Details

Time bar (total: 18.1s)

sample21.0ms

Algorithm
intervals
Results
6.0ms201×body80valid
2.0ms17×body640valid
2.0ms21×body320valid
1.0ms6×body1280valid
1.0ms11×body160valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
144122
133069
122474
112032
101843
91602
81334
7972
6535
5248
4118
371
233
116
08

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
4.3b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
10×add-cbrt-cube add-exp-log
7×add-cube-cbrt
5×pow1 associate-*l* add-log-exp
4×associate-/r* times-frac associate-*l/
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ diff-log pow-prod-down *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 63
Calls
3 calls:
18.0ms
(* (- 1.0 x) y)
22.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
19.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series205.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* (- 1.0 x) y)
94.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
71.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.4s

Counts
72 → 72
Iterations
IterNodes
done5001
21286
1346
0128

prune378.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
4.3b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite85.0ms

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-cbrt-cube add-exp-log
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-- flip-- associate-/l*
2×frac-times cbrt-undiv flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×clear-num sub-neg frac-2neg diff-log pow-prod-down associate-*r/ *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 88
Calls
3 calls:
10.0ms
(/ y (+ y 1.0))
64.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
9.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series252.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(/ y (+ y 1.0))
65.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
118.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.5s

Counts
97 → 97
Iterations
IterNodes
done5002
21614
1424
0157

prune474.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 x) (/ (+ y 1.0) y))
0.1b
(* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))
4.3b
(- (* 1.0 (* 1.0 1.0)) (* (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))) (/ (- 1.0 x) (/ (+ y 1.0) y))))
15.3b
(/ (- (* 1.0 (* 1.0 1.0)) (* (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))) (/ (- 1.0 x) (/ (+ y 1.0) y)))) (+ (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (+ (/ (- 1.0 x) (/ (+ y 1.0) y)) 1.0)) (* 1.0 1.0)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
1022×times-frac
1002×*-un-lft-identity
600×add-sqr-sqrt
378×add-cube-cbrt
159×swap-sqr
137×distribute-lft-out--
132×distribute-lft-out
93×difference-of-squares
85×associate-*r* associate-*l*
47×add-cbrt-cube add-exp-log
36×div-inv
22×cbrt-undiv div-exp
19×associate-/r*
11×pow1
9×prod-exp cbrt-unprod associate-/l* unswap-sqr
7×associate-/r/
6×add-log-exp
5×difference-cubes cube-unmult pow3
4×associate-/l/
3×flip3-- flip--
2×clear-num frac-2neg div-sub
1×pow2 frac-times sub-neg flip3-+ pow-plus diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 540
Calls
4 calls:
25.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
274.0ms
(* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))
198.0ms
(- (* 1.0 (* 1.0 1.0)) (* (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))) (/ (- 1.0 x) (/ (+ y 1.0) y))))
801.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))) (/ (- 1.0 x) (/ (+ y 1.0) y)))) (+ (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (+ (/ (- 1.0 x) (/ (+ y 1.0) y)) 1.0)) (* 1.0 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
67.0ms
(* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y)))
200.0ms
(- (* 1.0 (* 1.0 1.0)) (* (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))) (/ (- 1.0 x) (/ (+ y 1.0) y))))
822.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (/ (- 1.0 x) (/ (+ y 1.0) y))) (/ (- 1.0 x) (/ (+ y 1.0) y)))) (+ (* (/ (- 1.0 x) (/ (+ y 1.0) y)) (+ (/ (- 1.0 x) (/ (+ y 1.0) y)) 1.0)) (* 1.0 1.0)))

simplify2.2s

Counts
552 → 552
Iterations
IterNodes
done5001
12245
0564

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 1.0 y) (- x (/ 1.0 (/ y x))))
0.0b
(- x (/ 1.0 (/ y x)))
0.4b
(/ 1.0 (/ y x))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
54×add-sqr-sqrt
53×*-un-lft-identity
45×add-cube-cbrt
13×associate-/r*
10×add-log-exp
8×add-cbrt-cube add-exp-log
5×div-inv
3×pow1 cbrt-undiv div-exp associate-/l* difference-of-squares
2×associate-+r+ sum-log sub-neg flip3-- diff-log frac-add associate-/r/ flip-- distribute-lft-out distribute-lft-out--
1×+-commutative clear-num associate-+r- frac-2neg flip3-+ distribute-rgt-out-- flip-+
Counts
3 → 106
Calls
3 calls:
84.0ms
(+ (/ 1.0 y) (- x (/ 1.0 (/ y x))))
20.0ms
(- x (/ 1.0 (/ y x)))
8.0ms
(/ 1.0 (/ y x))

series94.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (/ 1.0 y) (- x (/ 1.0 (/ y x))))
38.0ms
(- x (/ 1.0 (/ y x)))
19.0ms
(/ 1.0 (/ y x))

simplify1.9s

Counts
115 → 115
Iterations
IterNodes
done5001
21886
1548
0210

prune534.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes150.0ms

Accuracy

99.7% (0.0b remaining)

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

bsearch127.0ms

Steps
ItersRangePoint
10
595377.2589799166
3.2296043314775124e+20
256213875.7381433
8
-1.972074682316576e+16
-17239113253358.373
-17413228841055.012

simplify3.0ms

Iterations
IterNodes
done25
125
019

end0.0ms

sample855.0ms

Algorithm
intervals
Results
269.0ms6095×body80valid
192.0ms717×body640valid
100.0ms381×body1280valid
92.0ms535×body320valid
21.0ms272×body160valid