Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
3.0ms	28×	body	640	valid
1.0ms	19×	body	320	valid
1.0ms	11×	body	1280	valid
0.0ms	6×	body	160	valid

simplify106.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
1.8b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

6.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ y (+ y 1.0))
70.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify129.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228

prune155.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ 1 (/ (+ y 1.0) y))
1.8b	(fma (/ 1 (/ (+ y 1.0) y)) (- x 1.0) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
93×	`*-un-lft-identity`
61×	`add-sqr-sqrt` `add-cube-cbrt`
19×	`associate-/r*`
16×	`add-exp-log` `distribute-lft-out`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`associate-/l*`
6×	`div-inv`
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-+` `associate-/r/` `flip-+` `fma-udef` `inv-pow`

Counts

3 → 135

Calls

3 calls:

8.0ms	(/ (+ y 1.0) y)
9.0ms	(/ 1 (/ (+ y 1.0) y))
0.0ms	(fma (/ 1 (/ (+ y 1.0) y)) (- x 1.0) 1.0)

series172.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (+ y 1.0) y)
39.0ms	(/ 1 (/ (+ y 1.0) y))
70.0ms	(fma (/ 1 (/ (+ y 1.0) y)) (- x 1.0) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	437	929
1	2015	813
2	5002	717

prune268.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ (- x 1.0) (/ (+ y 1.0) y))
1.8b	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

304×	`times-frac`
276×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
85×	`fma-def`
38×	`distribute-lft-out`
33×	`distribute-lft-out--` `difference-of-squares`
19×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `associate-/r/` `flip-+`
1×	`+-commutative` `associate-+l-` `flip3--` `sum-log` `flip--`

Counts

3 → 256

Calls

3 calls:

8.0ms	(/ (+ y 1.0) y)
18.0ms	(/ (- x 1.0) (/ (+ y 1.0) y))
84.0ms	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

series196.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (+ y 1.0) y)
51.0ms	(/ (- x 1.0) (/ (+ y 1.0) y))
84.0ms	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	702	1484
1	2723	1425
2	5001	1422

prune640.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
15.3b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite16.0ms

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:

13.0ms	(/ (- x 1.0) (+ y 1.0))
1.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series114.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (- x 1.0) (+ y 1.0))
80.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify128.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	276	398
1	840	371
2	4158	364
3	5001	364

prune162.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes70.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.0b

bsearch77.0ms

Steps

Iters	Range		Point
10	0.003064448021395057	556939279.5099251	132206673.37722518
4	-30253971797.634922	-15640006985.087824	-15892410532.141876

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	9
1	28	9
2	28	9

end0.0ms

sample456.0ms

Algorithm

intervals

Results

157.0ms	6156×	body	80	valid
67.0ms	709×	body	640	valid
44.0ms	371×	body	1280	valid
37.0ms	489×	body	320	valid
13.0ms	275×	body	160	valid