Details

analyze610.0ms (15.5%)

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

sample44.0ms (1.1%)

Algorithm

1×

intervals

Results

10.0ms	33×	body	1280	valid
9.0ms	171×	body	80	valid
5.0ms	20×	body	2560	valid
3.0ms	19×	body	640	valid
1.0ms	25×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	11×	body	80	invalid
0.0ms	4×	body	160	valid

simplify504.0ms (12.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms (0.3%)

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: 33.1b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))

series62.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (- (* b_2 b_2) (* a c)))
21.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))

simplify60.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5743	1403

prune142.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	7	95

Merged error: 6.5b

Counts

95 → 7

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.8b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.7b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`times-frac`
38×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`div-inv` `distribute-lft-out` `add-log-exp`
5×	`pow1` `flip3-+` `flip-+`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

11.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(/ (* a (neg c)) (+ 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))

series107.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
40.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(- (* b_2 b_2) (* a c))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4932	2261
1	4932	2261

prune150.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	125	7	132

Merged error: 6.5b

Counts

132 → 7

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
0.4b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms (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_2 (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(+ 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))

series76.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(+ 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))

simplify46.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5326	1109

prune109.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	82	8	90

Merged error: 6.5b

Counts

90 → 8

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 160

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
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 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))

simplify69.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4972	3316
1	4972	3316

prune186.0ms (4.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	172	8	180

Merged error: 6.5b

Counts

180 → 8

regimes233.0ms (5.9%)

Accuracy

Total 1.7b remaining (23.3%)

Threshold costs 0b (0%)

bsearch73.0ms (1.9%)

Steps

Iters	Range	Point
6	1.3353262233380745e+19	9.277097108016213e+19	6.9512572766954365e+19
7	-1.685469550775479e-305	-2.9189873276785382e-307	-1.243685732710164e-305
10	-6.291459953144265e+77	-1.9066222415164845e+66	-6.205007535037304e+77

Iters

Range

Point

1.3353262233380745e+19

9.277097108016213e+19

6.9512572766954365e+19

-1.685469550775479e-305

-2.9189873276785382e-307

-1.243685732710164e-305

-6.291459953144265e+77

-1.9066222415164845e+66

-6.205007535037304e+77

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	94	64
1	94	64

end0.0ms (0%)

sample1.1s (29.1%)

Algorithm

1×

intervals

Results

284.0ms	1082×	body	2560	valid
237.0ms	5055×	body	80	valid
196.0ms	922×	body	1280	valid
82.0ms	473×	body	640	valid
39.0ms	123×	body	5120	valid
36.0ms	771×	body	80	nan
27.0ms	220×	body	320	valid
12.0ms	247×	body	80	invalid
11.0ms	125×	body	160	valid

Details

analyze610.0ms (15.5%)

sample44.0ms (1.1%)

simplify504.0ms (12.8%)

prune11.0ms (0.3%)

localize10.0ms (0.3%)

rewrite39.0ms (1%)

series62.0ms (1.6%)

simplify60.0ms (1.5%)

prune142.0ms (3.6%)

localize12.0ms (0.3%)

rewrite34.0ms (0.9%)

series107.0ms (2.7%)

simplify67.0ms (1.7%)

prune150.0ms (3.8%)

localize9.0ms (0.2%)

rewrite22.0ms (0.6%)

series76.0ms (1.9%)

simplify46.0ms (1.2%)

prune109.0ms (2.8%)

localize10.0ms (0.2%)

rewrite35.0ms (0.9%)

series63.0ms (1.6%)

simplify69.0ms (1.7%)

prune186.0ms (4.7%)

regimes233.0ms (5.9%)

bsearch73.0ms (1.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (29.1%)

Profiling