Details

sample83.0ms

Algorithm

intervals

Results

17.0ms	34×	body	2560	valid
16.0ms	179×	body	80	valid
12.0ms	29×	body	1280	valid
7.0ms	85×	body	80	nan
5.0ms	17×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	160	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: 35.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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:

11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune210.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 4.9b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.1b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
140.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
173.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	651	2692
1	3139	2439
2	5002	2426

prune392.0ms

Filtered

166 candidates to 111 candidates (66.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	164	10	174

Merged error: 4.8b

Counts

174 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series329.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	525	1588
1	2570	1375
2	5001	1308

prune227.0ms

Filtered

126 candidates to 71 candidates (56.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Merged error: 4.8b

Counts

136 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.0b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.0b	(- (* b b) (* (* 4.0 a) c))
23.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
13×	`add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`prod-exp`
8×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `associate-l`
6×	`associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `div-exp` `cbrt-unprod` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `distribute-rgt-in` `frac-times` `rec-exp` `distribute-lft-in` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

15.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
8.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
75.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	453	919
1	2109	802
2	5001	799

prune184.0ms

Filtered

96 candidates to 65 candidates (67.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	96	10	106

Merged error: 4.8b

Counts

106 → 10

regimes212.0ms

Accuracy

85.7% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 32.6b

bsearch212.0ms

Steps

Iters	Range		Point
9	14028.172733867412	3007116902181.375	4662246.201750503
8	-4.654091770266614e-259	-1.1349992526466847e-263	-3.0161999035837213e-263
10	-1.552489725432399e+46	-8.211399685419546e+34	-1.4899647929737788e+46

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	29
1	51	29
2	51	29

end0.0ms

sample1.4s

Algorithm

intervals

Results

311.0ms	1101×	body	2560	valid
292.0ms	5800×	body	80	valid
209.0ms	887×	body	1280	valid
139.0ms	2958×	body	80	nan
85.0ms	469×	body	640	valid
41.0ms	117×	body	5120	valid
31.0ms	215×	body	320	valid
10.0ms	110×	body	160	valid