Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

sample18.0ms (0.7%)

Algorithm

1×

intervals

Results

6.0ms	65×	body	640	valid
3.0ms	134×	body	80	valid
3.0ms	38×	body	320	valid
1.0ms	19×	body	160	valid

simplify32.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	497	9
1	497	9

prune4.0ms (0.2%)

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: 17.7b

Counts

2 → 1

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

3.0b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
8×	`distribute-lft-out--`
5×	`add-cube-cbrt`
4×	`difference-of-squares`
3×	`distribute-lft-out` `add-log-exp`
2×	`div-inv`
1×	`pow1` `add-exp-log` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--`

Counts

1 → 24

Calls

1 calls:

17.0ms

(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series4.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

4.0ms

(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify33.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4937	382
1	4937	382

prune52.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.5b

Counts

28 → 2

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (pow x 4))
0.6b	(/ (- (/ 1.0 x) 1.0) (* x x))
10.1b	(- (/ (- (/ 1.0 x) 1.0) (* x x)) (/ 1.0 (pow x 4)))

rewrite40.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
39×	`times-frac`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
14×	`unpow-prod-down`
13×	`add-exp-log`
12×	`difference-of-squares`
10×	`add-cbrt-cube`
9×	`associate-/l*`
8×	`associate-/r*`
6×	`sqr-pow`
5×	`div-exp` `add-log-exp`
3×	`pow1` `cbrt-undiv` `distribute-lft-out--`
2×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--` `div-inv` `associate-/l/`
1×	`associate--l-` `pow-to-exp` `sub-neg` `diff-log` `pow-exp` `prod-exp` `frac-sub` `cbrt-unprod`

Counts

3 → 97

Calls

3 calls:

23.0ms	(- (/ (- (/ 1.0 x) 1.0) (* x x)) (/ 1.0 (pow x 4)))
9.0ms	(/ (- (/ 1.0 x) 1.0) (* x x))
4.0ms	(/ 1.0 (pow x 4))

series14.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (- (/ 1.0 x) 1.0) (* x x))
4.0ms	(- (/ (- (/ 1.0 x) 1.0) (* x x)) (/ 1.0 (pow x 4)))
3.0ms	(/ 1.0 (pow x 4))

simplify49.0ms (2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5003	1390

prune224.0ms (9.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	101	7	108

Merged error: 0.0b

Counts

108 → 7

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (pow x 4))
0.1b	(/ (- (/ 1.0 x) 1.0) x)
0.1b	(/ (/ (- (/ 1.0 x) 1.0) x) x)
10.1b	(- (/ (/ (- (/ 1.0 x) 1.0) x) x) (/ 1.0 (pow x 4)))

rewrite109.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

216×	`add-sqr-sqrt` `times-frac`
132×	`*-un-lft-identity`
94×	`add-cube-cbrt`
44×	`difference-of-squares`
31×	`associate-/l*`
18×	`distribute-lft-out--`
16×	`add-exp-log`
15×	`unpow-prod-down`
13×	`associate-/r*` `add-cbrt-cube`
7×	`div-exp` `div-inv` `sqr-pow`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-sub`
4×	`pow1`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`flip3--` `flip--`
1×	`associate--l-` `pow-to-exp` `sub-neg` `diff-log` `pow-exp` `frac-sub`

Counts

4 → 221

Calls

4 calls:

74.0ms	(- (/ (/ (- (/ 1.0 x) 1.0) x) x) (/ 1.0 (pow x 4)))
12.0ms	(/ (/ (- (/ 1.0 x) 1.0) x) x)
8.0ms	(/ (- (/ 1.0 x) 1.0) x)
4.0ms	(/ 1.0 (pow x 4))

series19.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (/ (- (/ 1.0 x) 1.0) x) x)
5.0ms	(/ (- (/ 1.0 x) 1.0) x)
4.0ms	(- (/ (/ (- (/ 1.0 x) 1.0) x) x) (/ 1.0 (pow x 4)))
3.0ms	(/ 1.0 (pow x 4))

simplify83.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4955	3517
1	4955	3517

prune554.0ms (22.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	4	0	4
Picked	0	1	1
Done	0	2	2
Total	234	6	240

Merged error: 0.0b

Counts

240 → 6

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

10.1b	(- (* (* (cbrt (/ (- (/ 1.0 x) 1.0) x)) (cbrt (/ (- (/ 1.0 x) 1.0) x))) (/ (cbrt (/ (- (/ 1.0 x) 1.0) x)) x)) (/ 1.0 (pow x 4)))
16.3b	(cbrt (/ (- (/ 1.0 x) 1.0) x))
16.3b	(cbrt (/ (- (/ 1.0 x) 1.0) x))
16.3b	(cbrt (/ (- (/ 1.0 x) 1.0) x))

rewrite67.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`cbrt-prod`
63×	`times-frac`
52×	`*-un-lft-identity`
34×	`add-cube-cbrt`
18×	`difference-of-squares`
11×	`cbrt-div`
9×	`distribute-lft-out--`
7×	`frac-sub`
6×	`add-log-exp`
5×	`frac-times` `associate-*l/`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3` `associate-*r/` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 111

Calls

4 calls:

40.0ms	(- (* (* (cbrt (/ (- (/ 1.0 x) 1.0) x)) (cbrt (/ (- (/ 1.0 x) 1.0) x))) (/ (cbrt (/ (- (/ 1.0 x) 1.0) x)) x)) (/ 1.0 (pow x 4)))
8.0ms	(cbrt (/ (- (/ 1.0 x) 1.0) x))
7.0ms	(cbrt (/ (- (/ 1.0 x) 1.0) x))
7.0ms	(cbrt (/ (- (/ 1.0 x) 1.0) x))

series29.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt (/ (- (/ 1.0 x) 1.0) x))
8.0ms	(cbrt (/ (- (/ 1.0 x) 1.0) x))
8.0ms	(cbrt (/ (- (/ 1.0 x) 1.0) x))
5.0ms	(- (* (* (cbrt (/ (- (/ 1.0 x) 1.0) x)) (cbrt (/ (- (/ 1.0 x) 1.0) x))) (/ (cbrt (/ (- (/ 1.0 x) 1.0) x)) x)) (/ 1.0 (pow x 4)))

simplify70.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4950	2350
1	4950	2350

prune446.0ms (18%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	2	0	2
Picked	1	0	1
Done	2	1	3
Total	127	2	129

Merged error: 0b

Counts

129 → 2

regimes65.0ms (2.6%)

Accuracy

Total 0.7b remaining (91.3%)

Threshold costs 0.7b (91.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	49
1	53	49

end0.0ms (0%)

sample500.0ms (20.2%)

Algorithm

1×

intervals

Results

175.0ms	1858×	body	640	valid
112.0ms	4281×	body	80	valid
89.0ms	1262×	body	320	valid
30.0ms	599×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze4.0ms (0.2%)

sample18.0ms (0.7%)

simplify32.0ms (1.3%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

rewrite18.0ms (0.7%)

series4.0ms (0.2%)

simplify33.0ms (1.3%)

prune52.0ms (2.1%)

localize9.0ms (0.4%)

rewrite40.0ms (1.6%)

series14.0ms (0.6%)

simplify49.0ms (2%)

prune224.0ms (9.1%)

localize9.0ms (0.4%)

rewrite109.0ms (4.4%)

series19.0ms (0.7%)

simplify83.0ms (3.4%)

prune554.0ms (22.4%)

localize13.0ms (0.5%)

rewrite67.0ms (2.7%)

series29.0ms (1.2%)

simplify70.0ms (2.8%)

prune446.0ms (18%)

regimes65.0ms (2.6%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample500.0ms (20.2%)

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