Details

sample272.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	273×	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

prune4.0ms

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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 104

Calls

3 calls:

9.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series148.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
54.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify39.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	376	833
1	1103	797
2	5001	775

prune251.0ms

Filtered

113 candidates to 79 candidates (69.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 0b

Counts

114 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
60×	`add-sqr-sqrt`
56×	`times-frac`
40×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`associate-/r*`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 128

Calls

4 calls:

3.0ms	(sqrt (- 1.0 x))
3.0ms	(sqrt (+ 1.0 x))
1.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (- 1.0 x))
29.0ms	(sqrt (+ 1.0 x))
2.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
87.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	355	1269
1	1086	1195
2	5001	1132

prune300.0ms

Filtered

140 candidates to 80 candidates (57.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	141	1	142

Merged error: 0b

Counts

142 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (fabs (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))))
0.0b	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
0.0b	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
0.0b	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

210×	`sqrt-prod`
195×	`*-un-lft-identity`
168×	`times-frac`
145×	`add-sqr-sqrt`
124×	`exp-prod`
101×	`add-cube-cbrt`
63×	`log-pow`
25×	`distribute-lft-out`
22×	`distribute-lft-out--` `difference-of-squares`
8×	`sqrt-div` `associate-/l*`
7×	`add-exp-log` `associate-/r*`
6×	`associate-/r/` `add-cbrt-cube`
5×	`pow1` `add-log-exp`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`rem-log-exp` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 240

Calls

4 calls:

1.0ms	(atan (fabs (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))))
17.0ms	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
17.0ms	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (fabs (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))))
175.0ms	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
84.0ms	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
90.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	485	2318
1	1417	2187
2	5001	2006

prune553.0ms

Filtered

252 candidates to 122 candidates (48.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	252	1	253

Merged error: 0b

Counts

253 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample703.0ms

Algorithm

intervals

Results

321.0ms	8000×	body	80	valid
198.0ms	7716×	body	80	nan