Details

sample46.0ms

Algorithm

intervals

Results

11.0ms	182×	body	80	valid
6.0ms	26×	body	640	valid
4.0ms	27×	body	320	valid
3.0ms	12×	body	1280	valid
1.0ms	9×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (78.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	76	11
4	161	10
5	466	10
6	1868	10
done	5000	10

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.1b

localize18.0ms

Local error

Found 1 expressions with local error:

17.4b

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

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

series113.0ms

Counts

1 → 3

Calls

1 calls:

113.0ms

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

simplify1.2s

Counts

13 → 13

Iterations

Useful iterations: 3 (234.0ms)

Iter	Nodes	Cost
0	29	178
1	63	177
2	180	153
3	761	149
done	5000	149

prune103.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.8b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 78

Calls

2 calls:

42.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series198.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
80.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.9s

Counts

84 → 84

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	176	2554
1	499	2140
2	2808	1698
done	5000	1653

prune438.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(/ y (+ y 1.0))
2.2b	(fma (/ y (+ y 1.0)) (- (- 1.0 x)) (pow (cbrt 1.0) 3))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`associate-/r*` `distribute-lft-out`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`associate-/r/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`fma-udef`

Counts

3 → 80

Calls

3 calls:

23.0ms	(/ y (+ y 1.0))
30.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- (- 1.0 x)) (pow (cbrt 1.0) 3))

series225.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ y (+ y 1.0))
67.0ms	(/ y (+ y 1.0))
100.0ms	(fma (/ y (+ y 1.0)) (- (- 1.0 x)) (pow (cbrt 1.0) 3))

simplify1.1s

Counts

89 → 89

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	97	987
1	227	904
2	950	832
done	5001	826

prune768.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ 1 y) (/ x y))
0.0b	(fma 1.0 (- (/ 1 y) (/ x y)) x)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

257×	`times-frac`
210×	`add-sqr-sqrt`
207×	`*-un-lft-identity`
193×	`add-cube-cbrt`
169×	`prod-diff`
32×	`div-inv`
13×	`fma-neg`
6×	`difference-of-squares`
5×	`distribute-lft-out--`
4×	`add-log-exp`
3×	`distribute-rgt-out--`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `fma-udef` `sub-div`

Counts

2 → 222

Calls

2 calls:

73.0ms	(- (/ 1 y) (/ x y))
1.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)

series94.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (/ 1 y) (/ x y))
55.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)

simplify2.8s

Counts

228 → 228

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	315	8117
1	712	6868
2	2382	4946
done	5000	3484

prune404.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

regimes350.0ms

Accuracy

100% (0.0b remaining)

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

bsearch203.0ms

Steps

Iters	Range		Point
10	0.013914501587729765	1368294241.5238848	150372736.82230544
10	-1.5312203001569835e+19	-3934.6710789005906	-131050117.71074806

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	57
1	34	48
done	34	48

end0.0ms

sample1.4s

Algorithm

intervals

Results

486.0ms	6084×	body	80	valid
201.0ms	353×	body	1280	valid
166.0ms	738×	body	640	valid
91.0ms	526×	body	320	valid
34.0ms	299×	body	160	valid