Details

Time bar (total: 24.7s)

sample7.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 15.267944%

Guaranteed chance to sample good point: 24.181524%

Results
60.0ms68×body1280valid
33.0ms60×body640valid
13.0ms100×body80valid
6.0ms16×body320valid
6.0ms42×body80invalid
3.0ms12×body160valid
2.0ms3×body640invalid
1.0ms3×body160invalid
1.0ms1×body320invalid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04813
115813
290313
3500113

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.0b

Counts
2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (/ (pow t 3.0) (* l l)) (sin k))
2.7b
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
15.4b
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.1b
(/ (pow t 3.0) (* l l))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
108×add-exp-log
58×prod-exp
52×add-cbrt-cube
26×cbrt-unprod
24×div-exp
21×add-sqr-sqrt
20×pow1
19×*-un-lft-identity
17×times-frac
16×associate-*l/
14×add-cube-cbrt
13×associate-*l*
11×associate-*r*
10×frac-times unpow-prod-down pow-prod-down
8×tan-quot cbrt-undiv pow-to-exp pow-exp
7×associate-/l*
6×associate-*r/
4×flip3-+ flip-+ add-log-exp unswap-sqr sqr-pow
3×*-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 144
Calls
4 calls:
11.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
11.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
22.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
6.0ms
(/ (pow t 3.0) (* l l))

series328.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(* (/ (pow t 3.0) (* l l)) (sin k))
73.0ms
(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
162.0ms
(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
39.0ms
(/ (pow t 3.0) (* l l))

simplify121.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08571728
147841448
250011444

prune328.0ms

Filtered
96 candidates to 156 candidates (-62.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New14511156
Fresh000
Picked101
Done000
Total14611157

Merged error: 21.2b

Counts
157 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
7.7b
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.4b
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
304×add-exp-log
184×prod-exp
78×add-cbrt-cube
77×div-exp
50×add-sqr-sqrt
49×times-frac
44×associate-*l/ cbrt-unprod
42×*-un-lft-identity
37×add-cube-cbrt
36×associate-*l*
34×frac-times
33×pow-exp
29×pow1
24×unpow-prod-down
22×pow-to-exp
17×pow-prod-down
16×tan-quot
14×associate-*r/
12×cbrt-undiv
11×associate-*r*
10×cbrt-prod
8×flip3-+ flip-+ sqr-pow
5×associate-/l* unswap-sqr
4×add-log-exp
3×associate-/r* *-commutative distribute-lft-out
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num
Counts
4 → 229
Calls
4 calls:
16.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
10.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
5.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
28.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series574.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
52.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
45.0ms
(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
397.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify66.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014303890
150023397

prune618.0ms

Filtered
152 candidates to 241 candidates (-58.6%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New22813241
Fresh3710
Picked101
Done000
Total23220252

Merged error: 17.6b

Counts
252 → 20

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 2.0 (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
2.7b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
15.4b
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
1254×add-exp-log
867×prod-exp
323×div-exp
187×add-cbrt-cube
145×pow-to-exp pow-exp
117×cbrt-unprod
78×associate-*l/
63×frac-times
53×associate-*r/
42×add-sqr-sqrt
37×times-frac
36×associate-*l*
34×*-un-lft-identity
31×cbrt-undiv
29×pow1 add-cube-cbrt
28×tan-quot
23×associate-/r/
20×unpow-prod-down
17×pow-prod-down
16×flip3-+ flip-+
11×associate-*r*
10×cbrt-prod
5×unswap-sqr
4×add-log-exp sqr-pow
3×*-commutative distribute-lft-out associate-/l*
2×div-inv
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r*
Counts
4 → 397
Calls
4 calls:
42.0ms
(/ 2.0 (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
22.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
10.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
38.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series483.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ 2.0 (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))
80.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k))
54.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
182.0ms
(* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify103.0ms

Algorithm
egg-herbie
Counts
409 → 409
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
019058359
150017237

prune817.0ms

Filtered
174 candidates to 409 candidates (-135.1%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New39811409
Fresh61319
Picked101
Done000
Total40524429

Merged error: 15.3b

Counts
429 → 24

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt t) 3.0)
0.7b
(/ 2.0 (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))
4.3b
(* (/ (pow (cbrt t) 3.0) l) (sin k))
17.5b
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
1661×add-exp-log
1108×prod-exp
472×div-exp
239×add-cbrt-cube
194×pow-to-exp pow-exp
146×cbrt-unprod
62×associate-*r/
58×frac-times
51×associate-*l/
46×cbrt-undiv
43×add-sqr-sqrt
37×times-frac
35×associate-*l*
30×add-cube-cbrt *-un-lft-identity
28×pow1
26×unpow-prod-down
24×tan-quot
23×associate-/r/
16×flip3-+ pow-prod-down flip-+
13×cbrt-prod
5×unswap-sqr sqr-pow
4×distribute-rgt-in distribute-lft-in associate-*r* add-log-exp
3×pow-unpow associate-/l*
2×pow-pow *-commutative div-inv
1×frac-2neg pow1/3 clear-num associate-/r*
Counts
4 → 468
Calls
4 calls:
3.0ms
(pow (cbrt t) 3.0)
43.0ms
(/ 2.0 (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))
10.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
34.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

series447.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(pow (cbrt t) 3.0)
168.0ms
(/ 2.0 (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))))
53.0ms
(* (/ (pow (cbrt t) 3.0) l) (sin k))
179.0ms
(* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (* (tan k) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)))

simplify124.0ms

Algorithm
egg-herbie
Counts
480 → 480
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0209010418
150019483

prune748.0ms

Filtered
169 candidates to 480 candidates (-184.0%)
Pruning

26 alts after pruning (26 fresh and 0 done)

PrunedKeptTotal
New4746480
Fresh32023
Picked101
Done000
Total47826504

Merged error: 15.3b

Counts
504 → 26

regimes1.1s

Accuracy

6.3% (4.2b remaining)

Error of 17.6b against oracle of 13.4b and baseline of 17.9b

bsearch163.0ms

Steps
ItersRangePoint
9
-0.0020349930939526353
-4.734521697712597e-11
-6.682113404743575e-11
4
-3.7533101384246245e+80
-2.0396531279318153e+80
-2.327291140920426e+80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05940
15940

end0.0ms

sample11.0s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 15.267944%

Guaranteed chance to sample good point: 24.181524%

Results
1.7s2067×body1280valid
894.0ms1548×body640valid
445.0ms3300×body80valid
289.0ms719×body320valid
140.0ms1015×body80invalid
101.0ms366×body160valid
58.0ms108×body640invalid
55.0ms137×body320invalid
25.0ms31×body1280invalid
18.0ms65×body160invalid

Profiling

Loading profile data...