Details

analyze450.0ms

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

sample41.0ms

Algorithm

intervals

Results

9.0ms	177×	body	80	valid
9.0ms	30×	body	2560	valid
6.0ms	25×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	23×	body	80	nan
1.0ms	2×	body	5120	valid
1.0ms	14×	body	80	invalid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify179.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (177.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	16

prune11.0ms

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: 33.6b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(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))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5899	1226

prune166.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 6.6b

Counts

83 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.6b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
1.6b	(- (* b b) (* 3.0 (* a c)))
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
17.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
9.0ms	(- (* b b) (* 3.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4938	809
1	4938	809

prune112.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	69	10	79

Merged error: 6.6b

Counts

79 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.6b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
1.6b	(- (* b b) (* 3.0 (* a c)))
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite22.0ms

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
15.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
9.0ms	(- (* b b) (* 3.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4938	809
1	4938	809

prune111.0ms

Filtered

49 candidates to 70 candidates (-42.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	70	10	80

Merged error: 6.6b

Counts

80 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3.0 a))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.6b	(- (* b b) (* (* 3.0 a) c))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

4.0ms	(/ 1 (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(/ 1 (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4889	824
1	4889	824

prune97.0ms

Filtered

57 candidates to 81 candidates (-42.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	81	10	91

Merged error: 6.6b

Counts

91 → 10

regimes486.0ms

Accuracy

87.4% (3.6b remaining)

Error of 9.5b against oracle of 5.9b and baseline of 34.1b

bsearch77.0ms

Steps

Iters	Range		Point
9	0.00026424163106636965	77.40180627686225	25.009553698790317
6	1.846208854640814e-157	9.580791255185905e-157	4.836507236876167e-157
6	-3.451277334716786e+152	-5.649518197585434e+151	-9.958850451206072e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	113	71
1	113	71

end0.0ms

sample1.2s

Algorithm

intervals

Results

327.0ms	1073×	body	2560	valid
263.0ms	5136×	body	80	valid
217.0ms	879×	body	1280	valid
94.0ms	486×	body	640	valid
35.0ms	97×	body	5120	valid
33.0ms	683×	body	80	nan
29.0ms	200×	body	320	valid
23.0ms	402×	body	80	invalid
13.0ms	129×	body	160	valid

Details

analyze450.0ms

sample41.0ms

simplify179.0ms

prune11.0ms

localize14.0ms

rewrite30.0ms

series65.0ms

simplify40.0ms

prune166.0ms

localize10.0ms

rewrite22.0ms

series44.0ms

simplify42.0ms

prune112.0ms

localize12.0ms

rewrite22.0ms

series41.0ms

simplify43.0ms

prune111.0ms

localize11.0ms

rewrite22.0ms

series40.0ms

simplify62.0ms

prune97.0ms

regimes486.0ms

bsearch77.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling