Details

sample47.0ms

Algorithm

intervals

Results

21.0ms	206×	body	80	valid
5.0ms	24×	body	640	valid
3.0ms	14×	body	320	valid
3.0ms	9×	body	1280	valid
0.0ms	3×	body	160	valid

simplify4.8s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.9b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.2b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite73.0ms

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:

24.0ms	(* (- 1.0 x) y)
24.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
23.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series181.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- 1.0 x) y)
85.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
60.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: done (1.8s)

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

prune186.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
0.9b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite107.0ms

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:

12.0ms	(/ y (+ y 1.0))
83.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
10.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series167.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ y (+ y 1.0))
48.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
80.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.4s

Counts

97 → 97

Iterations

Useful iterations: done (1.4s)

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

prune248.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
0.9b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.9b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
0.9b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
11×	`pow1`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 84

Calls

4 calls:

60.0ms	(* (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
17.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
11.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
7.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series916.0ms

Counts

4 → 12

Calls

4 calls:

672.0ms	(* (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))) (cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))
72.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
76.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
95.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	125	2622
1	284	2412
2	804	2227
3	2533	1989
done	5000	1975

prune395.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

9.2b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.2b	(/ (* (- 1.0 x) y) (+ y 1.0))
9.2b	(/ (* (- 1.0 x) y) (+ y 1.0))
11.1b	(/ (- (* 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))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/r*`
11×	`distribute-lft-out`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`associate-*l/`
5×	`difference-of-squares`
4×	`pow1` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 122

Calls

4 calls:

31.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
33.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
29.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
74.0ms	(/ (- (* 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))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
57.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
48.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
547.0ms	(/ (- (* 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))))

simplify1.1s

Counts

134 → 134

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	153	3329
1	429	3135
2	1602	2867
done	5000	2581

prune448.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes126.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.8b

bsearch119.0ms

Steps

Iters	Range		Point
9	3495.1882749471233	4103444128.4880795	261047506.9367963
10	-2497197479928642.5	-1608.0958488538781	-147449421.01903394

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

390.0ms	6039×	body	80	valid
208.0ms	709×	body	640	valid
113.0ms	567×	body	320	valid
97.0ms	383×	body	1280	valid
28.0ms	302×	body	160	valid