Details

sample77.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
10.0ms	168×	body	80	valid
8.0ms	14×	body	640	valid
8.0ms	32×	body	1280	valid
4.0ms	85×	body	80	nan
2.0ms	5×	body	5120	valid
2.0ms	11×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 35.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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 → 77

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* 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))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune159.0ms

Filtered

89 candidates to 65 candidates (27.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	8	90

Merged error: 7.0b

Counts

90 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (* 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))))

simplify70.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune155.0ms

Filtered

137 candidates to 73 candidates (46.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	136	9	145

Merged error: 6.9b

Counts

145 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.9b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
17.0b	(- (pow b 2) (pow b 2))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
78×	`times-frac`
68×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`difference-of-squares`
27×	`associate-/l*`
22×	`unpow-prod-down`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`sqrt-prod`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`div-sub` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

27.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
23.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (pow b 2) (pow b 2))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
33.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify188.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	760	2835
1	3914	2397
2	5002	2370

prune379.0ms

Filtered

187 candidates to 124 candidates (33.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	186	10	196

Merged error: 6.9b

Counts

196 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))
23.8b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(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))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify102.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	203	606
1	762	588
2	3223	580
3	5001	576

prune181.0ms

Filtered

75 candidates to 60 candidates (20.0%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	75	10	85

Merged error: 6.9b

Counts

85 → 10

regimes409.0ms

Accuracy

87% (3.8b remaining)

Error of 9.8b against oracle of 6.0b and baseline of 35.2b

bsearch128.0ms

Steps

Iters	Range		Point
8	6.823316278298556e+61	7.483462020487317e+65	6.841384097904949e+62
8	-2.9266307033054667e-97	-1.0822712823597246e-101	-4.9416544507568687e-98
9	-1.5833291525376033e-90	-2.16736516441666e-95	-2.1910163229392338e-95
6	-1391.0173919854967	-99.04193821246227	-188.2213156809491

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	32
1	46	32

end0.0ms

sample1.6s

Algorithm

intervals

Results

320.0ms	1066×	body	2560	valid
286.0ms	5398×	body	80	valid
265.0ms	1058×	body	1280	valid
128.0ms	2483×	body	80	nan
104.0ms	543×	body	640	valid
43.0ms	276×	body	320	valid
32.0ms	90×	body	5120	valid
15.0ms	139×	body	160	valid

Details

sample77.0ms

simplify15.0ms

prune4.0ms

localize11.0ms

rewrite28.0ms

series59.0ms

simplify46.0ms

prune159.0ms

localize12.0ms

rewrite33.0ms

series71.0ms

simplify70.0ms

prune155.0ms

localize16.0ms

rewrite68.0ms

series78.0ms

simplify188.0ms

prune379.0ms

localize18.0ms

rewrite20.0ms

series58.0ms

simplify102.0ms

prune181.0ms

regimes409.0ms

bsearch128.0ms

simplify2.0ms

end0.0ms

sample1.6s

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