Details

sample314.0ms

Algorithm

intervals

Results

9.0ms	196×	body	80	valid
7.0ms	37×	body	1280	valid
7.0ms	26×	body	2560	valid
4.0ms	11×	body	640	valid
3.0ms	73×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify15.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 32.2b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.5b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
19.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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

series299.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms	(- (* b_2 b_2) (* a c))
80.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify144.0ms

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

prune224.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 4.6b

Counts

93 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
2.9b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.6b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
19.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 200

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
220.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
254.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	708	3365
1	3231	3197
2	5001	3171

prune448.0ms

Filtered

212 candidates to 142 candidates (67.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	1	6	7
Picked	1	0	1
Done	1	0	1
Total	212	9	221

Merged error: 4.5b

Counts

221 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.6b	(- (* b_2 b_2) (* a c))
2.9b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
19.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 485

Calls

4 calls:

13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0ms	(- (* b_2 b_2) (* a c))
30.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
32.0ms	(- (* b_2 b_2) (* a c))
206.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1525	8627
1	5002	7984

prune945.0ms

Filtered

497 candidates to 298 candidates (60.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	497	0	497
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	497	9	506

Merged error: 4.5b

Counts

506 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
19.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

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:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (49.0ms)

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

prune222.0ms

Filtered

174 candidates to 86 candidates (49.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	174	9	183

Merged error: 4.5b

Counts

183 → 9

regimes211.0ms

Accuracy

91.3% (2.3b remaining)

Error of 8.0b against oracle of 5.7b and baseline of 32.1b

bsearch136.0ms

Steps

Iters	Range	Point
7	3.263606559388633e+51	2.0290859359939484e+53	1.414047295565528e+53
7	-2.999445374281946e-225	-1.6701016132161723e-226	-2.551072681877994e-226
10	-1.563367407659085e+162	-1.2401372487940452e+151	-1.9482375324732485e+151

Iters

Range

Point

3.263606559388633e+51

2.0290859359939484e+53

1.414047295565528e+53

-2.999445374281946e-225

-1.6701016132161723e-226

-2.551072681877994e-226

-1.563367407659085e+162

-1.2401372487940452e+151

-1.9482375324732485e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

258.0ms	1065×	body	2560	valid
252.0ms	5911×	body	80	valid
168.0ms	862×	body	1280	valid
116.0ms	2880×	body	80	nan
75.0ms	452×	body	640	valid
34.0ms	110×	body	5120	valid
28.0ms	227×	body	320	valid
9.0ms	119×	body	160	valid

Details

sample314.0ms

simplify15.0ms

prune4.0ms

localize34.0ms

rewrite33.0ms

series299.0ms

simplify144.0ms

prune224.0ms

localize11.0ms

rewrite48.0ms

series570.0ms

simplify109.0ms

prune448.0ms

localize11.0ms

rewrite94.0ms

series537.0ms

simplify108.0ms

prune945.0ms

localize9.0ms

rewrite35.0ms

series326.0ms

simplify69.0ms

prune222.0ms

regimes211.0ms

bsearch136.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling