Details

Time bar (total: 10.4s)

sample59.0ms

Algorithm
intervals
Results
8.0ms170×body80valid
7.0ms38×body640valid
6.0ms26×body1280valid
4.0ms22×body1280nan
4.0ms26×body640nan
4.0ms97×body80nan
2.0ms16×body320nan
2.0ms13×body320valid
1.0ms12×body160nan
1.0ms9×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22912
34112
45912
57412
68712
710612
814612
918812
1022412
1125712
1229412
1333012
1436212
1539912
1643512
1746712
1850412
1954012
2057412
2161112
2264712
2368112
2471812
2575412
2678812
2782512
2886112
2989512
3093212
3196812
32100212
33103912
34107512
35110912
36114612
37118212
38121612
39125312
40128912
41132312
42136012
43139612
44143012
45146712
46150312
47153712
48157412
49161012
50164412
51168112
52171712
53175112
54178812
55182412
56185812
57189512
58193112
59196512
60200212
61203812
62207212
63210912
64214512
65217912
66221612
67225212
68228612
69232312
70235912
71239312
72243012
73246612
74250012
75253712
76257312
77260712
78264412
79268012
80271412
81275112
82278712
83282112
84285812
85289412
86292812
87296512
88300112
89303512
90307212
91310812
92314212
93317912
94321512
95324912
96328612
97332212
98335612
99339312
100342912
101346312
102350012
103353612
104357012
105360712
106364312
107367712
108371412
109375012
110378412
111382112
112385712
113389112
114392812
115396412
116399812
117403512
118407112
119410512
120414212
121417812
122421212
123424912
124428512
125431912
126435612
127439212
128442612
129446312
130449912
131453312
132457012
133460612
134464012
135467712
136471312
137474712
138478412
139482012
140485412
141489112
142492712
143496112
144499812
done500012

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 21.5b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x y) (- 1.0 y))
3.2b
(- 1.0 (/ (- x y) (- 1.0 y)))
4.4b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
44×*-un-lft-identity
27×times-frac
16×add-cube-cbrt difference-of-squares
14×distribute-lft-out--
6×add-exp-log log-prod
5×associate-/r* add-cbrt-cube associate-/l* add-log-exp
4×pow1 flip3-- flip--
2×log-div div-sub associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num log-pow div-inv associate--r-
Counts
3 → 85
Calls
3 calls:
9.0ms
(/ (- x y) (- 1.0 y))
14.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
18.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series31.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ (- x y) (- 1.0 y))
10.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
14.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify651.0ms

Counts
94 → 94
Iterations

Useful iterations: done (648.0ms)

IterNodesCost
01731423
14071355
210651266
330921259
done50001258

prune193.0ms

Filtered
69 candidates to 94 candidates (-36.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New89594
Fresh000
Picked101
Done000
Total90595

Merged error: 0.2b

Counts
95 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- 1.0 y))
0.1b
(* (- x y) (/ 1 (- 1.0 y)))
4.4b
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
6.6b
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
42×*-un-lft-identity
32×times-frac
25×add-cube-cbrt
21×associate-*r*
18×add-exp-log
11×add-cbrt-cube
8×pow1 distribute-lft-out-- difference-of-squares
6×flip3-- flip-- add-log-exp
5×associate-*l* associate-/r*
4×div-exp prod-exp associate-/r/
3×log-prod associate-/l* unswap-sqr
2×cbrt-undiv frac-times log-div rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ rem-log-exp pow-prod-down clear-num log-pow un-div-inv *-commutative inv-pow
Counts
4 → 117
Calls
4 calls:
6.0ms
(/ 1 (- 1.0 y))
15.0ms
(* (- x y) (/ 1 (- 1.0 y)))
3.0ms
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
3.0ms
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series32.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 1 (- 1.0 y))
7.0ms
(* (- x y) (/ 1 (- 1.0 y)))
13.0ms
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
10.0ms
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify473.0ms

Counts
129 → 129
Iterations

Useful iterations: done (469.0ms)

IterNodesCost
02081760
14941472
217171279
done50001275

prune168.0ms

Filtered
83 candidates to 129 candidates (-55.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1290129
Fresh044
Picked011
Done000
Total1295134

Merged error: 0.2b

Counts
134 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (/ (- x y) (- 1.0 y)) 3)
3.1b
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
4.4b
(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
9.8b
(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
510×add-sqr-sqrt
312×times-frac
222×*-un-lft-identity
212×difference-of-squares
175×unpow-prod-down cube-prod
105×log-prod
102×add-cube-cbrt
81×sqr-pow
60×distribute-lft-out--
33×associate-/l*
12×add-exp-log
9×add-cbrt-cube
8×difference-cubes associate-/r/
6×pow1 add-log-exp
4×flip3-- flip-- div-inv
3×pow-unpow div-exp associate-/r*
2×cbrt-undiv flip3-+ rem-log-exp pow-exp flip-+ associate-/l/ rem-cube-cbrt
1×cube-div cube-mult pow-to-exp sub-neg log-div pow-pow frac-2neg diff-log unpow3 div-sub clear-num log-pow
Counts
4 → 392
Calls
4 calls:
16.0ms
(pow (/ (- x y) (- 1.0 y)) 3)
46.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
87.0ms
(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
82.0ms
(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(pow (/ (- x y) (- 1.0 y)) 3)
68.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
102.0ms
(log (/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
86.0ms
(/ (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))

simplify1.1s

Counts
404 → 404
Iterations

Useful iterations: done (1.1s)

IterNodesCost
050021071
1137420337
2466619914
done500019890

prune1.3s

Filtered
207 candidates to 404 candidates (-95.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3986404
Fresh123
Picked101
Done011
Total4009409

Merged error: 0.2b

Counts
409 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))
3.1b
(- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y))))
4.4b
(log (/ (- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
9.8b
(/ (- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
84×*-un-lft-identity
81×times-frac
44×add-cube-cbrt
36×associate-*l*
35×unpow-prod-down
31×associate-*r*
29×add-exp-log
20×distribute-lft-out-- difference-of-squares
18×log-prod
12×unpow2
11×add-cbrt-cube
10×unswap-sqr
9×pow3
8×difference-cubes div-exp prod-exp associate-/r/
6×pow1 add-log-exp
4×flip3-- pow-exp flip-- div-inv associate-/l*
3×associate-/r* sqr-pow
2×cbrt-undiv pow-to-exp flip3-+ rem-log-exp cbrt-unprod flip-+ associate-/l/
1×sub-neg log-div frac-2neg pow-plus diff-log div-sub associate-*r/ clear-num log-pow *-commutative pow-prod-up
Counts
4 → 177
Calls
4 calls:
39.0ms
(* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))
25.0ms
(- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y))))
55.0ms
(log (/ (- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
53.0ms
(/ (- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))
53.0ms
(- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y))))
91.0ms
(log (/ (- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0))))
75.0ms
(/ (- (pow 1.0 3) (* (pow (/ (- x y) (- 1.0 y)) 2) (/ (- x y) (- 1.0 y)))) (+ (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))) (* 1.0 1.0)))

simplify931.0ms

Counts
189 → 189
Iterations

Useful iterations: 2 (329.0ms)

IterNodesCost
03597324
110125926
242025509
done50005509

prune590.0ms

Filtered
138 candidates to 189 candidates (-37.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1881189
Fresh077
Picked101
Done011
Total1899198

Merged error: 0.2b

Counts
198 → 9

regimes339.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 18.4b

bsearch85.0ms

Steps
ItersRangePoint
11
14848.343200454
6.43616546702885e+37
17432142.236941274
8
-6366268205916247.0
-8645744266892.621
-8726900086500.019

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02454
13239
done3239

end0.0ms

sample1.5s

Algorithm
intervals
Results
268.0ms5624×body80valid
214.0ms837×body1280valid
151.0ms819×body640valid
148.0ms763×body1280nan
116.0ms754×body640nan
101.0ms2723×body80nan
60.0ms460×body320valid
56.0ms451×body320nan
23.0ms260×body160valid
18.0ms242×body160nan

Profiling

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