Details

sample236.0ms

Algorithm

intervals

Results

190.0ms	191×	body	80	valid
10.0ms	38×	body	1280	valid
7.0ms	25×	body	2560	valid
4.0ms	83×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune5.0ms

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: 35.0b

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)
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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 → 91

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))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune167.0ms

Filtered

103 candidates to 72 candidates (30.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	90	13	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	13	104

Merged error: 5.9b

Counts

104 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
2.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`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 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune260.0ms

Filtered

196 candidates to 144 candidates (26.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	190	6	196
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	196	13	209

Merged error: 5.8b

Counts

209 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
2.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.9b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`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 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
24.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
55.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
40.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1530	7327
1	5001	6764

prune349.0ms

Filtered

449 candidates to 297 candidates (33.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	446	3	449
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	448	14	462

Merged error: 5.8b

Counts

462 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

23.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1746	7647
1	5002	6938

prune287.0ms

Filtered

435 candidates to 171 candidates (60.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	433	2	435
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	437	12	449

Merged error: 5.8b

Counts

449 → 12

regimes321.0ms

Accuracy

93.5% (1.6b remaining)

Error of 7.2b against oracle of 5.7b and baseline of 29.8b

bsearch84.0ms

Steps

Iters	Range	Point
7	1.7149020832264559e+31	1.2781008435600503e+33	1.2621837101452211e+33
8	-1.8476331085109416e-273	-7.661129585585241e-278	-7.822444393994548e-278
7	-1.9829548386146398e+113	-1.1476665911793802e+112	-9.36208266929759e+112

Iters

Range

Point

1.7149020832264559e+31

1.2781008435600503e+33

1.2621837101452211e+33

-1.8476331085109416e-273

-7.661129585585241e-278

-7.822444393994548e-278

-1.9829548386146398e+113

-1.1476665911793802e+112

-9.36208266929759e+112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

267.0ms	1044×	body	2560	valid
260.0ms	5847×	body	80	valid
200.0ms	923×	body	1280	valid
124.0ms	2952×	body	80	nan
77.0ms	460×	body	640	valid
31.0ms	100×	body	5120	valid
30.0ms	239×	body	320	valid
10.0ms	114×	body	160	valid

Details

sample236.0ms

simplify13.0ms

prune5.0ms

localize12.0ms

rewrite33.0ms

series68.0ms

simplify42.0ms

prune167.0ms

localize11.0ms

rewrite42.0ms

series121.0ms

simplify101.0ms

prune260.0ms

localize11.0ms

rewrite115.0ms

series115.0ms

simplify94.0ms

prune349.0ms

localize10.0ms

rewrite67.0ms

series61.0ms

simplify99.0ms

prune287.0ms

regimes321.0ms

bsearch84.0ms

simplify2.0ms

end0.0ms

sample1.4s

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