Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	191×	body	80	valid
4.0ms	25×	body	640	valid
2.0ms	12×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	14×	body	160	valid

simplify10.5s

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	76	11
4	131	10
5	242	10
6	309	10
7	374	10
8	424	10
9	513	10
10	582	10
11	591	10
12	610	10
13	648	10
14	777	10
15	915	10
16	1233	10
17	1689	10
18	2270	10
19	2436	10
20	2442	10
done	2442	10

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
15.2b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

2 → 58

Calls

2 calls:

50.0ms	(/ (- x 1.0) (+ y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series130.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (- x 1.0) (+ y 1.0))
99.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.2s

Counts

64 → 64

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	114	834
1	277	799
2	718	745
3	1747	739
done	5000	737

prune187.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
3.2b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.3b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `prod-diff`
24×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
5×	`pow1` `associate-l` `distribute-lft-out` `add-log-exp`
4×	`flip3-+` `associate-l/` `associate-/r` `flip-+` `div-inv`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `flip--` `log1p-expm1-u`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `unswap-sqr`

Counts

3 → 102

Calls

3 calls:

50.0ms	(* (- 1.0 x) y)
46.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
27.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series199.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* (- 1.0 x) y)
110.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
56.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.6s

Counts

111 → 111

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	202	2757
1	528	2323
2	1965	1851
done	5000	1619

prune259.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
35×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
13×	`associate-l`
10×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-r`
4×	`pow1` `sub-neg` `add-log-exp`
3×	`fma-def`
2×	`expm1-log1p-u` `frac-times` `flip3--` `associate-*r/` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out--`

Counts

2 → 101

Calls

2 calls:

13.0ms	(+ x (* (/ 1.0 y) (- 1 x)))
62.0ms	(* (/ 1.0 y) (- 1 x))

series126.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(+ x (* (/ 1.0 y) (- 1 x)))
70.0ms	(* (/ 1.0 y) (- 1 x))

simplify1.8s

Counts

107 → 107

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	189	1649
1	457	1210
2	1293	1033
done	5000	1029

prune255.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

15.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series1.2s

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (cbrt y) (cbrt y))
294.0ms	(cbrt y)
271.0ms	(cbrt y)
271.0ms	(cbrt y)

simplify5.6s

Counts

93 → 93

Iterations

Useful iterations: done (5.6s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune386.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes208.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch128.0ms

Steps

Iters	Range		Point
9	6884452.324493753	1848124645084217.8	191468540.1676344
9	-186345010136707.7	-3592450.023809973	-319655046.4933925

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	36
1	26	28
done	26	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

407.0ms	6103×	body	80	valid
168.0ms	704×	body	640	valid
116.0ms	528×	body	320	valid
112.0ms	369×	body	1280	valid
28.0ms	296×	body	160	valid