Details

Time bar (total: 5.8s)

sample509.0ms

Algorithm
intervals
Results
162.0ms70×body2560valid
136.0ms36×body5120valid
115.0ms148×body1280valid
44.0ms85×body640valid
12.0ms32×body320valid
9.0ms72×body80valid
2.0ms9×body160valid

simplify28.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04413
114713
285712
3500211

prune14.0ms

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: 33.6b

Counts
2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ k t) 2.0)
0.8b
(* (pow t 3.0) (tan k))
15.1b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
26.9b
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite53.0ms

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))
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)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(pow (/ k t) 2.0)
54.0ms
(* (pow t 3.0) (tan k))
112.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
73.0ms
(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify46.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011232068
150021738

prune299.0ms

Filtered
191 candidates to 93 candidates (51.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1838191
Fresh011
Picked101
Done000
Total1849193

Merged error: 24.8b

Counts
193 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (pow t 3.0) (tan k))
13.6b
(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
15.1b
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
17.3b
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
1610×add-exp-log
1168×prod-exp
346×div-exp
341×pow-exp
205×pow-to-exp
95×add-cbrt-cube
55×cbrt-unprod
41×associate-*l*
30×unpow-prod-down
28×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
19×times-frac
15×cbrt-undiv
9×associate-*r/
5×associate-*r*
4×tan-quot pow1 add-log-exp sqr-pow
3×*-commutative div-inv unswap-sqr
1×frac-2neg associate-*l/ clear-num associate-/r* associate-/r/ associate-/l*
Counts
4 → 408
Calls
4 calls:
6.0ms
(* (pow t 3.0) (tan k))
17.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
29.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
11.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (pow t 3.0) (tan k))
71.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
115.0ms
(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))
77.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify88.0ms

Algorithm
egg-herbie
Counts
420 → 420
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
017716487
150025612

prune376.0ms

Filtered
420 candidates to 111 candidates (73.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4191420
Fresh268
Picked011
Done000
Total4218429

Merged error: 24.8b

Counts
429 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (* l l) (sin k))
13.6b
(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
14.1b
(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
17.3b
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
1610×add-exp-log
1029×prod-exp
485×div-exp
340×pow-exp
204×pow-to-exp
98×add-cbrt-cube
48×cbrt-unprod
42×associate-*l*
30×add-sqr-sqrt
28×times-frac
26×add-cube-cbrt unpow-prod-down *-un-lft-identity
24×cbrt-undiv
9×associate-*r/ associate-*r*
6×pow1
5×div-inv
4×add-log-exp
3×tan-quot associate-/r* *-commutative
2×unswap-sqr sqr-pow
1×frac-times frac-2neg pow-prod-down associate-*l/ clear-num associate-/r/ associate-/l*
Counts
4 → 418
Calls
4 calls:
5.0ms
(/ (* l l) (sin k))
17.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
33.0ms
(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
12.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (* l l) (sin k))
71.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
400.0ms
(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
69.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify86.0ms

Algorithm
egg-herbie
Counts
430 → 430
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
017306648
150015458

prune362.0ms

Filtered
430 candidates to 107 candidates (75.1%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New4219430
Fresh156
Picked011
Done101
Total42315438

Merged error: 20.5b

Counts
438 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (* l l) (sin k))
12.1b
(* (/ 1 (pow (/ k t) (/ 2.0 2))) (* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
13.5b
(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
17.3b
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
4987×add-exp-log
2928×prod-exp
1997×div-exp
846×pow-exp
509×pow-to-exp
220×rec-exp 1-exp
217×add-cbrt-cube
105×cbrt-unprod
97×times-frac
80×associate-*l*
66×cbrt-undiv
64×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
52×unpow-prod-down
11×pow1
10×associate-*r/
9×associate-*r*
8×div-inv
6×frac-times
4×pow-prod-down associate-*l/ add-log-exp sqr-pow
3×associate-/r* *-commutative
2×tan-quot unswap-sqr
1×frac-2neg clear-num associate-/r/ associate-/l*
Counts
4 → 975
Calls
4 calls:
5.0ms
(/ (* l l) (sin k))
44.0ms
(* (/ 1 (pow (/ k t) (/ 2.0 2))) (* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
19.0ms
(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
11.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (* l l) (sin k))
204.0ms
(* (/ 1 (pow (/ k t) (/ 2.0 2))) (* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
204.0ms
(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
77.0ms
(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify195.0ms

Algorithm
egg-herbie
Counts
987 → 987
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0307517702
1500216681

prune552.0ms

Filtered
987 candidates to 158 candidates (84.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New9807987
Fresh6713
Picked101
Done011
Total987151002

Merged error: 19.6b

Counts
1002 → 15

regimes850.0ms

bsearch157.0ms

Profiling

Loading profile data...