Details

analyze266.0ms (6.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

sample51.0ms (1.3%)

Algorithm

1×

intervals

Results

17.0ms	111×	body	320	valid
10.0ms	104×	body	160	valid
8.0ms	287×	pre	80	true
3.0ms	15×	body	640	valid
1.0ms	31×	body	80	nan
1.0ms	26×	body	80	valid

simplify241.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (239.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 52.7b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
27.2b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series63.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* a 2.0))
17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4921	1309
1	4921	1309

prune153.0ms (4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 0.1b

Counts

83 → 3

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
0.3b	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac`
78×	`*-un-lft-identity`
38×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`associate-/l*`
20×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`pow1` `flip3-+` `flip-+` `div-inv`
3×	`div-sub` `distribute-frac-neg`
2×	`neg-sub0` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `associate-/l/`

Counts

4 → 155

Calls

4 calls:

13.0ms	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
11.0ms	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series118.0ms (3%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
40.0ms	(/ (/ (neg (* (* 4.0 a) c)) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) (* a 2.0))
14.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify60.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4978	3969
1	4978	3969

prune400.0ms (10.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	161	6	167
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	164	6	170

Merged error: 0b

Counts

170 → 6

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 71

Calls

4 calls:

7.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series78.0ms (2%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ c (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4930	1299
1	4930	1299

prune166.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 0b

Counts

89 → 5

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.3b	(/ 1 (/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log`
39×	`times-frac`
27×	`add-cbrt-cube`
25×	`*-un-lft-identity`
24×	`div-exp`
23×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-undiv`
9×	`associate-/r*`
8×	`prod-exp` `add-log-exp`
6×	`associate-/r/` `div-inv` `associate-/l*`
5×	`pow1` `associate-*r/`
4×	`rec-exp` `1-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sub-neg` `flip3--` `pow-flip` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `inv-pow`

Counts

4 → 111

Calls

4 calls:

14.0ms	(/ 1 (/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
13.0ms	(/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))

series100.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1 (/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
32.0ms	(/ 2.0 (* 4.0 (/ (neg c) (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))))
14.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5211	2380

prune223.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	123	5	128

Merged error: 0b

Counts

128 → 5

regimes155.0ms (4%)

Accuracy

Total 0.2b remaining (88.9%)

Threshold costs 0.2b (88.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	21
1	79	21

end0.0ms (0%)

sample1.5s (37.6%)

Algorithm

1×

intervals

Results

536.0ms	3739×	body	320	valid
279.0ms	2924×	body	160	valid
257.0ms	8863×	pre	80	true
94.0ms	486×	body	640	valid
44.0ms	851×	body	80	valid
40.0ms	863×	body	80	nan

Details

analyze266.0ms (6.9%)

sample51.0ms (1.3%)

simplify241.0ms (6.2%)

prune8.0ms (0.2%)

localize10.0ms (0.3%)

rewrite28.0ms (0.7%)

series63.0ms (1.6%)

simplify49.0ms (1.3%)

prune153.0ms (4%)

localize13.0ms (0.3%)

rewrite40.0ms (1%)

series118.0ms (3%)

simplify60.0ms (1.5%)

prune400.0ms (10.3%)

localize12.0ms (0.3%)

rewrite25.0ms (0.6%)

series78.0ms (2%)

simplify68.0ms (1.7%)

prune166.0ms (4.3%)

localize13.0ms (0.3%)

rewrite42.0ms (1.1%)

series100.0ms (2.6%)

simplify34.0ms (0.9%)

prune223.0ms (5.8%)

regimes155.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.5s (37.6%)

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