Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	280×	body	80	valid
5.0ms	83×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	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: 17.8b

Counts

2 → 1

localize124.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.9b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite202.0ms

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:

37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify143.0ms

Algorithm

egg-herbie

Counts

415 → 415

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	733	12242
1	2067	9625
2	5001	9326

prune543.0ms

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: 6.4b

Counts

416 → 8

localize127.0ms

Local error

Found 4 expressions with local error:

6.7b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite602.0ms

Algorithm

rewrite-expression-head

Rules

4608×	`sqrt-prod`
3648×	`add-sqr-sqrt`
2716×	`*-un-lft-identity`
1769×	`associate-l`
1640×	`prod-diff`
1173×	`unswap-sqr`
1098×	`swap-sqr`
982×	`distribute-lft-out--`
906×	`difference-of-squares`
632×	`add-cube-cbrt`
497×	`distribute-rgt-neg-in`
495×	`distribute-lft-neg-in`
300×	`associate-r`
200×	`*-commutative`
165×	`neg-mul-1`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 1805

Calls

4 calls:

170.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
235.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify830.0ms

Algorithm

egg-herbie

Counts

1817 → 1817

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	1953	110861
1	4777	51013
2	5001	51003

prune801.0ms

Filtered

1817 candidates to 148 candidates (8.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1816	1	1817
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	1817	8	1825

Merged error: 6.4b

Counts

1825 → 8

localize119.0ms

Local error

Found 4 expressions with local error:

11.1b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
54×	`*-un-lft-identity` `unswap-sqr`
48×	`cbrt-prod`
45×	`difference-of-squares`
29×	`associate-l`
24×	`sqrt-prod`
18×	`distribute-lft-out--`
10×	`add-cube-cbrt` `fma-def`
9×	`swap-sqr` `*-commutative`
8×	`add-log-exp`
5×	`pow1` `distribute-rgt-neg-in`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3--` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 139

Calls

4 calls:

46.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
43.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
101.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	478	1616
1	1716	1535
2	5002	1508

prune504.0ms

Filtered

151 candidates to 95 candidates (62.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	150	9	159

Merged error: 6.4b

Counts

159 → 9

localize125.0ms

Local error

Found 4 expressions with local error:

20.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (* -1 b))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
54×	`unswap-sqr`
48×	`cbrt-prod`
45×	`difference-of-squares`
43×	`*-un-lft-identity`
27×	`associate-l`
24×	`sqrt-prod`
18×	`distribute-lft-out--`
9×	`swap-sqr` `*-commutative`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`pow1/3` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 120

Calls

4 calls:

41.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
1.0ms	(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (* -1 b))
25.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series363.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
86.0ms	(fma (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (* -1 b))
102.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
100.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	402	1418
1	1187	1362
2	4279	1352
3	5001	1349

prune465.0ms

Filtered

132 candidates to 83 candidates (62.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	132	9	141

Merged error: 6.4b

Counts

141 → 9

regimes198.0ms

Accuracy

91.2% (1.1b remaining)

Error of 8.8b against oracle of 7.8b and baseline of 20.0b

bsearch179.0ms

Steps

Iters	Range		Point
7	8.70788314804275e+92	3.0899898012220906e+94	1.214024031535037e+94
10	-2.7851241427016145e+159	-9.354797223898085e+144	-1.024958645589419e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	58
1	48	58

end0.0ms

sample850.0ms

Algorithm

intervals

Results

454.0ms	8711×	body	80	valid
145.0ms	2987×	body	80	nan