Details

Time bar (total: 12.5s)

sample31.0ms

Algorithm
intervals
Results
8.0ms192×body80valid
4.0ms23×body640valid
2.0ms18×body320valid
2.0ms12×body1280valid
1.0ms11×body160valid

simplify934.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
61686
5419
4152
374
235
116
08

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (- 1.0 x) (/ y (+ 1.0 y)))
2.8b
(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt associate-*r*
13×times-frac
11×add-cube-cbrt
7×add-cbrt-cube add-exp-log
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 div-exp pow-prod-down associate-*r/ *-commutative flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 55
Calls
2 calls:
48.0ms
(* (- 1.0 x) (/ y (+ 1.0 y)))
4.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

series209.0ms

Counts
2 → 6
Calls
2 calls:
84.0ms
(* (- 1.0 x) (/ y (+ 1.0 y)))
126.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

simplify1.2s

Counts
61 → 61
Iterations
IterNodes
done5000
22233
1375
0134

prune283.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (/ y (+ 1.0 y)) (- 1.0 x))
2.8b
(- 1.0 (* 1 (* (/ y (+ 1.0 y)) (- 1.0 x))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-sqr-sqrt associate-*l*
13×times-frac
11×add-cube-cbrt
10×distribute-rgt-in distribute-lft-in
8×associate--r+
7×sub-neg add-cbrt-cube add-exp-log
5×associate-*r*
4×pow1 add-log-exp
3×flip3-- flip-- distribute-lft-out
2×frac-times prod-exp associate-*r/ associate-/r/ cbrt-unprod distribute-lft-out-- unswap-sqr
1×cbrt-undiv flip3-+ diff-log div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv difference-of-squares
Counts
2 → 68
Calls
2 calls:
63.0ms
(* (/ y (+ 1.0 y)) (- 1.0 x))
6.0ms
(- 1.0 (* 1 (* (/ y (+ 1.0 y)) (- 1.0 x))))

series173.0ms

Counts
2 → 6
Calls
2 calls:
55.0ms
(* (/ y (+ 1.0 y)) (- 1.0 x))
118.0ms
(- 1.0 (* 1 (* (/ y (+ 1.0 y)) (- 1.0 x))))

simplify1.5s

Counts
74 → 74
Iterations
IterNodes
done5001
22416
1418
0147

prune329.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) (- 1.0 y))
5.2b
(- 1.0 (* 1 (* (/ y (- (* 1.0 1.0) (* y y))) (* (- 1.0 x) (- 1.0 y)))))
6.2b
(* (/ y (- (* 1.0 1.0) (* y y))) (* (- 1.0 x) (- 1.0 y)))
11.9b
(/ y (- (* 1.0 1.0) (* y y)))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
34×distribute-rgt-in distribute-lft-in
29×add-sqr-sqrt
28×*-un-lft-identity
24×times-frac
23×associate-*l* add-cube-cbrt
21×flip3-- flip--
20×frac-times add-cbrt-cube add-exp-log
16×associate--r+
15×sub-neg
14×associate-*r/
11×pow1
9×difference-of-squares
7×associate-*l/ prod-exp cbrt-unprod
6×associate-*r* add-log-exp
4×associate-/r* pow-prod-down associate-/r/
3×cbrt-undiv div-exp associate-/l* distribute-lft-out--
2×*-commutative div-inv
1×clear-num frac-2neg diff-log unswap-sqr
Counts
4 → 158
Calls
4 calls:
57.0ms
(* (- 1.0 x) (- 1.0 y))
22.0ms
(- 1.0 (* 1 (* (/ y (- (* 1.0 1.0) (* y y))) (* (- 1.0 x) (- 1.0 y)))))
94.0ms
(* (/ y (- (* 1.0 1.0) (* y y))) (* (- 1.0 x) (- 1.0 y)))
20.0ms
(/ y (- (* 1.0 1.0) (* y y)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (- 1.0 x) (- 1.0 y))
222.0ms
(- 1.0 (* 1 (* (/ y (- (* 1.0 1.0) (* y y))) (* (- 1.0 x) (- 1.0 y)))))
58.0ms
(* (/ y (- (* 1.0 1.0) (* y y))) (* (- 1.0 x) (- 1.0 y)))
77.0ms
(/ y (- (* 1.0 1.0) (* y y)))

simplify530.0ms

Counts
170 → 170
Iterations
IterNodes
done5000
1888
0276

prune900.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ y (/ (+ 1.0 y) (- 1.0 x)))
0.1b
(* (sqrt (- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))) (sqrt (- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))))
2.8b
(- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))
2.8b
(- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))

rewrite680.0ms

Algorithm
rewrite-expression-head
Rules
177×add-sqr-sqrt
176×times-frac
169×*-un-lft-identity
79×add-cube-cbrt
38×sqrt-prod
34×difference-of-squares
26×associate-/r*
24×distribute-lft-out--
20×distribute-lft-out
19×pow1
14×swap-sqr
12×flip3-- sqrt-div flip--
11×add-cbrt-cube add-exp-log
10×associate-*r* associate-*l*
9×associate-/r/
8×sqrt-pow1 pow1/2 add-log-exp
5×pow-prod-up div-inv
4×frac-times unswap-sqr
3×cbrt-undiv div-exp pow-prod-down pow-sqr associate-/l*
2×sub-neg diff-log associate-*l/ associate-*r/
1×pow2 clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 225
Calls
4 calls:
38.0ms
(/ y (/ (+ 1.0 y) (- 1.0 x)))
524.0ms
(* (sqrt (- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))) (sqrt (- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))))
52.0ms
(- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))
44.0ms
(- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ y (/ (+ 1.0 y) (- 1.0 x)))
134.0ms
(* (sqrt (- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))) (sqrt (- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))))
119.0ms
(- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))
156.0ms
(- 1.0 (/ y (/ (+ 1.0 y) (- 1.0 x))))

simplify1.5s

Counts
237 → 237
Iterations
IterNodes
done5001
23775
1785
0326

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes248.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.2b

bsearch130.0ms

Steps
ItersRangePoint
9
6968.3439428623215
12923530959.442633
97640792.5914523
6
-531429590.62988466
-72632609.50044116
-92380677.54763953

simplify6.0ms

Iterations
IterNodes
done35
235
134
025

end0.0ms

sample1.5s

Algorithm
intervals
Results
789.0ms6117×body80valid
165.0ms709×body640valid
139.0ms504×body320valid
78.0ms375×body1280valid
29.0ms295×body160valid