Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	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

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms	49×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	129×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

prune7.0ms (0.1%)

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: 29.7b

Counts

2 → 1

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.6b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 103

Calls

3 calls:

29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
8.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))

series13.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.0ms	(/ (+ x 1.0) (- x 1.0))
3.0ms	(/ x (+ x 1.0))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune223.0ms (3.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.3b

Counts

113 → 5

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(pow (/ x (+ x 1.0)) 3)
2.5b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite157.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 302

Calls

4 calls:

101.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
10.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms	(pow (/ x (+ x 1.0)) 3)

series24.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
3.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.0ms	(pow (/ x (+ x 1.0)) 3)
3.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5059	5149

prune1.5s (26.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	313	6	319

Merged error: 0.1b

Counts

319 → 6

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
2.5b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite113.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`*-un-lft-identity`
91×	`add-sqr-sqrt`
88×	`times-frac`
60×	`unpow-prod-down` `cube-prod`
53×	`distribute-lft-out--`
36×	`difference-of-squares`
32×	`distribute-lft-out`
12×	`sqr-pow`
9×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`cube-div`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 119

Calls

4 calls:

99.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series83.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt x)
22.0ms	(cbrt x)
22.0ms	(cbrt x)
14.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5130	2578

prune704.0ms (11.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	131	6	137

Merged error: 0.1b

Counts

137 → 6

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
2.5b	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
2.5b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite233.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

380×	`*-un-lft-identity`
176×	`add-sqr-sqrt` `times-frac`
120×	`unpow-prod-down` `cube-prod`
106×	`distribute-lft-out--`
78×	`log-pow`
77×	`exp-prod`
72×	`difference-of-squares`
64×	`distribute-lft-out`
24×	`sqr-pow`
8×	`add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `log-prod` `add-cbrt-cube`
2×	`difference-cubes` `cube-div` `sub-neg` `pow1/3`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `exp-sum` `frac-sub` `flip--`

Counts

4 → 199

Calls

4 calls:

109.0ms	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
103.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series78.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt x)
22.0ms	(cbrt x)
15.0ms	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
15.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5396	3678

prune1.5s (25.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	211	6	217

Merged error: 0.1b

Counts

217 → 6

regimes52.0ms (0.9%)

Accuracy

Total 0.2b remaining (70.7%)

Threshold costs 0.2b (70.7%)

bsearch25.0ms (0.4%)

Steps

Iters	Range		Point
6	6804.156044569223	82961.0911706557	13029.469918336774
8	-3761650.680535558	-5468.27390325817	-23307.635529317067

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	159	132
1	159	132

end0.0ms (0%)

sample683.0ms (11.6%)

Algorithm

1×

intervals

Results

245.0ms	1706×	body	1280	valid
146.0ms	1233×	body	640	valid
124.0ms	4145×	body	80	valid
57.0ms	624×	body	320	valid
19.0ms	292×	body	160	valid

Details

analyze4.0ms (0.1%)

sample24.0ms (0.4%)

simplify82.0ms (1.4%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

rewrite46.0ms (0.8%)

series13.0ms (0.2%)

simplify58.0ms (1%)

prune223.0ms (3.8%)

localize16.0ms (0.3%)

rewrite157.0ms (2.7%)

series24.0ms (0.4%)

simplify81.0ms (1.4%)

prune1.5s (26.1%)

localize28.0ms (0.5%)

rewrite113.0ms (1.9%)

series83.0ms (1.4%)

simplify33.0ms (0.6%)

prune704.0ms (11.9%)

localize30.0ms (0.5%)

rewrite233.0ms (4%)

series78.0ms (1.3%)

simplify43.0ms (0.7%)

prune1.5s (25.6%)

regimes52.0ms (0.9%)

bsearch25.0ms (0.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample683.0ms (11.6%)

Profiling