Details

sample314.0ms

Algorithm

intervals

Results

10.0ms	175×	body	80	valid
10.0ms	36×	body	2560	valid
6.0ms	28×	body	1280	valid
3.0ms	18×	body	640	valid
3.0ms	70×	body	80	nan
1.0ms	11×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify16.0ms

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

prune24.0ms

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: 32.5b

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	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
21.6b	(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:

11.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
70.0ms	(- (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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

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

prune243.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 4.5b

Counts

104 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.6b	(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:

4.0ms	(- (* 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)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
195.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
246.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (78.0ms)

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

prune454.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	190	6	196
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	194	12	206

Merged error: 4.5b

Counts

206 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.6b	(- (* b_2 b_2) (* a c))
2.7b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite77.0ms

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:

11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
34.0ms	(- (* b_2 b_2) (* a c))
167.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1530	7328
1	5001	6764

prune917.0ms

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	452	9	461

Merged error: 4.5b

Counts

461 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `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` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

11.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (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)))

series285.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
68.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	586	1945
1	2424	1777
2	5001	1652

prune210.0ms

Filtered

166 candidates to 80 candidates (48.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	165	10	175

Merged error: 4.5b

Counts

175 → 10

regimes222.0ms

Accuracy

96% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.6b

bsearch161.0ms

Steps

Iters	Range	Point
5	2.4830732657334904e+107	7.560458574844312e+107	5.949838845413457e+107
11	4.138069067404569e-191	1.7002785745994172e-168	5.379504553252756e-190
9	-1.269270905055957e+156	-1.2401372487940452e+151	-3.149142078055873e+153

Iters

Range

Point

2.4830732657334904e+107

7.560458574844312e+107

5.949838845413457e+107

4.138069067404569e-191

1.7002785745994172e-168

5.379504553252756e-190

-1.269270905055957e+156

-1.2401372487940452e+151

-3.149142078055873e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	32
1	46	32
2	46	32

end0.0ms

sample1.2s

Algorithm

intervals

Results

275.0ms	1124×	body	2560	valid
258.0ms	5823×	body	80	valid
175.0ms	882×	body	1280	valid
118.0ms	2875×	body	80	nan
74.0ms	476×	body	640	valid
32.0ms	93×	body	5120	valid
25.0ms	212×	body	320	valid
10.0ms	126×	body	160	valid

Details

sample314.0ms

simplify16.0ms

prune24.0ms

localize12.0ms

rewrite33.0ms

series269.0ms

simplify43.0ms

prune243.0ms

localize10.0ms

rewrite42.0ms

series537.0ms

simplify106.0ms

prune454.0ms

localize10.0ms

rewrite77.0ms

series482.0ms

simplify96.0ms

prune917.0ms

localize9.0ms

rewrite32.0ms

series285.0ms

simplify67.0ms

prune210.0ms

regimes222.0ms

bsearch161.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling