Details

sample36.0ms

Algorithm

intervals

Results

15.0ms	281×	body	80	valid
5.0ms	113×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	18
1	79	18
2	136	18
3	161	18
4	173	18
5	177	18
6	177	18

prune8.0ms

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: 21.6b

Counts

2 → 1

localize120.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
49×	`sqrt-prod`
38×	`*-un-lft-identity`
36×	`unswap-sqr`
32×	`difference-of-squares`
18×	`associate-l`
14×	`distribute-lft-out--`
12×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `swap-sqr` `*-commutative`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `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 → 105

Calls

4 calls:

40.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	313	1102
1	1029	1062
2	4175	1047
3	5001	1031

prune297.0ms

Filtered

117 candidates to 72 candidates (38.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	110	7	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	7	118

Merged error: 7.1b

Counts

118 → 7

localize122.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt`
73×	`sqrt-prod`
54×	`unswap-sqr`
47×	`*-un-lft-identity` `difference-of-squares`
27×	`associate-l`
20×	`distribute-lft-out--`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 126

Calls

4 calls:

41.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
30.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify127.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	275	1293
1	905	1272
2	3581	1261
3	5002	1239

prune383.0ms

Filtered

138 candidates to 78 candidates (43.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	139	6	145

Merged error: 7.1b

Counts

145 → 6

localize129.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite118.0ms

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` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 144

Calls

4 calls:

28.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
31.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
82.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	196	1452
1	568	1432
2	2007	1428
3	5001	1396

prune470.0ms

Filtered

156 candidates to 84 candidates (46.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	156	6	162

Merged error: 7.1b

Counts

162 → 6

localize125.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.3b	(/ (* a c) b)
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

300×	`*-un-lft-identity`
178×	`add-sqr-sqrt`
156×	`times-frac`
136×	`distribute-lft-out--`
80×	`associate-l`
76×	`add-cube-cbrt`
45×	`associate-r`
40×	`distribute-rgt-neg-in`
33×	`unswap-sqr`
28×	`difference-of-squares`
24×	`sqrt-prod`
22×	`associate-/l*`
18×	`*-commutative`
15×	`associate-/r*`
14×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-sub` `div-exp`
3×	`swap-sqr`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `sum-log` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out` `associate--r+`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 278

Calls

4 calls:

40.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
8.0ms	(/ (* a c) b)
32.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
21.0ms	(/ (* a c) b)
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	973	2998
1	4518	2909
2	5001	2901

prune764.0ms

Filtered

290 candidates to 155 candidates (46.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	285	5	290
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	287	9	296

Merged error: 6.3b

Counts

296 → 9

regimes226.0ms

Accuracy

89.4% (1.5b remaining)

Error of 8.1b against oracle of 6.6b and baseline of 20.7b

bsearch93.0ms

Steps

Iters	Range		Point
0	1.3836563058951246e+50	1.390978468581987e+50	1.3873173872385558e+50
9	-1.1122706149547327e+40	-5.692476046189149e+32	-1.087684368982218e+40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	65
1	56	65

end0.0ms

sample846.0ms

Algorithm

intervals

Results

455.0ms	8767×	body	80	valid
132.0ms	2796×	body	80	nan