Details

sample54.0ms

Algorithm

intervals

Results

12.0ms	38×	body	2560	valid
9.0ms	181×	body	80	valid
7.0ms	29×	body	1280	valid
5.0ms	96×	body	80	nan
4.0ms	20×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	9

prune3.0ms

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: 35.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

15.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	590	3305
1	2101	2212
2	5002	2128

prune315.0ms

Filtered

169 candidates to 89 candidates (52.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 5.8b

Counts

170 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 205

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
10.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series300.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify96.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	718	4221
1	3099	2976
2	5001	2863

prune304.0ms

Filtered

217 candidates to 97 candidates (44.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	219	7	226

Merged error: 5.7b

Counts

226 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log` `distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

14.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
13.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify89.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	656	3422
1	2594	2238
2	5001	2193

prune282.0ms

Filtered

177 candidates to 90 candidates (50.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	177	7	184

Merged error: 5.7b

Counts

184 → 7

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	2	2
Total	7	7

Merged error: 5.7b

Counts

7 → 7

regimes227.0ms

Accuracy

82% (5.1b remaining)

Error of 11.0b against oracle of 5.9b and baseline of 34.1b

bsearch97.0ms

Steps

Iters	Range		Point
6	2087876908255263.8	9946277058360104.0	9787957843074626.0
8	-1.2666093820352762e-45	-1.3998468795388318e-48	-1.4259994173393273e-48

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	16
1	36	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

327.0ms	1064×	body	2560	valid
320.0ms	5940×	body	80	valid
212.0ms	854×	body	1280	valid
147.0ms	2835×	body	80	nan
87.0ms	435×	body	640	valid
43.0ms	108×	body	5120	valid
31.0ms	213×	body	320	valid
11.0ms	111×	body	160	valid

Details

sample54.0ms

simplify15.0ms

prune3.0ms

localize11.0ms

rewrite41.0ms

series281.0ms

simplify82.0ms

prune315.0ms

localize13.0ms

rewrite38.0ms

series300.0ms

simplify96.0ms

prune304.0ms

localize12.0ms

rewrite41.0ms

series283.0ms

simplify89.0ms

prune282.0ms

localize4.0ms

rewrite0.0ms

series0.0ms

simplify3.0ms

prune0.0ms

regimes227.0ms

bsearch97.0ms

simplify1.0ms

end0.0ms

sample1.4s

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