Details

sample33.0ms

Algorithm

intervals

Results

9.0ms	188×	body	80	valid
5.0ms	27×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	10×	body	1280	valid
1.0ms	12×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	74	11
4	123	11
5	210	11
6	232	11
7	248	11
8	275	11
9	327	11
10	346	11
11	352	11
12	367	11
13	383	11
14	470	11
15	561	11
16	816	11
17	1118	11
18	1527	11
19	1608	11
done	1608	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.8b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.8b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite132.0ms

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:

37.0ms	(* (- 1.0 x) y)
47.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series238.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(* (- 1.0 x) y)
111.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
76.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	128	885
1	335	828
2	1274	746
done	5001	744

prune223.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite95.0ms

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:

20.0ms	(/ y (+ y 1.0))
62.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
6.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series247.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ y (+ y 1.0))
80.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
108.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.6s

Counts

97 → 97

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	157	1229
1	395	1148
2	1387	1056
done	5000	1054

prune243.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (/ 1.0 y))
0.3b	(- (+ x (/ 1.0 y)) (* 1.0 (/ x y)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
4×	`*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `diff-log` `associate-*r/` `sum-log` `frac-sub` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

11.0ms	(+ x (/ 1.0 y))
133.0ms	(- (+ x (/ 1.0 y)) (* 1.0 (/ x y)))

series93.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ x (/ 1.0 y))
57.0ms	(- (+ x (/ 1.0 y)) (* 1.0 (/ x y)))

simplify2.7s

Counts

34 → 34

Iterations

Useful iterations: 3 (819.0ms)

Iter	Nodes	Cost
0	64	508
1	181	476
2	638	436
3	2910	415
done	5000	415

prune99.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (* (+ (- x) 1) (/ 1.0 y)))) (cbrt (+ x (* (+ (- x) 1) (/ 1.0 y)))))
8.1b	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))
8.1b	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))
8.1b	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

56.0ms	(* (cbrt (+ x (* (+ (- x) 1) (/ 1.0 y)))) (cbrt (+ x (* (+ (- x) 1) (/ 1.0 y)))))
3.0ms	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))
3.0ms	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))
3.0ms	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

272.0ms	(* (cbrt (+ x (* (+ (- x) 1) (/ 1.0 y)))) (cbrt (+ x (* (+ (- x) 1) (/ 1.0 y)))))
190.0ms	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))
177.0ms	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))
167.0ms	(cbrt (+ x (* (+ (- x) 1) (/ 1.0 y))))

simplify2.7s

Counts

99 → 99

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	150	2829
1	359	2615
2	1057	2226
3	3457	1996
done	5001	1954

prune429.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes283.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.7b

bsearch91.0ms

Steps

Iters	Range		Point
9	20796729.49276672	3744461241692.0635	210063334.38182023
6	-60439154737701.01	-6045414056204.408	-6160286086042.848

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	19	41
1	26	31
done	26	31

end0.0ms

sample1.2s

Algorithm

intervals

Results

451.0ms	6059×	body	80	valid
180.0ms	724×	body	640	valid
122.0ms	554×	body	320	valid
86.0ms	362×	body	1280	valid
32.0ms	301×	body	160	valid