Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	188×	body	80	valid
6.0ms	27×	body	640	valid
4.0ms	19×	body	320	valid
3.0ms	10×	body	1280	valid
1.0ms	12×	body	160	valid

simplify11.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (52.0ms)

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: 15.6b

localize23.0ms

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)

rewrite28.0ms

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:

26.0ms	(/ (- x 1.0) (+ y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series189.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- x 1.0) (+ y 1.0))
130.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.5s

Counts

64 → 64

Iterations

Useful iterations: done (2.5s)

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

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)

rewrite238.0ms

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:

16.0ms	(/ 1.0 (+ y 1.0))
13.0ms	(/ x (+ y 1.0))
148.0ms	(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
0.0ms	(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1.0 (+ y 1.0))
56.0ms	(/ x (+ y 1.0))
44.0ms	(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
111.0ms	(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

simplify2.6s

Counts

464 → 464

Iterations

Useful iterations: done (2.5s)

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

prune867.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

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)

rewrite258.0ms

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:

14.0ms	(/ 1 (+ y 1.0))
66.0ms	(* (/ 1 (+ y 1.0)) (- x 1.0))
99.0ms	(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
69.0ms	(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

series239.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (+ y 1.0))
31.0ms	(* (/ 1 (+ y 1.0)) (- x 1.0))
53.0ms	(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
128.0ms	(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

simplify1.8s

Counts

164 → 164

Iterations

Useful iterations: done (1.8s)

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

prune474.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite98.0ms

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:

1.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
72.0ms	(- (/ 1 y) (/ x y))

series83.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
39.0ms	(- (/ 1 y) (/ x y))

simplify3.3s

Counts

228 → 228

Iterations

Useful iterations: 3 (1.7s)

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

prune235.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes131.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.7b

bsearch92.0ms

Steps

Iters	Range		Point
9	20796729.49276672	3744461241692.0635	150550976.72319537
6	-433630756157860.06	-60439154737701.01	-61215075097455.13

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	19	42
1	25	33
done	25	33

end0.0ms

sample1.6s

Algorithm

intervals

Results

932.0ms	6059×	body	80	valid
122.0ms	724×	body	640	valid
119.0ms	554×	body	320	valid
79.0ms	362×	body	1280	valid
60.0ms	301×	body	160	valid