Details

analyze258.0ms (8.3%)

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

sample39.0ms (1.3%)

Algorithm

1×

intervals

Results

13.0ms	137×	body	160	valid
10.0ms	277×	pre	80	true
6.0ms	119×	body	80	valid
1.0ms	21×	body	80	nan

simplify205.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (203.0ms)

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: 27.5b

Counts

2 → 1

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
0.2b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.3b	(- (* b b) (* 4.0 (* a c)))
27.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)

rewrite27.0ms (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:

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

series64.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms	(- (* b b) (* 4.0 (* a c)))

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune212.0ms (6.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	66	16	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	16	83

Merged error: 9.1b

Counts

83 → 16

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

prune58.0ms (1.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	15	15
Picked	1	1
Done	0	0
Total	16	16

Merged error: 9.1b

Counts

16 → 16

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite17.0ms (0.6%)

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)

series12.0ms (0.4%)

Counts

2 → 6

Calls

2 calls:

7.0ms	(* (/ a b) c)
5.0ms	(/ (* -2.0 (* (/ a b) c)) (* a 2.0))

simplify42.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4991	490
1	4991	490

prune183.0ms (5.9%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	56	12	68
Fresh	0	14	14
Picked	1	0	1
Done	0	1	1
Total	57	27	84

Merged error: 9.0b

Counts

84 → 27

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log` `add-cbrt-cube`
30×	`prod-exp` `cbrt-unprod`
24×	`add-sqr-sqrt`
14×	`cbrt-undiv` `add-cube-cbrt` `-un-lft-identity` `div-exp` `associate-l*`
12×	`times-frac` `associate-r`
10×	`pow1`
8×	`sqrt-prod`
5×	`associate-*l/`
4×	`pow-prod-down` `unswap-sqr`
3×	`add-log-exp`
2×	`*-commutative` `div-inv`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r` `associate-/l/` `associate-/l*`

Counts

3 → 95

Calls

3 calls:

13.0ms	(/ (* -2.0 (* (* (/ a b) (sqrt c)) (sqrt c))) (* a 2.0))
8.0ms	(* (* (/ a b) (sqrt c)) (sqrt c))
7.0ms	(* (/ a b) (sqrt c))

series29.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

12.0ms	(* (/ a b) (sqrt c))
9.0ms	(* (* (/ a b) (sqrt c)) (sqrt c))
8.0ms	(/ (* -2.0 (* (* (/ a b) (sqrt c)) (sqrt c))) (* a 2.0))

simplify29.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5341	981

prune127.0ms (4.1%)

Pruning

31 alts after pruning (30 fresh and 1 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	2	23	25
Picked	1	0	1
Done	0	1	1
Total	100	31	131

Merged error: 8.9b

Counts

131 → 31

regimes599.0ms (19.3%)

Accuracy

Total 7.6b remaining (45.7%)

Threshold costs 0b (0%)

bsearch2.0ms (0.1%)

Steps

Iters	Range		Point
0	387.5367379430292	395.61572319468746	391.5762305688583

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	39
1	96	39

end0.0ms (0%)

sample1.1s (35%)

Algorithm

1×

intervals

Results

417.0ms	4452×	body	160	valid
250.0ms	8857×	pre	80	true
177.0ms	3548×	body	80	valid
41.0ms	857×	body	80	nan

Details

analyze258.0ms (8.3%)

sample39.0ms (1.3%)

simplify205.0ms (6.6%)

prune8.0ms (0.2%)

localize11.0ms (0.3%)

rewrite27.0ms (0.9%)

series64.0ms (2.1%)

simplify39.0ms (1.2%)

prune212.0ms (6.8%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify2.0ms (0.1%)

prune58.0ms (1.9%)

localize7.0ms (0.2%)

rewrite17.0ms (0.6%)

series12.0ms (0.4%)

simplify42.0ms (1.4%)

prune183.0ms (5.9%)

localize9.0ms (0.3%)

rewrite33.0ms (1%)

series29.0ms (0.9%)

simplify29.0ms (0.9%)

prune127.0ms (4.1%)

regimes599.0ms (19.3%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (35%)

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