Details

Time bar (total: 18.3s)

sample38.0ms

Algorithm
intervals
Results
11.0ms198×body80valid
4.0ms22×body640valid
3.0ms20×body320valid
2.0ms8×body1280valid
1.0ms8×body160valid

simplify5.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11611
23511
37411
412311
521011
623211
724811
827511
932711
1034611
1135211
1236711
1338311
1447011
1556111
1681611
17111811
18152711
19160811
done160811

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.3b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite74.0ms

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:
22.0ms
(* (- 1.0 x) y)
24.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
25.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series210.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* (- 1.0 x) y)
106.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
63.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.5s

Counts
72 → 72
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0128885
1335828
21274746
done5001744

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.3b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt associate-*r*
13×times-frac
11×add-cube-cbrt
7×add-exp-log add-cbrt-cube
5×associate-*l*
4×pow1 add-log-exp
3×flip3-- flip-- distribute-lft-out
2×frac-times associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv sub-neg flip3-+ diff-log associate-*r/ div-exp pow-prod-down *-commutative flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 55
Calls
2 calls:
76.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
7.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series167.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
92.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.5s

Counts
61 → 61
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0134863
1357803
21303739
done5000737

prune169.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
5.2b
(- 1.0 (* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
5.9b
(/ y (+ (pow y 3) (pow 1.0 3)))
14.3b
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
105×*-un-lft-identity
55×times-frac
40×add-sqr-sqrt
36×associate-*r*
35×distribute-lft-out
33×add-cube-cbrt
28×unpow-prod-down cube-prod
20×add-exp-log add-cbrt-cube
18×frac-times
13×associate-*l/
11×pow1
9×flip3-- associate-/r* flip--
8×flip3-+ flip-+
7×prod-exp sum-cubes cbrt-unprod
6×associate-*r/ associate-*l* add-log-exp
4×pow-prod-down associate-/r/
3×cbrt-undiv div-exp associate-/l*
2×distribute-rgt-in distribute-lft-in *-commutative div-inv associate--r+ unswap-sqr
1×sub-neg frac-2neg diff-log clear-num distribute-lft-out-- difference-of-squares
Counts
4 → 164
Calls
4 calls:
109.0ms
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
5.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
36.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
244.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series620.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
291.0ms
(- 1.0 (* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
100.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
112.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify2.4s

Counts
176 → 176
Iterations

Useful iterations: 2 (718.0ms)

IterNodesCost
02664125
18183558
238213232
done50013232

prune719.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
5.9b
(/ y (+ (pow y 3) (pow 1.0 3)))
9.7b
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (- (* 1.0 1.0) (* y 1.0)))
23.5b
(/ (* (- 1.0 x) (pow y 3)) (+ (pow y 3) (pow 1.0 3)))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
127×*-un-lft-identity
64×times-frac
45×distribute-lft-out
42×add-sqr-sqrt
37×associate-*r*
36×unpow-prod-down cube-prod
35×add-cube-cbrt
30×add-exp-log
25×add-cbrt-cube
18×frac-times associate-/r*
15×flip3-- associate-*l/ flip--
11×pow1
10×prod-exp
9×sum-cubes
8×cbrt-unprod
7×div-exp
6×associate-*r/ associate-*l* associate-/r/
5×cbrt-undiv
4×pow-prod-down associate-/l* add-log-exp
3×flip3-+ flip-+ div-inv
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num *-commutative associate-/l/ unswap-sqr
1×pow-to-exp distribute-rgt-out-- pow-exp distribute-lft-out-- difference-of-squares
Counts
4 → 192
Calls
4 calls:
98.0ms
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
42.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
140.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (- (* 1.0 1.0) (* y 1.0)))
57.0ms
(/ (* (- 1.0 x) (pow y 3)) (+ (pow y 3) (pow 1.0 3)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3))))
107.0ms
(/ y (+ (pow y 3) (pow 1.0 3)))
124.0ms
(* (* (- 1.0 x) (/ y (+ (pow y 3) (pow 1.0 3)))) (- (* 1.0 1.0) (* y 1.0)))
126.0ms
(/ (* (- 1.0 x) (pow y 3)) (+ (pow y 3) (pow 1.0 3)))

simplify2.4s

Counts
204 → 204
Iterations

Useful iterations: 2 (937.0ms)

IterNodesCost
02934080
18583627
242033253
done50023253

prune640.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes110.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.4b

bsearch131.0ms

Steps
ItersRangePoint
10
1810750790637.4219
3.7273233967199085e+29
528433753610563.25
8
-1.6853749013735252e+30
-4.159371291780153e+27
-4.2011980442598443e+27

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02969
13959
done3959

end0.0ms

sample997.0ms

Algorithm
intervals
Results
328.0ms6091×body80valid
142.0ms354×body1280valid
114.0ms754×body640valid
105.0ms505×body320valid
24.0ms296×body160valid