Details

analyze451.0ms

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

sample48.0ms

Algorithm

intervals

Results

10.0ms	26×	body	2560	valid
9.0ms	39×	body	1280	valid
8.0ms	154×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	31×	body	80	nan
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	invalid
0.0ms	5×	body	160	valid

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (219.0ms)

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: 34.8b

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))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

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

series57.0ms

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)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5248	1448

prune195.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	10	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	10	88

Merged error: 3.8b

Counts

88 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.9b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(/ (/ (* 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))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (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))
58.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4962	2514
1	4962	2514

prune205.0ms

Filtered

85 candidates to 124 candidates (-45.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	5	124
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Merged error: 3.8b

Counts

134 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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:

10.0ms	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(- (* 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))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ c (- (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)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5269	1600

prune165.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 3.8b

Counts

101 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(/ 1 (* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (* 1 (/ 2.0 c)) 4.0)))
0.9b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
35×	`div-exp`
30×	`prod-exp`
24×	`add-cbrt-cube`
13×	`1-exp`
12×	`add-sqr-sqrt`
9×	`cbrt-undiv` `*-un-lft-identity`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt` `rec-exp`
6×	`cbrt-unprod`
5×	`flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod`
3×	`times-frac` `associate-/l*`
2×	`frac-times` `sub-neg` `pow-flip` `sqrt-div` `diff-log` `associate-*l/` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(/ 1 (* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (* 1 (/ 2.0 c)) 4.0)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(/ 1 (* (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (/ (* 1 (/ 2.0 c)) 4.0)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4946	1669
1	4946	1669

prune120.0ms

Filtered

60 candidates to 103 candidates (-71.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 3.8b

Counts

112 → 9

regimes302.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.4b against oracle of 5.3b and baseline of 29.1b

bsearch90.0ms

Steps

Iters	Range	Point
9	2.7669584825073803e+65	2.011957623685665e+71	1.8806831440231258e+68
8	3.717086819349826e-270	5.412127724858915e-267	6.81105569789334e-270
8	-4.0680525424981645e+155	-3.057930823141505e+152	-1.2478898225028821e+154

Iters

Range

Point

2.7669584825073803e+65

2.011957623685665e+71

1.8806831440231258e+68

3.717086819349826e-270

5.412127724858915e-267

6.81105569789334e-270

-4.0680525424981645e+155

-3.057930823141505e+152

-1.2478898225028821e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	229	65
1	229	65

end0.0ms

sample1.3s

Algorithm

intervals

Results

327.0ms	1043×	body	2560	valid
281.0ms	5090×	body	80	valid
229.0ms	904×	body	1280	valid
92.0ms	468×	body	640	valid
53.0ms	132×	body	5120	valid
37.0ms	736×	body	80	nan
34.0ms	225×	body	320	valid
24.0ms	405×	body	80	invalid
17.0ms	138×	body	160	valid

Details

analyze451.0ms

sample48.0ms

simplify220.0ms

prune7.0ms

localize11.0ms

rewrite30.0ms

series57.0ms

simplify46.0ms

prune195.0ms

localize11.0ms

rewrite42.0ms

series131.0ms

simplify59.0ms

prune205.0ms

localize12.0ms

rewrite28.0ms

series85.0ms

simplify60.0ms

prune165.0ms

localize13.0ms

rewrite34.0ms

series64.0ms

simplify47.0ms

prune120.0ms

regimes302.0ms

bsearch90.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling