Details

Time bar (total: 12.8s)

sample21.0ms

Algorithm
intervals
Results
5.0ms185×body80valid
4.0ms16×body1280valid
3.0ms31×body640valid
1.0ms15×body320valid
0.0ms9×body160valid

simplify6.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0811
11611
23511
37011
413011
521211
624811
728511
838211
951511
1058811
1192011
12457611
done500011

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.5b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.4b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite33.0ms

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)))
11.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series146.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(* (- 1.0 x) y)
69.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
44.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify597.0ms

Counts
72 → 72
Iterations

Useful iterations: 2 (142.0ms)

IterNodesCost
0128885
1336828
21244746
done5000746

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
2.5b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
25×times-frac
21×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-- flip-- associate-/l*
2×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×sub-neg frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 88
Calls
3 calls:
5.0ms
(/ y (+ y 1.0))
26.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series146.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(/ y (+ y 1.0))
46.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
65.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify646.0ms

Counts
97 → 97
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
01571229
13991148
214581056
done50001056

prune183.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ y 1.0) y)
0.1b
(/ (- 1.0 x) (/ (+ y 1.0) y))
2.5b
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

rewrite70.0ms

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:
8.0ms
(/ (+ y 1.0) y)
15.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
39.0ms
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

series160.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ (+ y 1.0) y)
42.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
69.0ms
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

simplify846.0ms

Counts
178 → 178
Iterations

Useful iterations: 2 (265.0ms)

IterNodesCost
02493046
16852843
221762731
done50002731

prune296.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
0.2b
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
2.4b
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
9.7b
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
51×frac-times
47×add-exp-log add-cbrt-cube
45×pow1
31×associate-*l/
30×*-un-lft-identity
29×add-sqr-sqrt
28×flip3-- flip--
25×times-frac
23×prod-exp cbrt-unprod
22×add-cube-cbrt
19×associate-*r*
18×associate-*r/ pow-prod-down
8×cbrt-undiv div-exp
6×associate-*l* add-log-exp difference-of-squares
4×associate-/r/ pow-sqr pow-prod-up associate-/l*
3×associate-/r* distribute-lft-out
2×flip3-+ pow-plus *-commutative flip-+ div-inv associate-/l/ unswap-sqr
1×pow2 sub-neg frac-2neg diff-log div-sub swap-sqr clear-num distribute-lft-out--
Counts
4 → 171
Calls
4 calls:
23.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
82.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
5.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
21.0ms
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
52.0ms
(* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))
87.0ms
(- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0)))))
388.0ms
(/ (- (* 1.0 1.0) (* (* (- 1.0 x) (/ y (+ y 1.0))) (* (- 1.0 x) (/ y (+ y 1.0))))) (+ 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))

simplify1.3s

Counts
183 → 183
Iterations

Useful iterations: 2 (404.0ms)

IterNodesCost
02935328
19094800
238124206
done50004206

prune333.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes118.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.1b

bsearch65.0ms

Steps
ItersRangePoint
7
117627206.70733242
11334711170.833195
152679725.13905564
8
-64880754058.88788
-1357526.7243520434
-127752568.37720934

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01941
12631
done2631

end0.0ms

sample435.0ms

Algorithm
intervals
Results
153.0ms6124×body80valid
63.0ms723×body640valid
48.0ms388×body1280valid
31.0ms474×body320valid
13.0ms291×body160valid