune900.0ms

Filtered
191 candidates to 88 candidates (53.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1856191
Fresh011
Picked101
Done000
Total1867193

Merged error: 24.1b

Counts
193 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow k 2.0) (pow t 1.0)))
6.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.4b
(* (pow k 2.0) (pow t 1.0))
17.2b
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite101.0ms

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:
6.0ms
(/ 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))
21.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
380.0ms
(/ 1 (* (pow k 2.0) (pow t 1.0)))
103.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
362.0ms
(* (pow k 2.0) (pow t 1.0))
743.0ms
(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify151.0ms

Algorithm
egg-herbie
Counts
612 → 612
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
013167192
141627023
250027016

prune1.3s

Filtered
612 candidates to 99 candidates (83.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New60111612
Fresh336
Picked101
Done000
Total60514619

Merged error: 18.6b

Counts
619 → 14

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))))
6.2b
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.2b
(* (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)))

rewrite273.0ms

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:
2.0ms
(pow (sin k) 2)
11.0ms
(/ 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:
23.0ms
(pow (sin k) 2)
385.0ms
(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
103.0ms
(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
763.0ms
(* (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)))

simplify296.0ms

Algorithm
egg-herbie
Counts
1472 → 1472
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
0174223541
1457419109
2500217856

prune1.1s

Filtered
1472 candidates to 86 candidates (94.2%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New146481472
Fresh4913
Picked101
Done000
Total1469171486

Merged error: 12.8b

Counts
1486 → 17

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
0.8b
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
0.9b
(pow (cbrt (sin k)) 4)
17.2b
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
29087×times-frac
11908×add-sqr-sqrt
11455×add-cube-cbrt *-un-lft-identity
10275×add-exp-log
7945×unpow-prod-down
6428×div-exp
5073×prod-exp
4257×pow-exp
3951×cbrt-prod
3557×associate-*r*
2490×pow-to-exp
1378×sqr-pow
668×unpow2
589×rec-exp 1-exp
326×associate-/l*
319×div-inv
117×associate-/r*
108×unswap-sqr
47×add-cbrt-cube
26×cbrt-undiv
24×associate-/r/
11×associate-*l*
5×pow1 cbrt-unprod
4×add-log-exp
3×pow-unpow
2×pow-pow frac-2neg clear-num
1×pow1/3 associate-*r/ *-commutative associate-/l/
Counts
4 → 9901
Calls
4 calls:
33.0ms
(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
129.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
3.0ms
(pow (cbrt (sin k)) 4)
992.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

series1.2s

Counts
4 → 12
Calls
4 calls:
212.0ms
(/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l))
108.0ms
(/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))
148.0ms
(pow (cbrt (sin k)) 4)
746.0ms
(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2)))

simplify2.8s

Algorithm
egg-herbie
Counts
9913 → 9913
Iterations

Useful iterations: 0 (139.0ms)

IterNodesCost
010810272306

prune2.2m

Filtered
9913 candidates to 6952 candidates (29.9%)

Profiling

Loading profile data...