Details

analyze611.0ms (15.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample41.0ms (1%)

Algorithm

1×

intervals

Results

8.0ms	31×	body	2560	valid
8.0ms	172×	body	80	valid
6.0ms	25×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	24×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	9×	body	80	invalid
0.0ms	3×	body	160	valid

simplify512.0ms (13.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune8.0ms (0.2%)

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: 30.5b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 89

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series74.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))

simplify60.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune165.0ms (4.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 5.5b

Counts

102 → 10

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 175

Calls

4 calls:

17.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series63.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5176	3699

prune239.0ms (6.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	182	5	187
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	187	10	197

Merged error: 5.5b

Counts

197 → 10

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
1.8b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.6b	(/ (* a c) a)
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
5×	`pow1`
3×	`times-frac` `associate-/r*` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `sqrt-div` `div-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 62

Calls

4 calls:

8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series36.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(- (* b_2 b_2) (* a c))
2.0ms	(/ (* a c) a)

simplify57.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5179	644

prune112.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	74	10	84

Merged error: 5.4b

Counts

84 → 10

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(- (* b_2 b_2) (* a c))
1.8b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 78

Calls

4 calls:

9.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(- (* b_2 b_2) (* a c))

series79.0ms (2%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ c (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5677	1193

prune99.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	91	9	100

Merged error: 5.4b

Counts

100 → 9

regimes284.0ms (7.2%)

Accuracy

Total 1.5b remaining (20.8%)

Threshold costs 0b (0%)

bsearch83.0ms (2.1%)

Steps

Iters	Range		Point
7	19273454904189.21	1041603463041951.4	1028948765099707.4
8	1.4006328130161814e-259	8.060327091088768e-255	1.2852416291713516e-256
8	-2.0168463992321823e+147	-1.049047891908715e+143	-1.1144738873289328e+144

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	55
1	116	55

end0.0ms (0%)

sample1.1s (28.2%)

Algorithm

1×

intervals

Results

268.0ms	1052×	body	2560	valid
232.0ms	5131×	body	80	valid
191.0ms	925×	body	1280	valid
73.0ms	452×	body	640	valid
34.0ms	834×	body	80	nan
33.0ms	107×	body	5120	valid
32.0ms	232×	body	320	valid
12.0ms	270×	body	80	invalid
8.0ms	101×	body	160	valid

Details

analyze611.0ms (15.6%)

sample41.0ms (1%)

simplify512.0ms (13.1%)

prune8.0ms (0.2%)

localize12.0ms (0.3%)

rewrite33.0ms (0.8%)

series74.0ms (1.9%)

simplify60.0ms (1.5%)

prune165.0ms (4.2%)

localize11.0ms (0.3%)

rewrite41.0ms (1.1%)

series63.0ms (1.6%)

simplify62.0ms (1.6%)

prune239.0ms (6.1%)

localize11.0ms (0.3%)

rewrite21.0ms (0.5%)

series36.0ms (0.9%)

simplify57.0ms (1.5%)

prune112.0ms (2.9%)

localize9.0ms (0.2%)

rewrite27.0ms (0.7%)

series79.0ms (2%)

simplify58.0ms (1.5%)

prune99.0ms (2.5%)

regimes284.0ms (7.2%)

bsearch83.0ms (2.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (28.2%)

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