Details

sample275.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
6.0ms	245×	body	80	nan

simplify11.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite28.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

3 calls:

0.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))
12.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
36.0ms	(/ (- 1.0 x) (+ 1.0 x))
106.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	370	779
1	1128	734
2	5001	719

prune225.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-prod`
74×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
56×	`times-frac`
38×	`add-cube-cbrt`
10×	`distribute-lft-out`
8×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
7×	`associate-/r*`
6×	`sqrt-div`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `flip--` `hypot-def` `div-inv`

Counts

3 → 118

Calls

3 calls:

4.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
4.0ms	(sqrt (+ 1.0 x))
12.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series123.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
30.0ms	(sqrt (+ 1.0 x))
91.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	357	1186
1	1106	1120
2	5001	1062

prune236.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample719.0ms

Algorithm

intervals

Results

310.0ms	8000×	body	80	valid
209.0ms	8243×	body	80	nan