Details

analyze4.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample12.0ms (1.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

simplify29.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	523	11
1	523	11

prune4.0ms (0.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.0b

Counts

2 → 1

localize10.0ms (1%)

Local error

Found 3 expressions with local error:

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

rewrite37.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`times-frac`
30×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `distribute-lft-out--`
5×	`add-log-exp`
4×	`associate-/r/` `difference-of-squares`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `flip3--` `frac-add` `sum-log` `flip--`

Counts

3 → 87

Calls

3 calls:

24.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ x (+ x 1.0))

series11.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))
3.0ms	(/ x (+ x 1.0))
2.0ms	(/ 1.0 (- x 1.0))

simplify51.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5315	995

prune137.0ms (14.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	1	97

Merged error: 0b

Counts

97 → 1

localize10.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.0b	(log (exp (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))))
0.0b	(/ x (+ 1.0 x))
0.0b	(+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))
0.0b	(exp (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))))

rewrite85.0ms (8.9%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`*-un-lft-identity`
36×	`times-frac`
25×	`distribute-lft-out`
16×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod`
9×	`log-pow` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
5×	`pow1`
4×	`log-prod` `associate-/r*`
3×	`associate-/l*`
2×	`flip3-+` `exp-sum` `sum-log` `associate-/r/` `flip-+` `rem-exp-log`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `rem-log-exp` `frac-add` `clear-num` `div-inv`

Counts

4 → 89

Calls

4 calls:

26.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))
25.0ms	(log (exp (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))))
25.0ms	(exp (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))))
5.0ms	(/ x (+ 1.0 x))

series28.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))))
6.0ms	(log (exp (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))))
6.0ms	(+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x)))
5.0ms	(/ x (+ 1.0 x))

simplify49.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5282	1097

prune173.0ms (18%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	1	102

Merged error: 0b

Counts

102 → 1

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms (0%)

sample317.0ms (33.2%)

Algorithm

1×

intervals

Results

225.0ms

8000×

body

valid

Details

analyze4.0ms (0.4%)

sample12.0ms (1.3%)

simplify29.0ms (3%)

prune4.0ms (0.4%)

localize10.0ms (1%)

rewrite37.0ms (3.9%)

series11.0ms (1.1%)

simplify51.0ms (5.3%)

prune137.0ms (14.3%)

localize10.0ms (1.1%)

rewrite85.0ms (8.9%)

series28.0ms (2.9%)

simplify49.0ms (5.2%)

prune173.0ms (18%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample317.0ms (33.2%)

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