Details

sample18.0ms

Algorithm

intervals

Results

4.0ms	197×	body	80	valid
2.0ms	24×	body	640	valid
1.0ms	17×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	11×	body	160	valid

simplify7.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (27.0ms)

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: 13.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
13.9b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite30.0ms

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:

28.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- x 1.0) (+ y 1.0))
65.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.5s

Counts

64 → 64

Iterations

Useful iterations: done (1.5s)

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

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
13.9b	(fma (* 1 (/ (- x 1.0) (+ y 1.0))) y 1.0)

rewrite25.0ms

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:

23.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (* 1 (/ (- x 1.0) (+ y 1.0))) y 1.0)

series96.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (- x 1.0) (+ y 1.0))
65.0ms	(fma (* 1 (/ (- x 1.0) (+ y 1.0))) y 1.0)

simplify1.4s

Counts

64 → 64

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	115	860
1	280	799
2	760	745
3	1989	739
done	5001	737

prune131.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ 1.0 y) (- x 1.0))
0.1b	(/ 1 (/ (+ 1.0 y) (- x 1.0)))
13.9b	(fma (* 1 (/ 1 (/ (+ 1.0 y) (- x 1.0)))) y 1.0)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
175×	`*-un-lft-identity`
123×	`add-sqr-sqrt`
81×	`add-cube-cbrt`
31×	`associate-/r*`
26×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
5×	`flip3--` `flip--`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `flip3-+` `flip-+` `fma-udef` `inv-pow`

Counts

3 → 187

Calls

3 calls:

24.0ms	(/ (+ 1.0 y) (- x 1.0))
24.0ms	(/ 1 (/ (+ 1.0 y) (- x 1.0)))
0.0ms	(fma (* 1 (/ 1 (/ (+ 1.0 y) (- x 1.0)))) y 1.0)

series108.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (+ 1.0 y) (- x 1.0))
28.0ms	(/ 1 (/ (+ 1.0 y) (- x 1.0)))
43.0ms	(fma (* 1 (/ 1 (/ (+ 1.0 y) (- x 1.0)))) y 1.0)

simplify2.1s

Counts

196 → 196

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	255	3303
1	567	2807
2	1361	2521
3	3685	2447
done	5000	2443

prune276.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (/ 1.0 y) (- 1 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
13×	`associate-l`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
3×	`pow1`
2×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `prod-exp` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `add-log-exp`

Counts

1 → 63

Calls

1 calls:

35.0ms

(* (/ 1.0 y) (- 1 x))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(* (/ 1.0 y) (- 1 x))

simplify3.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	148	1063
1	364	794
2	1029	684
3	4153	662
done	5000	662

prune91.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes79.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.8b

bsearch74.0ms

Steps

Iters	Range		Point
6	45518631.428277716	530980983.61658055	160471059.99581912
11	-2.8163082396285558e+17	-1.4864914298183363e-09	-163886191.99208534

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	19	38
1	28	28
done	28	28

end0.0ms

sample471.0ms

Algorithm

intervals

Results

141.0ms	6046×	body	80	valid
62.0ms	764×	body	640	valid
39.0ms	508×	body	320	valid
39.0ms	378×	body	1280	valid
13.0ms	304×	body	160	valid