Details

sample287.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	264×	body	80	nan

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	6
1	19	6
2	21	6
3	21	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
24×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `associate-/r*` `associate-/r/`
3×	`add-log-exp`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

3 → 91

Calls

3 calls:

1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
30.0ms	(/ (- 1.0 x) (+ 1.0 x))
18.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series131.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
30.0ms	(/ (- 1.0 x) (+ 1.0 x))
97.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	354	753
1	1071	709
2	5001	690

prune285.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
56×	`times-frac`
52×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
17×	`sqrt-prod`
16×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`associate-/r/`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `difference-of-squares`
6×	`distribute-rgt-out--` `flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 125

Calls

4 calls:

88.0ms	(sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))))
12.0ms	(/ x (+ x 1.0))
10.0ms	(/ 1.0 (+ x 1.0))
72.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0))))
31.0ms	(/ x (+ x 1.0))
23.0ms	(/ 1.0 (+ x 1.0))
55.0ms	(- (/ 1.0 (+ x 1.0)) (/ x (+ x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	461	975
1	1562	939
2	5001	916

prune456.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
88×	`times-frac`
72×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
26×	`distribute-lft-out`
24×	`swap-sqr`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`sqrt-div`
12×	`pow1` `associate-/r/`
11×	`associate-r/` `associate-l/`
9×	`frac-times` `frac-sub`
8×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `associate-/l*`
5×	`sub-div`
4×	`prod-exp` `sqrt-prod` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow2` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `difference-of-squares`

Counts

4 → 184

Calls

4 calls:

10.0ms	(/ 1.0 (+ x 1.0))
13.0ms	(/ 1.0 (+ x 1.0))
33.0ms	(sqrt (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
52.0ms	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1.0 (+ x 1.0))
23.0ms	(/ 1.0 (+ x 1.0))
120.0ms	(sqrt (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
32.0ms	(* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	767	1601
1	3640	1482
2	5001	1451

prune1.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	18	21

end0.0ms

sample727.0ms

Algorithm

intervals

Results

322.0ms	8000×	body	80	valid
216.0ms	7993×	body	80	nan