Details

sample66.0ms

Algorithm

intervals

Results

20.0ms	182×	body	80	valid
18.0ms	32×	body	640	valid
9.0ms	27×	body	320	valid
4.0ms	7×	body	1280	valid
2.0ms	8×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
13	4169
12	3568
11	3113
10	2621
9	2078
8	1683
7	1107
6	562
5	259
4	129
3	73
2	33
1	16
0	8

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.8b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ 1.0 y))
18.2b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

rewrite19.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `flip3--` `div-sub` `div-exp` `flip-+` `fma-udef` `div-inv` `flip--`

Counts

2 → 60

Calls

2 calls:

17.0ms	(/ (- x 1.0) (+ 1.0 y))
0.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

series158.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- x 1.0) (+ 1.0 y))
112.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

simplify2.7s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3563
2	882
1	284
0	116

prune305.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (/ (- x 1.0) (+ 1.0 y)) y 1.0))
18.2b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
18.2b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
18.2b	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 47

Calls

4 calls:

2.0ms	(cbrt (fma (/ (- x 1.0) (+ 1.0 y)) y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
1.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
1.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

series685.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(cbrt (fma (/ (- x 1.0) (+ 1.0 y)) y 1.0))
126.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
103.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)
112.0ms	(fma (/ (- x 1.0) (+ 1.0 y)) y 1.0)

simplify2.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
3	1681
2	514
1	182
0	78

prune378.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.9b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.5b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
30×	`add-sqr-sqrt` `prod-diff`
24×	`add-cube-cbrt`
16×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`associate-/r/`
5×	`pow1` `associate-l` `distribute-lft-out` `add-log-exp`
4×	`associate-/r` `flip3-+` `associate-l/` `flip-+` `div-inv`
3×	`expm1-log1p-u` `flip3--` `fma-neg` `associate-r` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `-commutative` `associate-/l` `unswap-sqr`

Counts

3 → 105

Calls

3 calls:

15.0ms	(* (- 1.0 x) y)
15.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
19.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series195.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(* (- 1.0 x) y)
87.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
61.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.3s

Counts

114 → 114

Iterations

Iter	Nodes
done	5003
2	1821
1	554
0	205

prune442.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

257×	`times-frac`
209×	`add-sqr-sqrt`
206×	`*-un-lft-identity`
192×	`add-cube-cbrt`
169×	`prod-diff`
32×	`div-inv`
13×	`fma-neg`
6×	`difference-of-squares`
5×	`distribute-lft-out--`
3×	`distribute-rgt-out--` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u` `flip--` `sub-div`

Counts

1 → 213

Calls

1 calls:

31.0ms

(- (/ 1 y) (/ x y))

series42.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(- (/ 1 y) (/ x y))

simplify2.8s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
3	3732
2	1464
1	681
0	300

prune257.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.1b

regimes273.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.6b

bsearch93.0ms

Steps

Iters	Range		Point
7	3450257.8595304484	695318447.7085649	221673187.8082131
8	-2960407307.968478	-8916862.296519369	-148588481.45705655

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

602.0ms	6072×	body	80	valid
267.0ms	722×	body	640	valid
181.0ms	391×	body	1280	valid
115.0ms	510×	body	320	valid
46.0ms	305×	body	160	valid