Details

analyze587.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample41.0ms

Algorithm

intervals

Results

8.0ms	164×	body	80	valid
7.0ms	29×	body	2560	valid
7.0ms	32×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	23×	body	80	nan
1.0ms	7×	body	320	valid
0.0ms	8×	body	80	invalid
0.0ms	3×	body	160	valid

simplify434.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	13
1	16	13

prune5.0ms

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: 35.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5082	1589

prune138.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 7.0b

Counts

102 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
3.0b	(/ (/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))) a)
12.1b	(/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

58×	`times-frac`
55×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`distribute-lft-out`
12×	`associate-/l*`
10×	`associate-/r/`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `distribute-rgt-neg-in` `div-exp`
6×	`flip3-+` `flip-+` `div-inv`
5×	`pow1`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `unsub-neg` `neg-log` `flip--` `associate-/l/`

Counts

4 → 122

Calls

4 calls:

8.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
14.0ms	(/ (/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))) a)
13.0ms	(/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series122.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
40.0ms	(/ (/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))) a)
56.0ms	(/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4986	2465
1	4986	2465

prune138.0ms

Filtered

100 candidates to 134 candidates (-34.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	134	9	143

Merged error: 6.9b

Counts

143 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `unsub-neg` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

11.0ms	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5114	1196

prune107.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	90	10	100

Merged error: 6.9b

Counts

100 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (/ a (* (cbrt a) (cbrt a))) (/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))))
0.9b	(/ (* (/ a (* (cbrt a) (cbrt a))) (/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))) (cbrt a))
0.9b	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
39×	`add-cbrt-cube`
36×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
28×	`times-frac`
21×	`cbrt-undiv` `div-exp` `associate-r`
20×	`add-cube-cbrt`
16×	`prod-exp` `cbrt-unprod`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1` `associate-l`
6×	`cbrt-prod` `associate-/r*`
4×	`distribute-rgt-neg-in` `unswap-sqr`
3×	`sqrt-prod` `div-inv` `associate-/l/`
2×	`frac-times` `flip3-+` `sqrt-div` `associate-r/` `associate-l/` `sum-log` `associate-/r/` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `unsub-neg` `pow-prod-down` `neg-log` `clear-num` `-commutative` `flip--` `associate-/l`

Counts

4 → 127

Calls

4 calls:

20.0ms	(* (/ a (* (cbrt a) (cbrt a))) (/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))))
19.0ms	(/ (* (/ a (* (cbrt a) (cbrt a))) (/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))) (cbrt a))
8.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(* (/ a (* (cbrt a) (cbrt a))) (/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))))
47.0ms	(/ (* (/ a (* (cbrt a) (cbrt a))) (/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))) (cbrt a))
16.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4986	2398
1	4986	2398

prune117.0ms

Filtered

96 candidates to 139 candidates (-44.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	138	11	149

Merged error: 6.9b

Counts

149 → 11

regimes310.0ms

Accuracy

93.3% (1.6b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 28.9b

bsearch700.0ms

Steps

Iters	Range	Point
10	6.7241623180276495e+125	2.7444084895603776e+144	1.1464830517773706e+127
10	8.855607528160837e-200	2.8442880663450218e-183	3.1101824716100656e-199
9	-4.5308935369177574e+17	-12218420085.200514	-4.460103823913966e+17

Iters

Range

Point

6.7241623180276495e+125

2.7444084895603776e+144

1.1464830517773706e+127

8.855607528160837e-200

2.8442880663450218e-183

3.1101824716100656e-199

-4.5308935369177574e+17

-12218420085.200514

-4.460103823913966e+17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	58
1	44	58

end0.0ms

analyze392.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample1.1s

Algorithm

intervals

Results

267.0ms	1077×	body	2560	valid
222.0ms	5119×	body	80	valid
181.0ms	892×	body	1280	valid
76.0ms	456×	body	640	valid
33.0ms	106×	body	5120	valid
29.0ms	713×	body	80	nan
27.0ms	222×	body	320	valid
10.0ms	128×	body	160	valid
10.0ms	231×	body	80	invalid

Details

analyze587.0ms

sample41.0ms

simplify434.0ms

prune5.0ms

localize11.0ms

rewrite32.0ms

series66.0ms

simplify45.0ms

prune138.0ms

localize10.0ms

rewrite43.0ms

series122.0ms

simplify65.0ms

prune138.0ms

localize10.0ms

rewrite28.0ms

series82.0ms

simplify45.0ms

prune107.0ms

localize19.0ms

rewrite55.0ms

series221.0ms

simplify71.0ms

prune117.0ms

regimes310.0ms

bsearch700.0ms

simplify2.0ms

end0.0ms

analyze392.0ms

sample1.1s

Profiling