Details

analyze528.0ms (13.9%)

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample37.0ms (1%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	27×	body	80	nan
1.0ms	11×	body	80	invalid

simplify277.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (275.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune13.0ms (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: 20.1b

Counts

2 → 1

localize23.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 61

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series61.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms (2%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4879	1082
1	4879	1082

prune227.0ms (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Merged error: 6.9b

Counts

74 → 7

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

10.3b	(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

15.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series59.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5004	935

prune242.0ms (6.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 6.9b

Counts

76 → 7

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

5.2b	(exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.5b	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`sqrt-prod`
9×	`add-cube-cbrt`
8×	`pow1` `log-prod` `exp-sum` `add-log-exp`
6×	`exp-prod` `sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-pow1` `pow1/2` `log-pow` `difference-of-squares`
2×	`rem-sqrt-square` `log-div` `exp-diff` `diff-log` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log` `rem-exp-log`

Counts

4 → 70

Calls

4 calls:

12.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
6.0ms	(exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series58.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(exp (log (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4900	1140
1	4900	1140

prune255.0ms (6.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	81	8	89

Merged error: 6.9b

Counts

89 → 8

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.2b	(/ (* c 2.0) (- (- (* 2.0 (/ (* a c) b)) b) b))
5.6b	(/ (* a c) b)
20.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

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

series51.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (* c 2.0) (- (- (* 2.0 (/ (* a c) b)) b) b))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(/ (* a c) b)

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5243	1214

prune201.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 6.1b

Counts

100 → 8

regimes274.0ms (7.2%)

Accuracy

Total 1.0b remaining (13.4%)

Threshold costs 0b (0%)

bsearch51.0ms (1.3%)

Steps

Iters	Range		Point
5	9.803037244659017e+91	3.4843437681471106e+92	2.485959951540932e+92
9	-1.3495067265639191e+126	-3.595720007866579e+117	-4.250178820340957e+119

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	151	129
1	151	129

end0.0ms (0%)

sample991.0ms (26.1%)

Algorithm

1×

intervals

Results

692.0ms	8000×	body	80	valid
55.0ms	687×	body	80	nan
36.0ms	421×	body	80	invalid

Details

analyze528.0ms (13.9%)

sample37.0ms (1%)

simplify277.0ms (7.3%)

prune13.0ms (0.3%)

localize23.0ms (0.6%)

rewrite26.0ms (0.7%)

series61.0ms (1.6%)

simplify77.0ms (2%)

prune227.0ms (6%)

localize28.0ms (0.7%)

rewrite29.0ms (0.8%)

series59.0ms (1.6%)

simplify44.0ms (1.2%)

prune242.0ms (6.4%)

localize26.0ms (0.7%)

rewrite31.0ms (0.8%)

series58.0ms (1.5%)

simplify80.0ms (2.1%)

prune255.0ms (6.7%)

localize28.0ms (0.7%)

rewrite30.0ms (0.8%)

series51.0ms (1.4%)

simplify41.0ms (1.1%)

prune201.0ms (5.3%)

regimes274.0ms (7.2%)

bsearch51.0ms (1.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample991.0ms (26.1%)

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