Details

sample58.0ms

Algorithm

intervals

Results

11.0ms	29×	body	1280	valid
10.0ms	32×	body	2560	valid
10.0ms	186×	body	80	valid
4.0ms	88×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

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: 35.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune166.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	10	90

Merged error: 5.7b

Counts

90 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune159.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	138	9	147

Merged error: 5.7b

Counts

147 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series61.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify104.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	203	606
1	762	588
2	3223	580
3	5001	576

prune215.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	75	9	84

Merged error: 5.7b

Counts

84 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

10.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	203	609
1	756	588
2	3186	580
3	5001	576

prune215.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	75	9	84

Merged error: 5.7b

Counts

84 → 9

regimes440.0ms

Accuracy

88.3% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 34.1b

bsearch121.0ms

Steps

Iters	Range		Point
9	7.012417207579252e+108	6.866534780894548e+114	2.8384604739772647e+111
10	-2.401872770955694e-71	-7.96432185149569e-88	-8.098688237357708e-88
9	-8.123118303304505e+80	-8.66777673642249e+74	-3.8197990184324156e+80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	31
1	50	31

end0.0ms

sample1.7s

Algorithm

intervals

Results

335.0ms	1103×	body	2560	valid
315.0ms	5861×	body	80	valid
231.0ms	923×	body	1280	valid
148.0ms	2909×	body	80	nan
87.0ms	431×	body	640	valid
40.0ms	107×	body	5120	valid
34.0ms	220×	body	320	valid
12.0ms	119×	body	160	valid

Details

sample58.0ms

simplify13.0ms

prune3.0ms

localize11.0ms

rewrite28.0ms

series60.0ms

simplify46.0ms

prune166.0ms

localize13.0ms

rewrite35.0ms

series73.0ms

simplify69.0ms

prune159.0ms

localize18.0ms

rewrite20.0ms

series61.0ms

simplify104.0ms

prune215.0ms

localize20.0ms

rewrite23.0ms

series58.0ms

simplify100.0ms

prune215.0ms

regimes440.0ms

bsearch121.0ms

simplify2.0ms

end0.0ms

sample1.7s

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