Details

analyze257.0ms (7.9%)

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 (1.5%)

Algorithm

1×

intervals

Results

14.0ms	100×	body	320	valid
11.0ms	115×	body	160	valid
10.0ms	288×	pre	80	true
3.0ms	15×	body	640	valid
1.0ms	32×	body	80	nan
1.0ms	26×	body	80	valid

simplify196.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (194.0ms)

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: 51.7b

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))
29.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

rewrite28.0ms (0.9%)

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:

12.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series60.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

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

simplify38.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune190.0ms (5.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 2.8b

Counts

83 → 8

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune27.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Merged error: 2.8b

Counts

8 → 8

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(* (/ a b) c)
0.3b	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
16×	`prod-exp` `cbrt-unprod`
15×	`add-sqr-sqrt`
13×	`associate-l`
11×	`cbrt-undiv` `times-frac` `div-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1`
3×	`associate-r`
2×	`associate-*l/` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `associate-/l`

Counts

2 → 62

Calls

2 calls:

9.0ms	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))
6.0ms	(* (/ a b) c)

series10.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))
5.0ms	(* (/ a b) c)

simplify43.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4991	490
1	4991	490

prune155.0ms (4.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	58	10	68
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	59	17	76

Merged error: 2.7b

Counts

76 → 17

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt a) b)
0.3b	(/ (* -2.0 (* (/ (sqrt a) 1) (* c (/ (sqrt a) b)))) (* a 2.0))
0.3b	(* c (/ (sqrt a) b))
0.4b	(* (/ (sqrt a) 1) (* c (/ (sqrt a) b)))

rewrite47.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-exp-log`
116×	`add-cbrt-cube`
78×	`prod-exp`
57×	`times-frac`
54×	`add-sqr-sqrt` `cbrt-unprod`
51×	`div-exp`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`cbrt-undiv`
31×	`sqrt-prod`
25×	`associate-l`
23×	`associate-r`
11×	`pow1`
10×	`associate-*r/`
9×	`1-exp`
7×	`associate-/l*`
4×	`pow-prod-down` `associate-/r*` `div-inv` `add-log-exp`
3×	`associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 186

Calls

4 calls:

15.0ms	(/ (* -2.0 (* (/ (sqrt a) 1) (* c (/ (sqrt a) b)))) (* a 2.0))
11.0ms	(* (/ (sqrt a) 1) (* c (/ (sqrt a) b)))
8.0ms	(* c (/ (sqrt a) b))
4.0ms	(/ (sqrt a) b)

series47.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (* -2.0 (* (/ (sqrt a) 1) (* c (/ (sqrt a) b)))) (* a 2.0))
12.0ms	(* (/ (sqrt a) 1) (* c (/ (sqrt a) b)))
11.0ms	(* c (/ (sqrt a) b))
9.0ms	(/ (sqrt a) b)

simplify83.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4982	1873
1	4982	1873

prune253.0ms (7.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	194	4	198
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	199	16	215

Merged error: 2.7b

Counts

215 → 16

regimes293.0ms (9%)

Accuracy

Total 3.4b remaining (56.1%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	5
1	6	5

end0.0ms (0%)

sample1.4s (43.6%)

Algorithm

1×

intervals

Results

514.0ms	3608×	body	320	valid
280.0ms	2963×	body	160	valid
249.0ms	8832×	pre	80	true
99.0ms	532×	body	640	valid
43.0ms	897×	body	80	valid
38.0ms	832×	body	80	nan

Details

analyze257.0ms (7.9%)

sample51.0ms (1.5%)

simplify196.0ms (6%)

prune8.0ms (0.2%)

localize10.0ms (0.3%)

rewrite28.0ms (0.9%)

series60.0ms (1.8%)

simplify38.0ms (1.2%)

prune190.0ms (5.8%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify2.0ms (0.1%)

prune27.0ms (0.8%)

localize7.0ms (0.2%)

rewrite17.0ms (0.5%)

series10.0ms (0.3%)

simplify43.0ms (1.3%)

prune155.0ms (4.7%)

localize11.0ms (0.3%)

rewrite47.0ms (1.5%)

series47.0ms (1.4%)

simplify83.0ms (2.5%)

prune253.0ms (7.8%)

regimes293.0ms (9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.4s (43.6%)

Profiling