Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	197×	body	80	valid
6.0ms	27×	body	640	valid
2.0ms	8×	body	1280	valid
2.0ms	12×	body	320	valid
1.0ms	12×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1686
5	419
4	152
3	74
2	35
1	16
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ 1.0 y))
3.0b	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-exp` `flip-+` `div-inv` `flip--`

Counts

2 → 45

Calls

2 calls:

9.0ms	(/ y (+ 1.0 y))
4.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

series111.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ y (+ 1.0 y))
76.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

simplify635.0ms

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
2	1086
1	251
0	102

prune236.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ 1.0 y))
0.1b	(* y (/ 1 (+ 1.0 y)))
4.4b	(- 1.0 (* (- 1.0 x) (* y (/ 1 (+ 1.0 y)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
26×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`distribute-lft-out`
6×	`pow1`
5×	`add-log-exp`
4×	`associate-/r*` `div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `flip--` `inv-pow`

Counts

3 → 90

Calls

3 calls:

9.0ms	(/ 1 (+ 1.0 y))
35.0ms	(* y (/ 1 (+ 1.0 y)))
9.0ms	(- 1.0 (* (- 1.0 x) (* y (/ 1 (+ 1.0 y)))))

series204.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 1 (+ 1.0 y))
54.0ms	(* y (/ 1 (+ 1.0 y)))
112.0ms	(- 1.0 (* (- 1.0 x) (* y (/ 1 (+ 1.0 y)))))

simplify1.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	2007
1	388
0	145

prune316.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ y (+ 1.0 y)) (- 1.0 x)) (+ 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))))
0.1b	(pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3)
2.9b	(- (pow 1.0 3) (pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3))
13.6b	(/ (- (pow 1.0 3) (pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3)) (+ (* (* (/ y (+ 1.0 y)) (- 1.0 x)) (+ 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x)))) (* 1.0 1.0)))

rewrite326.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
40×	`difference-of-squares`
39×	`times-frac`
34×	`*-un-lft-identity`
31×	`sqr-pow`
24×	`add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
18×	`frac-times`
13×	`associate-/l*`
12×	`pow1`
11×	`unpow-prod-down` `cube-prod`
10×	`flip3--` `associate-*r/` `flip--`
9×	`associate-*l/`
7×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
6×	`add-log-exp`
5×	`cube-div` `difference-cubes` `distribute-lft-out--`
4×	`pow-prod-down`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `div-exp` `associate-r*` `pow-exp` `rem-cube-cbrt`
2×	`pow-pow` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `associate-l` `*-commutative` `div-inv`

Counts

4 → 162

Calls

4 calls:

66.0ms	(* (* (/ y (+ 1.0 y)) (- 1.0 x)) (+ 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))))
16.0ms	(pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3)
29.0ms	(- (pow 1.0 3) (pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3))
203.0ms	(/ (- (pow 1.0 3) (pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3)) (+ (* (* (/ y (+ 1.0 y)) (- 1.0 x)) (+ 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x)))) (* 1.0 1.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (* (/ y (+ 1.0 y)) (- 1.0 x)) (+ 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))))
79.0ms	(pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3)
282.0ms	(- (pow 1.0 3) (pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3))
928.0ms	(/ (- (pow 1.0 3) (pow (* (/ y (+ 1.0 y)) (- 1.0 x)) 3)) (+ (* (* (/ y (+ 1.0 y)) (- 1.0 x)) (+ 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x)))) (* 1.0 1.0)))

simplify589.0ms

Counts

174 → 174

Iterations

Iter	Nodes
done	5001
1	1095
0	317

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

7.8b	(/ (* y (- 1.0 x)) (+ y 1.0))
7.8b	(/ (* y (- 1.0 x)) (+ y 1.0))
9.0b	(/ (+ (* (/ (* y (- 1.0 x)) (+ y 1.0)) (+ 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))) (* 1.0 1.0)) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0))))
9.0b	(/ (+ (* 1.0 1.0) (+ (* (* (/ y (+ 1.0 y)) (- 1.0 x)) (* (/ y (+ 1.0 y)) (- 1.0 x))) (* 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))))) (/ (+ (* (/ (* y (- 1.0 x)) (+ y 1.0)) (+ 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))) (* 1.0 1.0)) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

146×	`times-frac`
116×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
76×	`add-cube-cbrt`
34×	`associate-/r*`
21×	`add-cbrt-cube` `add-exp-log`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
8×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l*` `associate-/l/`
7×	`flip3--` `flip--`
4×	`pow1` `clear-num` `frac-2neg` `flip3-+` `associate-*r/` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`prod-exp` `cbrt-unprod`

Counts

4 → 197

Calls

4 calls:

18.0ms	(/ (* y (- 1.0 x)) (+ y 1.0))
29.0ms	(/ (* y (- 1.0 x)) (+ y 1.0))
219.0ms	(/ (+ (* (/ (* y (- 1.0 x)) (+ y 1.0)) (+ 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))) (* 1.0 1.0)) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0))))
975.0ms	(/ (+ (* 1.0 1.0) (+ (* (* (/ y (+ 1.0 y)) (- 1.0 x)) (* (/ y (+ 1.0 y)) (- 1.0 x))) (* 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))))) (/ (+ (* (/ (* y (- 1.0 x)) (+ y 1.0)) (+ 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))) (* 1.0 1.0)) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (* y (- 1.0 x)) (+ y 1.0))
67.0ms	(/ (* y (- 1.0 x)) (+ y 1.0))
309.0ms	(/ (+ (* (/ (* y (- 1.0 x)) (+ y 1.0)) (+ 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))) (* 1.0 1.0)) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0))))
867.0ms	(/ (+ (* 1.0 1.0) (+ (* (* (/ y (+ 1.0 y)) (- 1.0 x)) (* (/ y (+ 1.0 y)) (- 1.0 x))) (* 1.0 (* (/ y (+ 1.0 y)) (- 1.0 x))))) (/ (+ (* (/ (* y (- 1.0 x)) (+ y 1.0)) (+ 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))) (* 1.0 1.0)) (- 1.0 (/ (* y (- 1.0 x)) (+ y 1.0)))))

simplify407.0ms

Counts

209 → 209

Iterations

Iter	Nodes
done	5000
1	946
0	321

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes299.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.8b

bsearch165.0ms

Steps

Iters	Range		Point
10	257785.57693934403	2.1403836343929554e+18	279165547.0253698
11	-496427297.3881253	-4.632829109756021e-12	-100161581.36651158

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

597.0ms	774×	body	640	valid
295.0ms	6044×	body	80	valid
154.0ms	569×	body	320	valid
104.0ms	306×	body	1280	valid
28.0ms	307×	body	160	valid