Details

analyze726.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample40.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
2.0ms	24×	body	80	nan
1.0ms	8×	body	80	invalid

simplify629.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (213.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.6b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
31.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4901	985
1	4901	985

prune174.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Merged error: 5.5b

Counts

71 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

10.3b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `flip3-+` `neg-log` `flip-+`

Counts

4 → 58

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4959	931
1	4959	931

prune198.0ms

Filtered

60 candidates to 70 candidates (-16.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Merged error: 5.5b

Counts

76 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4955	932
1	4955	932

prune252.0ms

Filtered

61 candidates to 72 candidates (-18.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	7	78

Merged error: 5.4b

Counts

78 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 4.0 a) c))
3.9b	(* c (/ a b))
4.8b	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
20.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
7×	`pow1`
6×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `associate-/r*` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--` `div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(* c (/ a b))
10.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(* c (/ a b))
17.0ms	(/ (* 2.0 c) (+ (* 2.0 (* c (/ a b))) (* b -2)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify37.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4982	1072
1	4982	1072

prune145.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	93	7	100

Merged error: 5.4b

Counts

100 → 7

regimes273.0ms

Accuracy

90.5% (1.3b remaining)

Error of 7.4b against oracle of 6.1b and baseline of 19.9b

bsearch56.0ms

Steps

Iters	Range		Point
9	9.533859582991347e+68	1.470629172063746e+74	1.451640594726255e+74
7	-2.545885652918081e+107	-2.977440294561841e+105	-4.016676815484529e+106

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	154	111
1	154	111

end0.0ms

sample977.0ms

Algorithm

intervals

Results

697.0ms	8000×	body	80	valid
54.0ms	661×	body	80	nan
34.0ms	418×	body	80	invalid

Details

analyze726.0ms

sample40.0ms

simplify629.0ms

prune13.0ms

localize23.0ms

rewrite25.0ms

series70.0ms

simplify53.0ms

prune174.0ms

localize28.0ms

rewrite18.0ms

series61.0ms

simplify49.0ms

prune198.0ms

localize30.0ms

rewrite19.0ms

series58.0ms

simplify47.0ms

prune252.0ms

localize24.0ms

rewrite28.0ms

series45.0ms

simplify37.0ms

prune145.0ms

regimes273.0ms

bsearch56.0ms

simplify3.0ms

end0.0ms

sample977.0ms

Profiling