Details

sample59.0ms

Algorithm

intervals

Results

12.0ms	524×	pre	80	true
11.0ms	112×	body	320	valid
8.0ms	268×	body	80	nan
7.0ms	103×	body	160	valid
2.0ms	15×	body	640	valid
1.0ms	26×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

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: 53.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
28.2b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

447×	`add-sqr-sqrt`
336×	`associate-l`
330×	`prod-diff`
300×	`*-un-lft-identity`
232×	`add-cube-cbrt`
183×	`associate-r`
111×	`unswap-sqr`
72×	`swap-sqr`
64×	`*-commutative`
60×	`times-frac`
28×	`distribute-lft-out`
17×	`distribute-rgt-neg-in`
15×	`fma-neg` `difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
10×	`fma-def` `add-log-exp`
9×	`pow1`
6×	`distribute-lft-out--`
5×	`associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `neg-log` `clear-num` `flip--` `div-inv`

Counts

4 → 536

Calls

4 calls:

34.0ms	(- (* b b) (* (* 3.0 a) c))
40.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(* (* 3.0 a) c)
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series253.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
20.0ms	(* (* 3.0 a) c)
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify100.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1399	8928
1	5001	6424

prune571.0ms

Filtered

548 candidates to 171 candidates (31.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	539	9	548
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	540	9	549

Merged error: 2.6b

Counts

549 → 9

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 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune20.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Merged error: 2.6b

Counts

9 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.3b	(/ (* a c) b)
0.3b	(* -1.5 (/ (* a c) b))
0.4b	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

1180×	`times-frac`
860×	`associate-r`
853×	`add-sqr-sqrt`
531×	`*-un-lft-identity`
527×	`add-cube-cbrt`
344×	`associate-l`
156×	`unswap-sqr`
114×	`*-commutative`
91×	`associate-/l*`
49×	`add-exp-log` `add-cbrt-cube`
36×	`associate-*r/`
21×	`associate-/r*` `associate-/l/`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp` `div-inv`
6×	`clear-num` `un-div-inv`
5×	`pow1`
4×	`frac-2neg`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`pow-prod-down`

Counts

3 → 875

Calls

3 calls:

7.0ms	(/ (* a c) b)
17.0ms	(* -1.5 (/ (* a c) b))
43.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

series73.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(/ (* a c) b)
27.0ms	(* -1.5 (/ (* a c) b))
28.0ms	(/ (* -1.5 (/ (* a c) b)) (* 3.0 a))

simplify154.0ms

Algorithm

egg-herbie

Counts

884 → 884

Iterations

Useful iterations: 1 (64.0ms)

Iter	Nodes	Cost
0	4176	8764
1	5001	8706

prune1.9s

Filtered

884 candidates to 630 candidates (71.3%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	871	13	884
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	872	21	893

Merged error: 2.6b

Counts

893 → 21

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series722.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt a)
176.0ms	(cbrt a)
186.0ms	(cbrt a)
179.0ms	(cbrt a)

simplify132.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	42	172
1	83	160
2	195	152
3	699	152
4	4132	152
5	5001	152

prune201.0ms

Filtered

64 candidates to 56 candidates (87.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	59	5	64
Fresh	6	13	19
Picked	1	0	1
Done	0	1	1
Total	66	19	85

Merged error: 2.6b

Counts

85 → 19

regimes358.0ms

Accuracy

17% (2.9b remaining)

Error of 5.6b against oracle of 2.7b and baseline of 6.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	27
1	27	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

350.0ms	3566×	body	320	valid
318.0ms	16079×	pre	80	true
253.0ms	8079×	body	80	nan
201.0ms	3001×	body	160	valid
69.0ms	520×	body	640	valid
30.0ms	913×	body	80	valid