Details

sample34.0ms

Algorithm

intervals

Results

15.0ms	286×	body	80	valid
4.0ms	79×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18

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: 20.0b

Counts

2 → 1

localize117.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

659×	`add-sqr-sqrt`
289×	`sqrt-prod`
270×	`prod-diff`
265×	`*-un-lft-identity`
216×	`unswap-sqr`
182×	`difference-of-squares`
113×	`add-cube-cbrt`
108×	`associate-l`
89×	`distribute-rgt-neg-in`
87×	`distribute-lft-neg-in`
74×	`distribute-lft-out--`
36×	`swap-sqr` `*-commutative`
29×	`neg-mul-1`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 403

Calls

4 calls:

40.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
41.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm

egg-herbie

Counts

415 → 415

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	740	12242
1	2144	9625
2	5001	9326

prune653.0ms

Filtered

415 candidates to 122 candidates (29.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	407	8	415
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	408	8	416

Merged error: 7.6b

Counts

416 → 8

localize117.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
96×	`sqrt-prod`
72×	`unswap-sqr`
60×	`difference-of-squares`
56×	`*-un-lft-identity`
36×	`associate-l`
24×	`distribute-lft-out--`
12×	`swap-sqr` `*-commutative`
8×	`pow1` `add-cube-cbrt` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

43.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	219	1500
1	689	1480
2	2737	1476
3	5001	1448

prune563.0ms

Filtered

164 candidates to 92 candidates (56.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	164	8	172

Merged error: 7.6b

Counts

172 → 8

localize122.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
96×	`sqrt-prod`
72×	`unswap-sqr`
60×	`difference-of-squares`
56×	`*-un-lft-identity`
36×	`associate-l`
24×	`distribute-lft-out--`
12×	`swap-sqr` `*-commutative`
8×	`pow1` `add-cube-cbrt` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

40.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	219	1500
1	689	1480
2	2737	1476
3	5001	1448

prune651.0ms

Filtered

164 candidates to 92 candidates (56.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	164	8	172

Merged error: 7.6b

Counts

172 → 8

localize120.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-sqr-sqrt`
96×	`sqrt-prod`
72×	`unswap-sqr`
60×	`difference-of-squares`
56×	`*-un-lft-identity`
36×	`associate-l`
24×	`distribute-lft-out--`
12×	`swap-sqr` `*-commutative`
8×	`pow1` `add-cube-cbrt` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 152

Calls

4 calls:

43.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
41.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	219	1500
1	689	1480
2	2737	1476
3	5001	1448

prune531.0ms

Filtered

164 candidates to 92 candidates (56.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	164	8	172

Merged error: 7.6b

Counts

172 → 8

regimes218.0ms

Accuracy

87.5% (1.5b remaining)

Error of 8.7b against oracle of 7.2b and baseline of 19.6b

bsearch185.0ms

Steps

Iters	Range		Point
9	4.546949039871578e+116	7.0067478635952275e+121	1.799130866881706e+118
7	-5.802167618308309e+55	-1.5322109559450533e+54	-5.702871009382978e+55

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	75
1	55	75

end0.0ms

sample844.0ms

Algorithm

intervals

Results

464.0ms	8683×	body	80	valid
140.0ms	2863×	body	80	nan