Details

Time bar (total: 2.5min)

analyze2.5s

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.5%0.5%11
0%99.1%0.9%12
0.4%97.3%2.3%13
0.7%95.8%3.5%14

sample480.0ms

Algorithm
intervals
Results
105.0ms42×body2560invalid
99.0ms112×body1280valid
92.0ms25×body5120invalid
56.0ms35×body2560valid
33.0ms56×body640valid
26.0msbody5120valid
17.0ms22×body1280invalid
12.0ms21×body640invalid
6.0ms16×body320valid
5.0ms13×body320invalid
4.0ms31×body80invalid
3.0ms21×body80valid
2.0ms10×body160valid
2.0msbody160invalid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
0484221
1484221

prune13.0ms

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: 36.1b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
5.7b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
7.7b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
28.3b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
356×add-exp-log
241×prod-exp
74×add-cbrt-cube
69×div-exp
48×pow-exp
40×cbrt-unprod
36×pow-to-exp
18×associate-*l*
14×add-sqr-sqrt
12×cbrt-undiv add-cube-cbrt *-un-lft-identity
11×pow1
associate-*r/
times-frac
associate-*r* associate-*l/
pow-prod-down add-log-exp
tan-quot unpow-prod-down *-commutative associate-/l*
associate-/r/ div-inv
frac-2neg clear-num associate-/r* unswap-sqr sqr-pow
Counts
4 → 168
Calls
4 calls:
13.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
20.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
16.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
12.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0)))))
127.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
162.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
78.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049933531
149933531

prune264.0ms

Filtered
82 candidates to 180 candidates (-119.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New16812180
Fresh101
Picked101
Done000
Total17012182

Merged error: 14.8b

Counts
182 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
5.7b
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
6.0b
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))
7.3b
(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
6676×add-exp-log
4537×prod-exp
4223×pow-exp
2300×div-exp
1455×pow-to-exp
572×unpow-prod-down
412×add-sqr-sqrt
392×times-frac
183×associate-*l*
152×sqr-pow
137×add-cube-cbrt *-un-lft-identity
119×unswap-sqr
43×add-cbrt-cube
30×associate-*r*
23×cbrt-unprod
11×pow1
10×div-inv
associate-*l/
cbrt-undiv pow-prod-down *-commutative unpow2 add-log-exp
associate-*r/
Counts
4 → 1673
Calls
4 calls:
10.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
69.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
26.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))
74.0ms
(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))

series296.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
101.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))))
112.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0)) 1.0))
63.0ms
(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))

simplify345.0ms

Algorithm
egg-herbie
Counts
1685 → 1685
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
0515553347

prune3.3s

Filtered
372 candidates to 1685 candidates (-353.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1671141685
Fresh7411
Picked101
Done000
Total1679181697

Merged error: 9.2b

Counts
1697 → 18

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
5.7b
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
6.0b
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))

rewrite5.5s

Algorithm
rewrite-expression-head
Rules
101846×add-exp-log
71721×prod-exp
65298×pow-exp
43941×div-exp
21908×pow-to-exp
6900×1-exp
38×add-cbrt-cube
36×add-sqr-sqrt
32×associate-*l*
28×times-frac
24×add-cube-cbrt *-un-lft-identity
21×cbrt-unprod
14×unpow-prod-down
12×pow1
associate-*r*
sqr-pow
associate-*l/ unpow2 unswap-sqr
pow-prod-down add-log-exp
cbrt-undiv pow-unpow *-commutative
associate-*r/
pow-pow div-inv
Counts
4 → 15090
Calls
4 calls:
3.0ms
(pow (sin k) 2)
26.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
695.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
217.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))

series249.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin k) 2)
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
103.0ms
(* l (* 2.0 (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))))
121.0ms
(* (* (/ (cos k) (pow (sin k) 2)) l) (pow (* (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0)))) 1.0))

simplify4.5s

Algorithm
egg-herbie
Counts
15102 → 15102
Iterations

Useful iterations: 0 (339.0ms)

IterNodesCost
05031831684

prune59.4s

Filtered
2789 candidates to 15102 candidates (-441.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New150911115102
Fresh11617
Picked101
Done000
Total151031715120

Merged error: 5.4b

Counts
15120 → 17

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin k) 2)
1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
3.3b
(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
5.7b
(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))

rewrite5.6s

Algorithm
rewrite-expression-head
Rules
117988×add-exp-log
89458×pow-exp
84493×prod-exp
48953×div-exp
26234×pow-to-exp
7020×1-exp
50×add-cbrt-cube
36×add-sqr-sqrt
32×associate-*l*
31×cbrt-unprod
28×times-frac
24×add-cube-cbrt *-un-lft-identity
14×unpow-prod-down
12×pow1
associate-*r*
associate-*l/
sqr-pow
unpow2 unswap-sqr
pow-prod-down add-log-exp
cbrt-undiv pow-unpow *-commutative
associate-*r/
pow-pow div-inv
Counts
4 → 17896
Calls
4 calls:
3.0ms
(pow (sin k) 2)
10.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
169.0ms
(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
723.0ms
(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))

series811.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(pow (sin k) 2)
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
681.0ms
(* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))
106.0ms
(* l (* 2.0 (* (* (* (/ (cos k) (pow (sin k) 2)) l) (pow (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) 1) 1.0)) (pow (* (pow (pow (/ -1 t) 1.0) 1.0) (/ (pow (pow (/ -1 k) (/ 2.0 2)) 1.0) (pow -1 3.0))) 1.0))))

simplify5.5s

Algorithm
egg-herbie
Counts
17908 → 17908
Iterations

Useful iterations: 0 (440.0ms)

IterNodesCost
051171019930

prune59.9s

Filtered
3227 candidates to 17908 candidates (-454.9%)

Profiling

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