Details

sample55.0ms

Algorithm

intervals

Results

11.0ms	157×	body	160	valid
10.0ms	524×	pre	80	true
9.0ms	268×	body	80	nan
4.0ms	39×	body	320	valid
2.0ms	60×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

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: 43.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite29.0ms

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 → 70

Calls

4 calls:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674

prune198.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.2b

Counts

83 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(- (* b b) (* (* 4.0 a) c))
151.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5003	2388

prune431.0ms

Filtered

163 candidates to 106 candidates (65.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	158	10	168

Merged error: 0b

Counts

168 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `add-cube-cbrt` `div-exp`
4×	`sub-neg` `flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-l`
2×	`distribute-rgt-in` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-prod` `associate-/r/`
1×	`associate--l-` `neg-sub0` `frac-2neg` `times-frac` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
108.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
155.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	512	1105
1	3243	867
2	5001	860

prune240.0ms

Filtered

97 candidates to 62 candidates (63.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Merged error: 0b

Counts

107 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 (* a c)) a)
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (* b b) (* (* 4.0 a) c))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
66×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`add-cube-cbrt`
27×	`add-exp-log` `add-cbrt-cube`
18×	`distribute-lft-out--` `difference-of-squares`
10×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv` `add-log-exp`
9×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`associate-/l*`
6×	`prod-exp` `cbrt-unprod`
4×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `clear-num` `associate-/r/`
1×	`associate--l-` `neg-sub0` `neg-log` `associate-/l/`

Counts

4 → 137

Calls

4 calls:

6.0ms	(/ (* 4.0 (* a c)) a)
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))

series286.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* 4.0 (* a c)) a)
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
48.0ms	(- (* b b) (* (* 4.0 a) c))

simplify95.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	635	2032
1	3308	1822
2	5001	1796

prune337.0ms

Filtered

149 candidates to 93 candidates (62.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	149	6	155

Merged error: 0b

Counts

155 → 6

regimes95.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

350.0ms	4856×	body	160	valid
302.0ms	16383×	pre	80	true
285.0ms	8383×	body	80	nan
145.0ms	1340×	body	320	valid
64.0ms	1804×	body	80	valid