Details

analyze456.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample47.0ms

Algorithm

intervals

Results

12.0ms	39×	body	2560	valid
8.0ms	153×	body	80	valid
8.0ms	32×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	19×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	11×	body	80	invalid

simplify163.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	1794	16
1	1794	16

prune12.0ms

Filtered

1 candidates to 1 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: 36.2b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.6b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 69

Calls

4 calls:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4961	1226
1	4961	1226

prune172.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 4.4b

Counts

83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 3.0 (* a c)))
5.3b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
8.3b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
23.6b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`sqrt-prod`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`distribute-rgt-neg-in` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

4.0ms	(- (* b b) (* 3.0 (* a c)))
17.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 3.0 (* a c)))
46.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
57.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify62.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4954	2399
1	4954	2399

prune194.0ms

Filtered

79 candidates to 125 candidates (-58.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	6	6
Picked	1	0	1
Done	1	0	1
Total	126	7	133

Merged error: 4.4b

Counts

133 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
0.3b	(* 3.0 (* a c))
0.8b	(- (* b b) (* 3.0 (* a c)))
23.6b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `*-commutative`

Counts

4 → 61

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(* 3.0 (* a c))
11.0ms	(- (* b b) (* 3.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4952	873
1	4952	873

prune128.0ms

Filtered

51 candidates to 73 candidates (-43.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 4.3b

Counts

80 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (* a c))
0.8b	(- (* b b) (* 3.0 (* a c)))
1.3b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
23.6b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 58

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
4.0ms	(- (* b b) (* 3.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
9.0ms	(- (* b b) (* 3.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4913	809
1	4913	809

prune92.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	70	9	79

Merged error: 4.3b

Counts

79 → 9

regimes310.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.6b

bsearch73.0ms

Steps

Iters	Range	Point
4	7.137245003772895e+116	1.2376544977376032e+117	8.28334187299858e+116
8	-1.1028276516524104e-226	-6.698944910233139e-231	-3.3499841613852864e-230
8	-1.4365190204482462e+156	-4.676631763409332e+151	-8.145597176203898e+152

Iters

Range

Point

7.137245003772895e+116

1.2376544977376032e+117

8.28334187299858e+116

-1.1028276516524104e-226

-6.698944910233139e-231

-3.3499841613852864e-230

-1.4365190204482462e+156

-4.676631763409332e+151

-8.145597176203898e+152

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	207	65
1	207	65

end0.0ms

sample1.3s

Algorithm

intervals

Results

315.0ms	1026×	body	2560	valid
290.0ms	5142×	body	80	valid
230.0ms	925×	body	1280	valid
99.0ms	469×	body	640	valid
39.0ms	105×	body	5120	valid
33.0ms	671×	body	80	nan
33.0ms	222×	body	320	valid
26.0ms	437×	body	80	invalid
11.0ms	111×	body	160	valid

Details

analyze456.0ms

sample47.0ms

simplify163.0ms

prune12.0ms

localize10.0ms

rewrite31.0ms

series65.0ms

simplify59.0ms

prune172.0ms

localize12.0ms

rewrite44.0ms

series126.0ms

simplify62.0ms

prune194.0ms

localize13.0ms

rewrite23.0ms

series45.0ms

simplify54.0ms

prune128.0ms

localize10.0ms

rewrite21.0ms

series43.0ms

simplify56.0ms

prune92.0ms

regimes310.0ms

bsearch73.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling