Details

Time bar (total: 13.6s)

sample18.0ms

Algorithm
intervals
Results
5.0ms195×body80valid
3.0ms27×body640valid
1.0ms17×body320valid
1.0ms9×body1280valid
0.0ms8×body160valid

simplify5.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0811
11611
23511
37011
413011
521311
625611
727211
829911
936811
1042011
1142611
1244111
1347711
1456511
1578811
16106311
17149711
18192011
19196611
done196611

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.9b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1 associate-*l* add-log-exp
4×times-frac associate-*l/ associate-/r*
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg flip3-+ diff-log pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 63
Calls
3 calls:
10.0ms
(* (- 1.0 x) y)
10.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
10.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series142.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* (- 1.0 x) y)
67.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify622.0ms

Counts
72 → 72
Iterations

Useful iterations: done (620.0ms)

IterNodesCost
0128885
1336828
21226746
done5000744

prune159.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ y 1.0) y)
0.1b
(/ (- 1.0 x) (/ (+ y 1.0) y))
2.9b
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
167×times-frac
157×*-un-lft-identity
120×add-sqr-sqrt
77×add-cube-cbrt
22×distribute-lft-out
20×difference-of-squares
19×associate-/r*
18×distribute-lft-out--
10×add-exp-log add-cbrt-cube
9×associate-/l*
8×div-inv
5×add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×pow1
2×flip3-- frac-2neg div-sub clear-num flip--
1×sub-neg flip3-+ diff-log associate-/r/ flip-+ associate--r-
Counts
3 → 169
Calls
3 calls:
7.0ms
(/ (+ y 1.0) y)
14.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
38.0ms
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

series161.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (+ y 1.0) y)
43.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
69.0ms
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

simplify822.0ms

Counts
178 → 178
Iterations

Useful iterations: 2 (378.0ms)

IterNodesCost
02493046
16852843
220092731
done50002731

prune333.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 x) (+ y 1.0))
0.1b
(* (/ (- 1.0 x) (+ y 1.0)) y)
5.1b
(- 1.0 (* (/ (- 1.0 x) (+ y 1.0)) y))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×add-sqr-sqrt
41×times-frac
26×associate-*l*
25×add-cube-cbrt
11×distribute-lft-out
10×add-exp-log add-cbrt-cube
9×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l* add-log-exp
4×associate-/r* associate-/r/
3×associate-*r*
2×cbrt-undiv flip3-- flip3-+ div-exp prod-exp flip-- cbrt-unprod flip-+ div-inv associate-/l/ unswap-sqr
1×sub-neg frac-2neg diff-log div-sub pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 103
Calls
3 calls:
11.0ms
(/ (- 1.0 x) (+ y 1.0))
24.0ms
(* (/ (- 1.0 x) (+ y 1.0)) y)
2.0ms
(- 1.0 (* (/ (- 1.0 x) (+ y 1.0)) y))

series144.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(/ (- 1.0 x) (+ y 1.0))
43.0ms
(* (/ (- 1.0 x) (+ y 1.0)) y)
71.0ms
(- 1.0 (* (/ (- 1.0 x) (+ y 1.0)) y))

simplify2.3s

Counts
112 → 112
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01661480
14321405
212151313
342721307
done50001304

prune190.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

6.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
6.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
6.2b
(/ (* (- 1.0 x) y) (+ y 1.0))
13.4b
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))) (* 1.0 1.0)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
92×*-un-lft-identity
87×times-frac
64×difference-of-squares
48×unpow-prod-down cube-prod
40×add-cube-cbrt
32×sqr-pow
28×associate-/l*
21×add-exp-log add-cbrt-cube
20×distribute-lft-out--
15×associate-/r*
8×associate-/r/ associate-/l/
7×cbrt-undiv div-exp
6×associate-*l/ distribute-lft-out
4×pow1 difference-cubes flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv add-log-exp
3×prod-exp cbrt-unprod
1×div-sub
Counts
4 → 201
Calls
4 calls:
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
150.0ms
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))) (* 1.0 1.0)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
43.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
615.0ms
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))) (* 1.0 1.0)))

simplify800.0ms

Counts
213 → 213
Iterations

Useful iterations: 2 (342.0ms)

IterNodesCost
02569815
16599471
222729187
done50009187

prune496.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes181.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.6b

bsearch82.0ms

Steps
ItersRangePoint
9
2942.2625356967415
559751770.533176
184531412.1859252
9
-155084744.97222546
-3.3588146519216853
-129624842.47456154

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01941
12631
done2631

end0.0ms

sample643.0ms

Algorithm
intervals
Results
340.0ms6059×body80valid
69.0ms712×body640valid
45.0ms380×body1280valid
36.0ms518×body320valid
16.0ms331×body160valid