Details

sample43.0ms

Algorithm

intervals

Results

13.0ms	198×	body	80	valid
5.0ms	22×	body	640	valid
4.0ms	20×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify12.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (77.0ms)

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
13.7b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite34.0ms

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:

31.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series152.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- x 1.0) (+ y 1.0))
96.0ms	(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

prune264.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y y) (* 1.0 1.0))
4.1b	(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
9.7b	(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
13.7b	(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
41×	`times-frac`
38×	`add-cube-cbrt`
26×	`associate-l`
22×	`difference-of-squares`
19×	`prod-diff`
11×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
10×	`distribute-lft-out--`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r` `associate-/l*`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `fma-neg` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `fma-udef`

Counts

4 → 150

Calls

4 calls:

9.0ms	(- (* y y) (* 1.0 1.0))
45.0ms	(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
147.0ms	(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
1.0ms	(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

series492.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (* y y) (* 1.0 1.0))
110.0ms	(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
118.0ms	(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
169.0ms	(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

simplify2.7s

Counts

162 → 162

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	266	3414
1	682	3177
2	2236	2886
done	5001	2450

prune554.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite64.0ms

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)
46.0ms	(- (/ 1 y) (/ x y))

series88.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma 1.0 (- (/ 1 y) (/ x y)) x)
31.0ms	(- (/ 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

prune247.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (pow (/ 1 (cbrt y)) 3) (/ x y))
0.3b	(/ 1 (cbrt y))
0.5b	(cbrt y)
0.7b	(pow (/ 1 (cbrt y)) 3)

rewrite406.0ms

Algorithm

rewrite-expression-head

Rules

1036×	`times-frac`
841×	`add-sqr-sqrt`
785×	`*-un-lft-identity`
775×	`add-cube-cbrt`
650×	`prod-diff`
340×	`unpow-prod-down` `cube-prod`
293×	`cbrt-prod`
81×	`div-inv`
50×	`fma-neg`
24×	`difference-of-squares`
17×	`sqr-pow`
15×	`cube-mult` `unpow3`
13×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
6×	`associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `pow-flip` `pow-pow` `div-exp` `pow-exp` `log1p-expm1-u`
3×	`pow-unpow` `pow1/3` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `rec-exp` `1-exp` `inv-pow` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 870

Calls

4 calls:

220.0ms	(- (pow (/ 1 (cbrt y)) 3) (/ x y))
14.0ms	(/ 1 (cbrt y))
2.0ms	(cbrt y)
17.0ms	(pow (/ 1 (cbrt y)) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (pow (/ 1 (cbrt y)) 3) (/ x y))
329.0ms	(/ 1 (cbrt y))
309.0ms	(cbrt y)
421.0ms	(pow (/ 1 (cbrt y)) 3)

simplify3.4s

Counts

882 → 882

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	620	35379
1	1432	27597
2	2627	13946
done	5002	12076

prune659.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes191.0ms

Accuracy

100% (0.0b remaining)

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

bsearch147.0ms

Steps

Iters	Range		Point
9	9556.682540875734	15966983906.555069	115806119.11227304
10	-9.405557600769291e+21	-1501.2167507114543	-197475236.47678238

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	38
1	24	29
done	24	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

342.0ms	6091×	body	80	valid
242.0ms	754×	body	640	valid
162.0ms	354×	body	1280	valid
116.0ms	505×	body	320	valid
80.0ms	296×	body	160	valid