Details

sample41.0ms

Algorithm

intervals

Results

12.0ms	188×	body	80	valid
6.0ms	27×	body	640	valid
3.0ms	19×	body	320	valid
3.0ms	10×	body	1280	valid
1.0ms	12×	body	160	valid

simplify10.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (69.0ms)

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
15.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite40.0ms

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:

37.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series126.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (- x 1.0) (+ y 1.0))
89.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.3s

Counts

64 → 64

Iterations

Useful iterations: done (2.3s)

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

prune196.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ y 1.0))
0.0b	(/ x (+ y 1.0))
0.0b	(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
15.9b	(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

582×	`*-un-lft-identity`
484×	`times-frac`
332×	`add-sqr-sqrt`
324×	`prod-diff`
320×	`add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/r/`
41×	`flip3-+` `flip-+` `div-inv`
18×	`fma-neg`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `fma-udef` `sub-div`

Counts

4 → 452

Calls

4 calls:

12.0ms	(/ 1.0 (+ y 1.0))
14.0ms	(/ x (+ y 1.0))
145.0ms	(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
1.0ms	(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

series221.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (+ y 1.0))
58.0ms	(/ x (+ y 1.0))
38.0ms	(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
92.0ms	(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

simplify2.7s

Counts

464 → 464

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	471	20743
1	1054	18233
2	2393	13844
done	5000	10461

prune811.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ y 1.0))
0.1b	(* (/ 1 (+ y 1.0)) (- x 1.0))
0.1b	(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
4.5b	(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
32×	`add-exp-log`
26×	`times-frac`
20×	`add-cbrt-cube`
19×	`associate-l`
18×	`prod-diff`
13×	`prod-exp`
12×	`pow1`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-r`
7×	`associate-*l/` `cbrt-unprod` `distribute-lft-out`
6×	`div-exp` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-r/` `pow-prod-down` `associate-/r` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `flip-+` `associate-/l*` `unswap-sqr`
2×	`sub-neg` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 152

Calls

4 calls:

26.0ms	(/ 1 (+ y 1.0))
54.0ms	(* (/ 1 (+ y 1.0)) (- x 1.0))
112.0ms	(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
86.0ms	(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

series278.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (+ y 1.0))
45.0ms	(* (/ 1 (+ y 1.0)) (- x 1.0))
72.0ms	(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
133.0ms	(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

simplify2.5s

Counts

164 → 164

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	260	2533
1	648	2014
2	1895	1686
done	5000	1644

prune390.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1.0 (- (/ 1 y) (/ x y)) x)
0.3b	(- (/ 1 y) (/ x y))

rewrite87.0ms

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:

0.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
63.0ms	(- (/ 1 y) (/ x y))

series86.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
37.0ms	(- (/ 1 y) (/ x y))

simplify3.5s

Counts

228 → 228

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	315	8117
1	688	6842
2	1328	4644
3	4184	3416
done	5000	3416

prune229.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

Details

sample41.0ms

simplify10.6s

prune6.0ms

localize7.0ms

rewrite40.0ms

series126.0ms

simplify2.3s

prune196.0ms

localize17.0ms

rewrite217.0ms

series221.0ms

simplify2.7s

prune811.0ms

localize24.0ms

rewrite292.0ms

series278.0ms

simplify2.5s

prune390.0ms

localize16.0ms

rewrite87.0ms

series86.0ms

simplify3.5s

prune229.0ms

regimes141.0ms

bsearch2.0ms