Details

sample278.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
8.0ms	273×	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

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))

rewrite23.0ms

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:

7.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms	(/ (- 1.0 x) (+ 1.0 x))

series153.0ms

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))))
58.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

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

prune220.0ms

Filtered

100 candidates to 70 candidates (70.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 x))
0.0b	(sqrt (+ 1.0 x))
0.0b	(atan (/ (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))
3.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (- 1.0 x))
29.0ms	(sqrt (+ 1.0 x))
2.0ms	(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
89.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	353	1256
1	1084	1184
2	5001	1121

prune268.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan (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)))

rewrite54.0ms

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×	`associate-/r*`
6×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
5×	`pow1` `add-log-exp`
3×	`log-prod` `flip3-+` `flip-+` `div-inv`
2×	`associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 239

Calls

4 calls:

1.0ms	(atan (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
13.0ms	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
16.0ms	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
10.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
176.0ms	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
86.0ms	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
92.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	483	2305
1	1415	2176
2	5002	1995

prune471.0ms

Filtered

251 candidates to 122 candidates (48.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	251	1	252

Merged error: 0b

Counts

252 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample660.0ms

Algorithm

intervals

Results

301.0ms	8000×	body	80	valid
181.0ms	7716×	body	80	nan