Details

sample286.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
6.0ms	234×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
41×	`times-frac`
26×	`sqrt-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/l*`
4×	`add-exp-log` `associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1`
2×	`expm1-log1p-u` `rem-sqrt-square` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num` `flip--`

Counts

2 → 88

Calls

2 calls:

8.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms	(/ (- 1.0 x) (+ 1.0 x))

series154.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(sqrt (/ (- 1.0 x) (+ 1.0 x)))
57.0ms	(/ (- 1.0 x) (+ 1.0 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	353	692
1	1094	658
2	5001	643

prune162.0ms

Filtered

94 candidates to 65 candidates (69.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	1	95

Merged error: 0b

Counts

95 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))
0.0b	(sqrt (log1p (expm1 (/ (- 1.0 x) (+ 1.0 x)))))
0.0b	(/ (- 1.0 x) (+ 1.0 x))
1.0b	(expm1 (/ (- 1.0 x) (+ 1.0 x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
20×	`times-frac`
16×	`add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1` `log1p-expm1-u` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `add-log-exp`
3×	`sqrt-prod`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `log1p-expm1` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `expm1-udef`

Counts

4 → 85

Calls

4 calls:

1.0ms	(log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))
1.0ms	(sqrt (log1p (expm1 (/ (- 1.0 x) (+ 1.0 x)))))
9.0ms	(/ (- 1.0 x) (+ 1.0 x))
1.0ms	(expm1 (/ (- 1.0 x) (+ 1.0 x)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(log1p (expm1 (/ (- 1.0 x) (+ 1.0 x))))
224.0ms	(sqrt (log1p (expm1 (/ (- 1.0 x) (+ 1.0 x)))))
33.0ms	(/ (- 1.0 x) (+ 1.0 x))
107.0ms	(expm1 (/ (- 1.0 x) (+ 1.0 x)))

simplify40.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	389	639
1	1223	599
2	5002	584

prune202.0ms

Filtered

97 candidates to 73 candidates (75.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	1	98

Merged error: 0b

Counts

98 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	13	8

end0.0ms

sample685.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
190.0ms	7952×	body	80	nan