Details

analyze616.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

12.0ms	43×	body	2560	valid
7.0ms	169×	body	80	valid
5.0ms	23×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	17×	body	80	nan
0.0ms	5×	body	160	valid
0.0ms	8×	body	80	invalid
0.0ms	1×	body	5120	valid

simplify366.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

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: 34.8b

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)
0.4b	(- (* b_2 b_2) (* a c))
1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

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-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify143.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune129.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 6.1b

Counts

93 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

12.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (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))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	564	2096
1	2553	1897
2	5001	1761

prune123.0ms

Filtered

86 candidates to 174 candidates (-102.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	173	7	180

Merged error: 6.0b

Counts

180 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `sum-log` `add-cbrt-cube` `distribute-lft-out`
2×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip--` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	205	516
1	740	480
2	2640	460
3	5002	456

prune92.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 6.0b

Counts

79 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.7b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune201.0ms

Filtered

146 candidates to 218 candidates (-49.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	2	4
Picked	1	0	1
Done	0	2	2
Total	219	6	225

Merged error: 6.0b

Counts

225 → 6

regimes319.0ms

Accuracy

90.5% (2.5b remaining)

Error of 8.1b against oracle of 5.6b and baseline of 31.8b

bsearch510.0ms

Steps

Iters	Range	Point
7	3.1504352188957632e+22	5.693559301591682e+23	3.741500408843493e+22
8	-4.1409031495419937e-227	-5.754951366226209e-230	-1.4104005242205834e-227
6	-9.531516042398887e+129	-2.3338329035268152e+129	-4.8489798423074927e+129

Iters

Range

Point

3.1504352188957632e+22

5.693559301591682e+23

3.741500408843493e+22

-4.1409031495419937e-227

-5.754951366226209e-230

-1.4104005242205834e-227

-9.531516042398887e+129

-2.3338329035268152e+129

-4.8489798423074927e+129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

analyze400.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

290.0ms	1125×	body	2560	valid
223.0ms	5115×	body	80	valid
182.0ms	883×	body	1280	valid
74.0ms	453×	body	640	valid
30.0ms	735×	body	80	nan
29.0ms	98×	body	5120	valid
26.0ms	219×	body	320	valid
9.0ms	219×	body	80	invalid
9.0ms	107×	body	160	valid

Details

analyze616.0ms

sample40.0ms

simplify366.0ms

prune5.0ms

localize11.0ms

rewrite42.0ms

series62.0ms

simplify143.0ms

prune129.0ms

localize9.0ms

rewrite33.0ms

series64.0ms

simplify67.0ms

prune123.0ms

localize13.0ms

rewrite23.0ms

series55.0ms

simplify77.0ms

prune92.0ms

localize11.0ms

rewrite50.0ms

series117.0ms

simplify111.0ms

prune201.0ms

regimes319.0ms

bsearch510.0ms

simplify2.0ms

end0.0ms

analyze400.0ms

sample1.1s

Profiling