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

sample47.0ms

Algorithm

intervals

Results

10.0ms	150×	body	80	valid
9.0ms	38×	body	1280	valid
9.0ms	32×	body	2560	valid
3.0ms	15×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	10×	body	320	valid
1.0ms	13×	body	80	nan
0.0ms	8×	body	80	invalid
0.0ms	4×	body	160	valid

simplify214.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (212.0ms)

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: 35.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.4b	(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)))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

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))))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5946	1448

prune149.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	7	88

Merged error: 4.8b

Counts

88 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.3b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
8.0b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

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)
16.0ms	(/ (/ (* 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))))

series128.0ms

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))
55.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5232	2497

prune172.0ms

Filtered

84 candidates to 124 candidates (-47.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	126	5	131

Merged error: 4.8b

Counts

131 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.4b	(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:

49.0ms	(/ 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)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune140.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Merged error: 4.8b

Counts

98 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.3b	(* (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* a 2.0)))
8.0b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-exp-log`
67×	`add-cbrt-cube`
64×	`prod-exp`
40×	`div-exp`
30×	`add-sqr-sqrt`
28×	`cbrt-unprod`
20×	`cbrt-undiv`
19×	`*-un-lft-identity`
15×	`times-frac`
12×	`associate-l`
11×	`add-cube-cbrt`
8×	`rec-exp` `1-exp` `difference-of-squares`
7×	`pow1` `associate-r` `sqrt-prod`
6×	`associate-/r*` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--` `distribute-lft-out--`
3×	`div-inv`
2×	`sqrt-div`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 133

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.0ms	(* (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* a 2.0)))
13.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
44.0ms	(* (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* a 2.0)))
55.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5120	2891

prune153.0ms

Filtered

83 candidates to 145 candidates (-74.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	145	6	151

Merged error: 4.8b

Counts

151 → 6

regimes316.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 29.6b

bsearch80.0ms

Steps

Iters	Range	Point
8	4.245378708602696e+126	4.4810348475887653e+129	1.3774829577522356e+129
11	6.091115727764442e-230	4.2099998847060053e-206	1.9883816765215883e-226
5	-2.398989886538497e+89	-1.1432136901367638e+89	-2.0309106700532098e+89

Iters

Range

Point

4.245378708602696e+126

4.4810348475887653e+129

1.3774829577522356e+129

6.091115727764442e-230

4.2099998847060053e-206

1.9883816765215883e-226

-2.398989886538497e+89

-1.1432136901367638e+89

-2.0309106700532098e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	114	57
1	114	57

end0.0ms

sample1.2s

Algorithm

intervals

Results

324.0ms	1077×	body	2560	valid
266.0ms	5171×	body	80	valid
217.0ms	901×	body	1280	valid
81.0ms	417×	body	640	valid
36.0ms	97×	body	5120	valid
34.0ms	240×	body	320	valid
32.0ms	626×	body	80	nan
20.0ms	350×	body	80	invalid
9.0ms	97×	body	160	valid

Details

analyze451.0ms

sample47.0ms

simplify214.0ms

prune7.0ms

localize12.0ms

rewrite31.0ms

series58.0ms

simplify43.0ms

prune149.0ms

localize13.0ms

rewrite45.0ms

series128.0ms

simplify39.0ms

prune172.0ms

localize15.0ms

rewrite28.0ms

series85.0ms

simplify64.0ms

prune140.0ms

localize13.0ms

rewrite49.0ms

series129.0ms

simplify55.0ms

prune153.0ms

regimes316.0ms

bsearch80.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling