Details

analyze606.0ms

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

sample45.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
8.0ms	166×	body	80	valid
6.0ms	26×	body	1280	valid
3.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	4×	body	80	invalid

simplify475.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune6.0ms

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: 33.0b

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)
1.4b	(- (* b_2 b_2) (* a c))
1.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

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:

29.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune139.0ms

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: 5.8b

Counts

102 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.8b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
10×	`associate-/r/`
9×	`associate-/r*` `sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`div-inv` `distribute-lft-out--` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 123

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
44.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4961	2488
1	4961	2488

prune141.0ms

Filtered

102 candidates to 135 candidates (-32.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	135	9	144

Merged error: 5.7b

Counts

144 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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_2 b_2) (* a c))) b_2))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4871	1374
1	4871	1374

prune109.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	11	102

Merged error: 5.7b

Counts

102 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.4b	(- (* b_2 b_2) (* a c))
1.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 175

Calls

4 calls:

15.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
7.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5176	3699

prune125.0ms

Filtered

103 candidates to 187 candidates (-81.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	187	11	198

Merged error: 5.7b

Counts

198 → 11

regimes379.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.2b

bsearch55.0ms

Steps

Iters	Range	Point
6	2.9554166031949814e+104	1.7558061727487926e+105	1.6886076224176782e+105
3	3.0398939818814196e-144	3.955038634091389e-144	3.0970905226445423e-144
7	-1.894739840907478e+143	-1.0967546375658848e+142	-2.864560261090598e+142

Iters

Range

Point

2.9554166031949814e+104

1.7558061727487926e+105

1.6886076224176782e+105

3.0398939818814196e-144

3.955038634091389e-144

3.0970905226445423e-144

-1.894739840907478e+143

-1.0967546375658848e+142

-2.864560261090598e+142

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	150	58
1	150	58

end0.0ms

sample1.1s

Algorithm

intervals

Results

269.0ms	1014×	body	2560	valid
232.0ms	5151×	body	80	valid
195.0ms	901×	body	1280	valid
78.0ms	473×	body	640	valid
34.0ms	106×	body	5120	valid
33.0ms	797×	body	80	nan
29.0ms	231×	body	320	valid
11.0ms	244×	body	80	invalid
10.0ms	124×	body	160	valid

Details

analyze606.0ms

sample45.0ms

simplify475.0ms

prune6.0ms

localize11.0ms

rewrite51.0ms

series60.0ms

simplify61.0ms

prune139.0ms

localize10.0ms

rewrite35.0ms

series120.0ms

simplify63.0ms

prune141.0ms

localize10.0ms

rewrite29.0ms

series82.0ms

simplify62.0ms

prune109.0ms

localize11.0ms

rewrite40.0ms

series67.0ms

simplify65.0ms

prune125.0ms

regimes379.0ms

bsearch55.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling