Details

analyze445.0ms

Algorithm: search

sample42.0ms

Algorithm

intervals

Results

8.0ms	165×	body	80	valid
8.0ms	28×	body	2560	valid
8.0ms	32×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	19×	body	80	nan
1.0ms	13×	body	80	invalid
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

prune5.0ms

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: 33.1b

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))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (34.0ms)

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

prune168.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	11	90

Merged error: 6.2b

Counts

90 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

16.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
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))))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	463	989
1	2033	868
2	5001	860

prune153.0ms

Filtered

64 candidates to 97 candidates (-51.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	99	9	108

Merged error: 6.2b

Counts

108 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 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))))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (55.0ms)

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

prune159.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	136	10	146

Merged error: 6.2b

Counts

146 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 4.0 (* a c)))
11.1b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
22.7b	(cbrt (- (* b b) (* 4.0 (* a c))))
22.7b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `pow1/3`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 52

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
35.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	344	834
1	1265	755
2	5001	736

prune160.0ms

Filtered

56 candidates to 64 candidates (-14.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	64	10	74

Merged error: 6.2b

Counts

74 → 10

regimes402.0ms

Accuracy

88% (3.5b remaining)

Error of 8.6b against oracle of 5.2b and baseline of 34.0b

bsearch593.0ms

Steps

Iters	Range		Point
5	3.3306943787406174e+83	9.404629383220504e+83	9.28588074484076e+83
9	-1.645336086641096e-205	-4.462308124153642e-215	-2.119498678969391e-207
7	-1.1292777164845942e+58	-4.962791110830647e+55	-1.1156211331137129e+56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	43	30

end0.0ms

analyze446.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

324.0ms	1065×	body	2560	valid
260.0ms	5085×	body	80	valid
222.0ms	909×	body	1280	valid
90.0ms	462×	body	640	valid
37.0ms	104×	body	5120	valid
35.0ms	242×	body	320	valid
34.0ms	653×	body	80	nan
19.0ms	376×	body	80	invalid
13.0ms	133×	body	160	valid

Details

analyze445.0ms

sample42.0ms

simplify13.0ms

prune5.0ms

localize11.0ms

rewrite27.0ms

series58.0ms

simplify44.0ms

prune168.0ms

localize12.0ms

rewrite33.0ms

series55.0ms

simplify55.0ms

prune153.0ms

localize12.0ms

rewrite34.0ms

series69.0ms

simplify72.0ms

prune159.0ms

localize19.0ms

rewrite16.0ms

series92.0ms

simplify46.0ms

prune160.0ms

regimes402.0ms

bsearch593.0ms

simplify2.0ms

end0.0ms

analyze446.0ms

sample1.2s

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