Details

sample42.0ms

Algorithm

intervals

Results

19.0ms	276×	body	80	valid
5.0ms	77×	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: 18.0b

Counts

2 → 1

localize112.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	406	2988
1	1431	1956
2	5002	1869

prune347.0ms

Filtered

152 candidates to 80 candidates (52.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	7	153

Merged error: 6.6b

Counts

153 → 7

localize118.0ms

Local error

Found 4 expressions with local error:

13.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 76

Calls

4 calls:

5.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(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)))

simplify118.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (109.0ms)

Iter	Nodes	Cost
0	249	756
1	969	641
2	4038	626
3	5001	624

prune355.0ms

Filtered

88 candidates to 79 candidates (89.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	88	7	95

Merged error: 6.6b

Counts

95 → 7

localize131.0ms

Local error

Found 4 expressions with local error:

5.8b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 83

Calls

4 calls:

5.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

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))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	428	1492
1	1667	1341
2	5002	1297

prune443.0ms

Filtered

95 candidates to 79 candidates (83.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	93	9	102

Merged error: 6.5b

Counts

102 → 9

localize134.0ms

Local error

Found 4 expressions with local error:

14.3b	(- (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 83

Calls

4 calls:

5.0ms	(- (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	430	1618
1	1669	1373
2	5002	1313

prune453.0ms

Filtered

95 candidates to 79 candidates (83.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	95	9	104

Merged error: 6.5b

Counts

104 → 9

regimes203.0ms

Accuracy

87.9% (1.5b remaining)

Error of 9.2b against oracle of 7.7b and baseline of 20.1b

bsearch130.0ms

Steps

Iters	Range		Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
5	-2.783673024614503e+98	-8.233152822480874e+97	-2.720129631643668e+98

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	58
1	49	58

end0.0ms

sample1.0s

Algorithm

intervals

Results

598.0ms	8737×	body	80	valid
192.0ms	2866×	body	80	nan