Details

analyze459.0ms

Algorithm

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

sample41.0ms

Algorithm

intervals

Results

9.0ms	31×	body	2560	valid
9.0ms	169×	body	80	valid
6.0ms	24×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	17×	body	80	nan
0.0ms	9×	body	80	invalid
0.0ms	3×	body	160	valid

simplify216.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (214.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 31.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

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:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5946	1448

prune161.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 7.6b

Counts

88 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
3.1b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.2b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm

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:

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

series127.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
46.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
59.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5287	2393

prune176.0ms

Filtered

81 candidates to 121 candidates (-49.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	122	10	132

Merged error: 7.5b

Counts

132 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.8b	(- (* b b) (* 4.0 (* a c)))
18.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune150.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	93	10	103

Merged error: 7.5b

Counts

103 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

11.2b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
18.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
18.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

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

series101.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* 4.0 (* a c)) (- (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))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify35.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5003	1388

prune241.0ms

Filtered

68 candidates to 88 candidates (-29.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	88	10	98

Merged error: 7.5b

Counts

98 → 10

regimes270.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.1b

bsearch79.0ms

Steps

Iters	Range	Point
5	4.779419445507541e+94	1.813133951197428e+95	1.6926019214523237e+95
8	2.599423232839541e-287	2.0246502009342751e-283	1.125215516807859e-284
8	-1.0547786272561615e+160	-3.846076668164928e+157	-3.8895171073387026e+157

Iters

Range

Point

4.779419445507541e+94

1.813133951197428e+95

1.6926019214523237e+95

2.599423232839541e-287

2.0246502009342751e-283

1.125215516807859e-284

-1.0547786272561615e+160

-3.846076668164928e+157

-3.8895171073387026e+157

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	187	62
1	187	62

end0.0ms

sample1.4s

Algorithm

intervals

Results

347.0ms	1066×	body	2560	valid
286.0ms	5060×	body	80	valid
251.0ms	940×	body	1280	valid
97.0ms	460×	body	640	valid
40.0ms	106×	body	5120	valid
39.0ms	695×	body	80	nan
37.0ms	239×	body	320	valid
21.0ms	386×	body	80	invalid
15.0ms	129×	body	160	valid

Details

analyze459.0ms

sample41.0ms

simplify216.0ms

prune7.0ms

localize15.0ms

rewrite31.0ms

series60.0ms

simplify45.0ms

prune161.0ms

localize11.0ms

rewrite38.0ms

series127.0ms

simplify40.0ms

prune176.0ms

localize15.0ms

rewrite27.0ms

series85.0ms

simplify66.0ms

prune150.0ms

localize23.0ms

rewrite26.0ms

series101.0ms

simplify35.0ms

prune241.0ms

regimes270.0ms

bsearch79.0ms

simplify3.0ms

end0.0ms

sample1.4s

Profiling