Details

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

prune1.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.0b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

16.0b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 31

Calls

1 calls:

5.0ms

(/ x (+ (* x x) 1.0))

series58.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(/ x (+ (* x x) 1.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	171	215
1	589	196
2	1979	191
3	5002	186

prune63.0ms

Filtered

34 candidates to 29 candidates (85.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	2	35

Merged error: 0b

Counts

35 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ 1 (fma x x 1.0))
14.7b	(* x (/ 1 (fma x x 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
15×	`add-exp-log`
13×	`associate-r`
9×	`add-cbrt-cube`
5×	`pow1`
4×	`div-exp` `prod-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `1-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 71

Calls

2 calls:

3.0ms	(/ 1 (fma x x 1.0))
10.0ms	(* x (/ 1 (fma x x 1.0)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ 1 (fma x x 1.0))
62.0ms	(* x (/ 1 (fma x x 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	278	377
1	1193	324
2	5001	294

prune88.0ms

Filtered

77 candidates to 48 candidates (62.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	2	79

Merged error: 0b

Counts

79 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
0.2b	(/ 1 (pow x 5))
0.3b	(/ 1 (pow x 3))
19.7b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

1934×	`times-frac`
1320×	`add-sqr-sqrt`
1236×	`*-un-lft-identity`
1171×	`add-cube-cbrt`
1000×	`prod-diff`
650×	`unpow-prod-down`
251×	`cube-prod`
238×	`sqr-pow`
79×	`cube-mult` `unpow3`
72×	`div-inv`
63×	`difference-of-squares`
25×	`fma-neg`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `fma-udef`

Counts

4 → 1250

Calls

4 calls:

1.0ms	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
67.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
41.0ms	(/ 1 (pow x 5))
35.0ms	(/ 1 (pow x 3))
94.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify286.0ms

Algorithm

egg-herbie

Counts

1262 → 1262

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2411	31677
1	5002	18173

prune404.0ms

Filtered

1262 candidates to 135 candidates (10.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	1262	0	1262
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	1262	2	1264

Merged error: 0b

Counts

1264 → 2

regimes21.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.9b

bsearch62.0ms

Steps

Iters	Range		Point
10	0.005370866090842012	4.21737757242384e+15	458.02780979250457
9	-6.681514996074174e+59	-1.5200911006536685e+53	-2.9357056044533087e+55

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	27	10

end0.0ms

sample255.0ms

Algorithm

intervals

Results

171.0ms

8000×

body

valid