Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

sample19.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
0.0ms	1×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	10	13

prune3.0ms

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

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`div-inv` `difference-of-squares`
4×	`sqrt-div`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 98

Calls

4 calls:

2.0ms	(sqrt (- 1.0 (* x x)))
18.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
22.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
5.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* x x)))
12.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
7.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify31.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5030	1641

prune181.0ms

Filtered

89 candidates to 110 candidates (-23.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	1	111

Merged error: 0b

Counts

111 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (- 1.0 (* x x))))
0.0b	(log (* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x))))))
0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-cube-cbrt` `associate-l`
11×	`times-frac`
10×	`pow1`
9×	`add-cbrt-cube`
8×	`prod-exp`
6×	`add-log-exp`
5×	`log-div` `flip3-+` `rem-log-exp` `flip-+`
4×	`frac-times` `associate-r/` `div-exp` `associate-r*` `sqrt-prod`
3×	`unswap-sqr`
2×	`rec-exp` `sqrt-div` `1-exp` `pow-prod-down` `associate-*l/` `log-pow` `cbrt-unprod` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `rem-sqrt-square` `log-prod` `flip3--` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log` `*-commutative` `flip--` `div-inv` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

5.0ms	(+ 1.0 (sqrt (- 1.0 (* x x))))
8.0ms	(log (* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x))))))
3.0ms	(sqrt (- 1.0 (* x x)))
10.0ms	(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (- 1.0 (* x x))))
11.0ms	(log (* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x))))))
4.0ms	(sqrt (- 1.0 (* x x)))
5.0ms	(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5202	1316

prune160.0ms

Filtered

81 candidates to 102 candidates (-25.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	1	103

Merged error: 0b

Counts

103 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	13
1	13	13

end0.0ms

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

sample505.0ms

Algorithm

intervals

Results

417.0ms	8000×	body	80	valid
0.0ms	5×	body	80	nan

Details

analyze5.0ms

sample19.0ms

simplify3.0ms

prune3.0ms

localize9.0ms

rewrite52.0ms

series30.0ms

simplify31.0ms

prune181.0ms

localize10.0ms

rewrite30.0ms

series24.0ms

simplify43.0ms

prune160.0ms

simplify1.0ms

end0.0ms

analyze5.0ms

sample505.0ms

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