Details

analyze580.0ms

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

sample42.0ms

Algorithm

intervals

Results

11.0ms	39×	body	2560	valid
7.0ms	160×	body	80	valid
6.0ms	27×	body	1280	valid
3.0ms	15×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	8×	body	320	valid
1.0ms	17×	body	80	nan
0.0ms	4×	body	160	valid
0.0ms	6×	body	80	invalid

simplify459.0ms

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: 34.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (neg b_2) (sqrt (- (* 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

prune143.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 5.1b

Counts

102 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
3.9b	(/ (/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))) a)
8.7b	(/ (* a c) (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

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))
13.0ms	(/ (/ (* 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)))
4.0ms	(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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4986	2465
1	4986	2465

prune142.0ms

Filtered

100 candidates to 134 candidates (-34.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	135	9	144

Merged error: 5.0b

Counts

144 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
0.4b	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
8.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
47.0ms	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
13.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5114	1196

prune103.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Merged error: 4.8b

Counts

100 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
0.4b	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
14.3b	(/ (* a c) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

11.0ms	(* a (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
8.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
12.0ms	(/ (* a c) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* a (+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2)))
13.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (neg b_2))
43.0ms	(/ (* a c) (* a (+ (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

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5249	1067

prune77.0ms

Filtered

68 candidates to 90 candidates (-32.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	90	9	99

Merged error: 4.8b

Counts

99 → 9

regimes275.0ms

Accuracy

90.8% (2.2b remaining)

Error of 7.7b against oracle of 5.5b and baseline of 29.6b

bsearch444.0ms

Steps

Iters	Range		Point
1	6.702224663973177e+24	7.053541985987684e+24	6.965712655484056e+24
9	8.147604587979608e-119	1.9498578354619682e-110	8.282282201376137e-119
7	-1.130439217872028e+121	-2.807608538967146e+119	-1.027656210917247e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	58
1	45	58

end0.0ms

analyze388.0ms

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

284.0ms	1140×	body	2560	valid
225.0ms	5051×	body	80	valid
175.0ms	888×	body	1280	valid
74.0ms	471×	body	640	valid
31.0ms	719×	body	80	nan
27.0ms	92×	body	5120	valid
27.0ms	231×	body	320	valid
11.0ms	256×	body	80	invalid
10.0ms	127×	body	160	valid

Details

analyze580.0ms

sample42.0ms

simplify459.0ms

prune5.0ms

localize11.0ms

rewrite30.0ms

series65.0ms

simplify45.0ms

prune143.0ms

localize10.0ms

rewrite42.0ms

series122.0ms

simplify68.0ms

prune142.0ms

localize10.0ms

rewrite27.0ms

series82.0ms

simplify50.0ms

prune103.0ms

localize10.0ms

rewrite40.0ms

series89.0ms

simplify65.0ms

prune77.0ms

regimes275.0ms

bsearch444.0ms

simplify2.0ms

end0.0ms

analyze388.0ms

sample1.1s

Profiling