Details

Time bar (total: 2.5min)

analyze2.7s (1.8%)

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

sample521.0ms (0.3%)

Algorithm
intervals
Results
134.0ms26×body5120invalid
124.0ms48×body2560invalid
90.0ms105×body1280valid
39.0ms28×body2560valid
39.0ms61×body640valid
30.0ms37×body1280invalid
11.0msbody5120valid
9.0ms17×body640invalid
6.0ms15×body320invalid
6.0ms15×body320valid
4.0ms30×body80valid
4.0ms30×body80invalid
4.0ms13×body160valid
1.0msbody160invalid

simplify37.0ms (0%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0484221
1484221

prune15.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 36.8b

Counts
2 → 2

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

0.8b
(* (tan k) (pow (/ k t) 2.0))
6.1b
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
6.8b
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
27.1b
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))

rewrite69.0ms (0%)

Algorithm
rewrite-expression-head
Rules
287×add-exp-log
200×prod-exp
62×add-cbrt-cube
48×div-exp
38×pow-exp
35×cbrt-unprod
29×add-sqr-sqrt
28×pow-to-exp
22×associate-*r*
21×associate-*l*
19×add-cube-cbrt *-un-lft-identity
18×unpow-prod-down
13×times-frac
11×pow1
cbrt-undiv
associate-*r/ associate-*l/ unswap-sqr
pow-prod-down *-commutative add-log-exp
tan-quot sqr-pow
div-inv
associate-/r/
Counts
4 → 165
Calls

4 calls:

19.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
18.0ms
(* l (* (/ 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))))
10.0ms
(* (tan k) (pow (/ k t) 2.0))

series430.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

161.0ms
(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l)
126.0ms
(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))) l))
77.0ms
(* (pow t 3.0) (* (sin k) (* (tan k) (pow (/ k t) 2.0))))
65.0ms
(* (tan k) (pow (/ k t) 2.0))

simplify45.0ms (0%)

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050223165

prune475.0ms (0.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1689177
Fresh101
Picked101
Done000
Total1709179

Merged error: 12.8b

Counts
179 → 9

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
4.2b
(* (* (/ (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))
6.1b
(* 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))))
7.6b
(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))

rewrite424.0ms (0.3%)

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:

69.0ms
(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))
65.0ms
(* 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))))
25.0ms
(* (* (/ (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))
9.0ms
(* (/ (cos k) (pow (sin k) 2)) l)

series291.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

111.0ms
(* (* (/ (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))
104.0ms
(* 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))))
54.0ms
(* (/ (pow (pow (/ -1 k) 2.0) 1.0) (pow -1 3.0)) (pow (pow (/ -1 t) 1.0) 1.0))
22.0ms
(* (/ (cos k) (pow (sin k) 2)) l)

simplify334.0ms (0.2%)

Algorithm
egg-herbie
Counts
1685 → 1685
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0515553347

prune15.9s (10.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1675101685
Fresh358
Picked101
Done000
Total1679151694

Merged error: 8.5b

Counts
1694 → 15

localize35.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(pow (sin k) 2)
1.9b
(* (/ (cos k) (pow (sin k) 2)) l)
4.2b
(* (* (/ (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))
6.1b
(* 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))))

rewrite5.1s (3.4%)

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:

649.0ms
(* 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))))
206.0ms
(* (* (/ (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))
9.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
3.0ms
(pow (sin k) 2)

series241.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

112.0ms
(* (* (/ (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))
105.0ms
(* 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))))
20.0ms
(* (/ (cos k) (pow (sin k) 2)) l)
3.0ms
(pow (sin k) 2)

simplify4.4s (2.9%)

Algorithm
egg-herbie
Counts
15102 → 15102
Iterations

Useful iterations: 0 (340.0ms)

IterNodesCost
05031831684

prune2.0min (79.3%)

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