Details

sample293.0ms

Algorithm

intervals

Results

10.0ms	185×	body	80	valid
8.0ms	36×	body	2560	valid
6.0ms	31×	body	1280	valid
4.0ms	91×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify13.0ms

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

prune6.0ms

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: 34.5b

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	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
22.7b	(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:

9.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
20.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
73.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify139.0ms

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

prune366.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	10	93

Merged error: 5.5b

Counts

93 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

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

series318.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
35.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (50.0ms)

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

prune409.0ms

Filtered

174 candidates to 86 candidates (49.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	5	3	8
Picked	0	1	1
Done	1	0	1
Total	176	8	184

Merged error: 5.5b

Counts

184 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.5b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.2b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

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)
11.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
213.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
247.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (79.0ms)

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

prune680.0ms

Filtered

212 candidates to 141 candidates (66.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	213	7	220

Merged error: 5.5b

Counts

220 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.0b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.5b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
25.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* b_2 b_2) (* a c))
224.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
190.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1525	8628
1	5001	7984

prune1.4s

Filtered

497 candidates to 298 candidates (60.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	497	0	497
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	497	7	504

Merged error: 5.5b

Counts

504 → 7

regimes295.0ms

Accuracy

90.1% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 31.7b

bsearch168.0ms

Steps

Iters	Range	Point
9	20077549570157524.0	7.523642411179348e+25	1.0455453897644399e+22
9	-4.089389642753783e-272	-9.492949728360576e-279	-6.331142239403903e-278
8	-1.1087701160625577e+106	-9.716082514065232e+101	-1.5972767397279323e+105

Iters

Range

Point

20077549570157524.0

7.523642411179348e+25

1.0455453897644399e+22

-4.089389642753783e-272

-9.492949728360576e-279

-6.331142239403903e-278

-1.1087701160625577e+106

-9.716082514065232e+101

-1.5972767397279323e+105

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

253.0ms	1042×	body	2560	valid
249.0ms	5907×	body	80	valid
173.0ms	918×	body	1280	valid
117.0ms	2920×	body	80	nan
70.0ms	452×	body	640	valid
28.0ms	100×	body	5120	valid
25.0ms	216×	body	320	valid
9.0ms	113×	body	160	valid

Details

sample293.0ms

simplify13.0ms

prune6.0ms

localize11.0ms

rewrite42.0ms

series295.0ms

simplify139.0ms

prune366.0ms

localize10.0ms

rewrite36.0ms

series318.0ms

simplify69.0ms

prune409.0ms

localize12.0ms

rewrite47.0ms

series558.0ms

simplify108.0ms

prune680.0ms

localize14.0ms

rewrite84.0ms

series511.0ms

simplify105.0ms

prune1.4s

regimes295.0ms

bsearch168.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling