Details

analyze458.0ms (11%)

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample47.0ms (1.1%)

Algorithm

1×

intervals

Results

12.0ms	34×	body	2560	valid
8.0ms	34×	body	1280	valid
8.0ms	150×	body	80	valid
4.0ms	20×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	22×	body	80	nan
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	6×	body	80	invalid

simplify212.0ms (5.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (210.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 38.0b

Counts

2 → 1

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

13.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series57.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5946	1448

prune201.0ms (4.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	8	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	8	88

Merged error: 6.1b

Counts

88 → 8

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
5.0b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.7b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
30×	`times-frac`
28×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod` `associate-/l*`
11×	`add-cube-cbrt`
8×	`difference-of-squares`
7×	`associate-/r*` `sqrt-prod`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv` `distribute-lft-out--`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 109

Calls

4 calls:

14.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series126.0ms (3%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
45.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
8.0ms	(- (* b b) (* 4.0 (* a c)))

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5287	2393

prune261.0ms (6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	120	9	129

Merged error: 6.0b

Counts

129 → 9

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b	(- (* b b) (* 4.0 (* a c)))
21.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms (0.6%)

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` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(- (* b b) (* 4.0 (* a c)))

series85.0ms (2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.0ms	(- (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)))

simplify64.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune199.0ms (4.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 5.9b

Counts

102 → 9

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* (/ 4.0 2.0) (* 1 (/ c (- (- (* a (/ 2.0 (/ b c))) b) b))))
1.0b	(/ 2.0 (/ b c))
4.9b	(/ c (- (- (* a (/ 2.0 (/ b c))) b) b))
5.6b	(* a (/ 2.0 (/ b c)))

rewrite61.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`times-frac`
116×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
99×	`add-cube-cbrt`
53×	`add-exp-log`
45×	`associate-r`
41×	`add-cbrt-cube`
21×	`prod-exp`
18×	`associate-/r*`
16×	`div-exp` `associate-l`
13×	`cbrt-unprod`
12×	`cbrt-undiv`
11×	`pow1` `div-inv`
6×	`associate-/l*`
4×	`1-exp` `associate-*r/` `pow-prod-down` `associate-/r/` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `flip3--` `associate-*l/` `flip--`

Counts

4 → 216

Calls

4 calls:

21.0ms	(* (/ 4.0 2.0) (* 1 (/ c (- (- (* a (/ 2.0 (/ b c))) b) b))))
13.0ms	(* a (/ 2.0 (/ b c)))
12.0ms	(/ c (- (- (* a (/ 2.0 (/ b c))) b) b))
6.0ms	(/ 2.0 (/ b c))

series42.0ms (1%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (/ 4.0 2.0) (* 1 (/ c (- (- (* a (/ 2.0 (/ b c))) b) b))))
15.0ms	(/ c (- (- (* a (/ 2.0 (/ b c))) b) b))
6.0ms	(* a (/ 2.0 (/ b c)))
3.0ms	(/ 2.0 (/ b c))

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5281	2890

prune407.0ms (9.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	224	4	228
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	225	12	237

Merged error: 5.9b

Counts

237 → 12

regimes312.0ms (7.5%)

Accuracy

Total 1.7b remaining (23.4%)

Threshold costs 0b (0%)

bsearch46.0ms (1.1%)

Steps

Iters	Range		Point
6	5.497054777965939e+32	2.720772085466593e+33	2.673025417100217e+33
9	1.5217707132634722e-201	2.4731489252075214e-192	1.5461279104521085e-201
0	-1.604960284102343e+99	-1.5858680620401842e+99	-1.5954141730712636e+99

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	187	62
1	187	62

end0.0ms (0%)

sample1.3s (30.6%)

Algorithm

1×

intervals

Results

334.0ms	1098×	body	2560	valid
269.0ms	5069×	body	80	valid
218.0ms	881×	body	1280	valid
93.0ms	477×	body	640	valid
42.0ms	116×	body	5120	valid
34.0ms	236×	body	320	valid
33.0ms	659×	body	80	nan
21.0ms	408×	body	80	invalid
12.0ms	123×	body	160	valid

Details

analyze458.0ms (11%)

sample47.0ms (1.1%)

simplify212.0ms (5.1%)

prune7.0ms (0.2%)

localize12.0ms (0.3%)

rewrite31.0ms (0.7%)

series57.0ms (1.4%)

simplify43.0ms (1%)

prune201.0ms (4.9%)

localize12.0ms (0.3%)

rewrite37.0ms (0.9%)

series126.0ms (3%)

simplify37.0ms (0.9%)

prune261.0ms (6.3%)

localize13.0ms (0.3%)

rewrite26.0ms (0.6%)

series85.0ms (2%)

simplify64.0ms (1.6%)

prune199.0ms (4.8%)

localize12.0ms (0.3%)

rewrite61.0ms (1.5%)

series42.0ms (1%)

simplify66.0ms (1.6%)

prune407.0ms (9.8%)

regimes312.0ms (7.5%)

bsearch46.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (30.6%)

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