Details

sample282.0ms

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))

rewrite25.0ms

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:

8.0ms	(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))

series160.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms	(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
56.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune251.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Merged error: 0b

Counts

107 → 2

localize11.0ms

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)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

85×	`sqrt-prod`
78×	`*-un-lft-identity`
62×	`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×	`expm1-log1p-u` `log1p-expm1-u` `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` `hypot-def` `div-inv`

Counts

4 → 137

Calls

4 calls:

5.0ms	(sqrt (- 1.0 x))
4.0ms	(sqrt (+ 1.0 x))
1.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
11.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (- 1.0 x))
35.0ms	(sqrt (+ 1.0 x))
2.0ms	(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
96.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify45.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	374	1306
1	1146	1231
2	5002	1169

prune344.0ms

Filtered

149 candidates to 89 candidates (59.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	1	151

Merged error: 0b

Counts

151 → 1

localize15.0ms

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)))

rewrite63.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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 → 247

Calls

4 calls:

1.0ms	(atan (fabs (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))))
18.0ms	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
17.0ms	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
11.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan (fabs (log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))))
189.0ms	(exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
94.0ms	(log (exp (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
97.0ms	(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	503	2365
1	1478	2236
2	5001	2059

prune569.0ms

Filtered

259 candidates to 130 candidates (50.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	259	1	260

Merged error: 0b

Counts

260 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample691.0ms

Algorithm

intervals

Results

308.0ms	8000×	body	80	valid
191.0ms	7716×	body	80	nan