Details

sample332.0ms

Algorithm

intervals

Results

10.0ms	44×	body	2560	valid
8.0ms	188×	body	80	valid
6.0ms	33×	body	1280	valid
6.0ms	105×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify14.0ms

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

prune28.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 36.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (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)))

simplify138.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

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

prune413.0ms

Filtered

92 candidates to 69 candidates (25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 5.6b

Counts

93 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.3b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.0b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
26.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

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))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (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)
52.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (78.0ms)

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

prune1.4s

Filtered

218 candidates to 147 candidates (32.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	218	10	228

Merged error: 5.6b

Counts

228 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.3b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.3b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
26.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
29.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
51.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
41.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune4.9s

Filtered

503 candidates to 303 candidates (39.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	502	1	503
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	503	10	513

Merged error: 5.6b

Counts

513 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (/ a (/ (- (neg b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
5.5b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
16.5b	(- (neg b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
26.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

891×	`times-frac`
581×	`add-sqr-sqrt`
506×	`*-un-lft-identity`
358×	`add-cube-cbrt`
111×	`difference-of-squares`
89×	`associate-/l*`
80×	`log-prod` `exp-sum`
74×	`distribute-lft-out--`
43×	`sqrt-prod`
37×	`distribute-rgt-neg-in`
17×	`div-inv`
13×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`cbrt-undiv` `exp-prod` `div-exp`
4×	`sqrt-div` `associate-/r/`
3×	`flip3--` `associate-/r*` `log-pow` `flip--`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `neg-log` `clear-num` `rem-exp-log` `associate-/l/`

Counts

4 → 432

Calls

4 calls:

30.0ms	(/ (/ a (/ (- (neg b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
8.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(- (neg b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (/ a (/ (- (neg b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c)))))) c)) a)
12.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(- (neg b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

444 → 444

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1788	9015
1	5002	7993

prune4.5s

Filtered

444 candidates to 257 candidates (42.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	442	2	444
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	443	11	454

Merged error: 5.6b

Counts

454 → 11

regimes394.0ms

Accuracy

90% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 31.9b

bsearch185.0ms

Steps

Iters	Range	Point
8	1.6057862524760164e+39	1.0779599711549289e+43	9.437195709563966e+40
8	-4.1001721289719087e-224	-2.0859121858352512e-228	-2.9351283692529764e-228
10	-8.56091843340189e+161	-1.1976703346365243e+147	-1.2169487858482428e+147

Iters

Range

Point

1.6057862524760164e+39

1.0779599711549289e+43

9.437195709563966e+40

-4.1001721289719087e-224

-2.0859121858352512e-228

-2.9351283692529764e-228

-8.56091843340189e+161

-1.1976703346365243e+147

-1.2169487858482428e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample1.3s

Algorithm

intervals

Results

259.0ms	1092×	body	2560	valid
238.0ms	5797×	body	80	valid
178.0ms	911×	body	1280	valid
112.0ms	2910×	body	80	nan
74.0ms	494×	body	640	valid
33.0ms	116×	body	5120	valid
26.0ms	230×	body	320	valid
7.0ms	94×	body	160	valid

Details

sample332.0ms

simplify14.0ms

prune28.0ms

localize12.0ms

rewrite30.0ms

series69.0ms

simplify138.0ms

prune413.0ms

localize11.0ms

rewrite53.0ms

series117.0ms

simplify109.0ms

prune1.4s

localize11.0ms

rewrite97.0ms

series118.0ms

simplify103.0ms

prune4.9s

localize15.0ms

rewrite93.0ms

series81.0ms

simplify102.0ms

prune4.5s

regimes394.0ms

bsearch185.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling