Details

analyze85.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

sample16.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	80	valid
1.0ms	26×	body	80	overflowed

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	8
1	7	8

prune9.0ms (0.5%)

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: 1.3b

Counts

2 → 1

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
1.2b	(/ (exp a) (+ (exp a) (exp b)))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 45

Calls

2 calls:

7.0ms	(/ (exp a) (+ (exp a) (exp b)))
4.0ms	(+ (exp a) (exp b))

series17.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

12.0ms	(/ (exp a) (+ (exp a) (exp b)))
5.0ms	(+ (exp a) (exp b))

simplify63.0ms (3%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4961	546
1	4961	546

prune73.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Merged error: 0.9b

Counts

52 → 5

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(exp (- a (log (+ (exp a) (exp b)))))
0.0b	(+ (exp a) (exp b))
0.5b	(- a (log (+ (exp a) (exp b))))
3.9b	(log (+ (exp a) (exp b)))

rewrite24.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`log-prod`
7×	`pow1` `add-cube-cbrt`
6×	`log-div` `exp-prod`
5×	`add-exp-log`
4×	`flip3-+` `add-cbrt-cube` `flip-+` `associate--r+` `distribute-lft-out--` `associate--r-`
3×	`exp-sum` `log-pow` `distribute-lft-out`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `flip3--` `exp-diff` `rem-log-exp` `sum-log` `flip--`

Counts

4 → 66

Calls

4 calls:

7.0ms	(- a (log (+ (exp a) (exp b))))
6.0ms	(+ (exp a) (exp b))
5.0ms	(exp (- a (log (+ (exp a) (exp b)))))
4.0ms	(log (+ (exp a) (exp b)))

series34.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (- a (log (+ (exp a) (exp b)))))
9.0ms	(log (+ (exp a) (exp b)))
8.0ms	(- a (log (+ (exp a) (exp b))))
5.0ms	(+ (exp a) (exp b))

simplify62.0ms (3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4898	734
1	4898	734

prune106.0ms (5.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0.9b

Counts

83 → 5

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.0b	(pow (/ (exp a) (+ (exp a) (exp b))) 3)
0.3b	(cbrt (pow (/ (exp a) (+ (exp a) (exp b))) 3))
1.2b	(/ (exp a) (+ (exp a) (exp b)))

rewrite35.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity`
60×	`times-frac`
47×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`cbrt-prod`
36×	`unpow-prod-down` `cube-prod`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `div-inv`
4×	`associate-/r*`
3×	`pow-unpow` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `sum-log` `rem-cbrt-cube`

Counts

4 → 153

Calls

4 calls:

9.0ms	(pow (/ (exp a) (+ (exp a) (exp b))) 3)
8.0ms	(cbrt (pow (/ (exp a) (+ (exp a) (exp b))) 3))
7.0ms	(/ (exp a) (+ (exp a) (exp b)))
4.0ms	(+ (exp a) (exp b))

series49.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (/ (exp a) (+ (exp a) (exp b))) 3)
14.0ms	(cbrt (pow (/ (exp a) (+ (exp a) (exp b))) 3))
11.0ms	(/ (exp a) (+ (exp a) (exp b)))
5.0ms	(+ (exp a) (exp b))

simplify34.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5308	2178

prune236.0ms (11.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	165	5	170

Merged error: 0.9b

Counts

170 → 5

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp a) (exp b)))
0.0b	(sqrt (+ (exp a) (exp b)))
1.2b	(/ (/ (exp a) (sqrt (+ (exp a) (exp b)))) (sqrt (+ (exp a) (exp b))))
1.4b	(/ (exp a) (sqrt (+ (exp a) (exp b))))

rewrite57.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac`
306×	`*-un-lft-identity`
232×	`sqrt-prod`
192×	`add-sqr-sqrt`
190×	`add-cube-cbrt`
58×	`distribute-lft-out`
30×	`associate-/l*`
24×	`sqrt-div`
20×	`associate-/r/`
14×	`associate-/r*`
12×	`flip3-+` `flip-+`
11×	`add-cbrt-cube`
10×	`div-inv`
9×	`add-exp-log`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 317

Calls

4 calls:

18.0ms	(/ (/ (exp a) (sqrt (+ (exp a) (exp b)))) (sqrt (+ (exp a) (exp b))))
8.0ms	(/ (exp a) (sqrt (+ (exp a) (exp b))))
4.0ms	(sqrt (+ (exp a) (exp b)))
4.0ms	(sqrt (+ (exp a) (exp b)))

series58.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (exp a) (sqrt (+ (exp a) (exp b))))
14.0ms	(/ (/ (exp a) (sqrt (+ (exp a) (exp b)))) (sqrt (+ (exp a) (exp b))))
9.0ms	(sqrt (+ (exp a) (exp b)))
9.0ms	(sqrt (+ (exp a) (exp b)))

simplify97.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4966	6657
1	4966	6657

prune344.0ms (16.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	329	5	334

Merged error: 0.9b

Counts

334 → 5

regimes250.0ms (11.9%)

Accuracy

Total 0.1b remaining (27.2%)

Threshold costs 0.1b (27.2%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	9
1	19	9

end0.0ms (0%)

sample396.0ms (18.9%)

Algorithm

1×

intervals

Results

233.0ms	8000×	body	80	valid
16.0ms	682×	body	80	overflowed

Details

analyze85.0ms (4%)

sample16.0ms (0.8%)

simplify3.0ms (0.1%)

prune9.0ms (0.5%)

localize6.0ms (0.3%)

rewrite12.0ms (0.6%)

series17.0ms (0.8%)

simplify63.0ms (3%)

prune73.0ms (3.5%)

localize9.0ms (0.4%)

rewrite24.0ms (1.2%)

series34.0ms (1.6%)

simplify62.0ms (3%)

prune106.0ms (5.1%)

localize8.0ms (0.4%)

rewrite35.0ms (1.6%)

series49.0ms (2.3%)

simplify34.0ms (1.6%)

prune236.0ms (11.3%)

localize8.0ms (0.4%)

rewrite57.0ms (2.7%)

series58.0ms (2.8%)

simplify97.0ms (4.6%)

prune344.0ms (16.4%)

regimes250.0ms (11.9%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample396.0ms (18.9%)

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