Details

sample52.0ms

Algorithm

intervals

Results

24.0ms	804×	body	80	nan
9.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	7
1	16	7
2	16	7

prune2.0ms

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: 0.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`frac-add`
10×	`sqrt-div`
9×	`frac-2neg` `clear-num`
8×	`associate-/l/`
5×	`flip3--` `flip--`
3×	`div-inv`
1×	`+-commutative` `distribute-rgt-out` `flip3-+` `pow1/2` `flip-+`

Counts

3 → 27

Calls

3 calls:

2.0ms	(sqrt (- 1.0 (* x x)))
5.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
3.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series317.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(sqrt (- 1.0 (* x x)))
119.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
134.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	410	451
1	1696	435
2	5001	431

prune116.0ms

Filtered

36 candidates to 34 candidates (94.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	1	37

Merged error: 0b

Counts

37 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(+ 1.0 (sqrt (- 1.0 (* x x))))
0.0b	(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
5×	`flip3-+` `flip-+`
3×	`+-commutative` `frac-2neg` `associate-*l/` `clear-num`
2×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`flip3--` `pow1/2` `associate-l` `*-commutative` `flip--` `div-inv`

Counts

3 → 23

Calls

3 calls:

2.0ms	(sqrt (- 1.0 (* x x)))
2.0ms	(+ 1.0 (sqrt (- 1.0 (* x x))))
5.0ms	(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

series221.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(sqrt (- 1.0 (* x x)))
56.0ms	(+ 1.0 (sqrt (- 1.0 (* x x))))
102.0ms	(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

simplify35.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	317	294
1	1230	280
2	5002	272

prune92.0ms

Filtered

32 candidates to 28 candidates (87.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	1	33

Merged error: 0b

Counts

33 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample1.4s

Algorithm

intervals

Results

710.0ms	23876×	body	80	nan
288.0ms	8000×	body	80	valid