Details

analyze536.0ms

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample40.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	17×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	38
1	68	38

prune13.0ms

Filtered

1 candidates to 1 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: 23.5b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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:

7.0ms	(- (* 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)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4970	985
1	4970	985

prune176.0ms

Filtered

59 candidates to 70 candidates (-18.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Merged error: 7.0b

Counts

72 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
2.9b	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
3.2b	(* c (/ a b))
25.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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`
5×	`associate-*r/`
4×	`associate-/l/`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-l` `prod-exp` `sqrt-prod` `flip--` `cbrt-unprod` `associate-/l*`
2×	`sqrt-div` `frac-sub` `div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip-+`

Counts

4 → 84

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
6.0ms	(* c (/ a b))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
5.0ms	(* c (/ a b))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4971	1082
1	4971	1082

prune205.0ms

Filtered

73 candidates to 96 candidates (-31.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	91	12	103

Merged error: 7.0b

Counts

103 → 12

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
3.2b	(* c (/ a b))
3.2b	(* c (* (/ a b) 2.0))
3.5b	(/ (* 2.0 c) (+ (neg b) (- (* c (* (/ a b) 2.0)) b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
25×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
14×	`associate-r`
11×	`pow1`
9×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l` `associate-/r`
4×	`pow-prod-down` `associate-/l/` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`div-inv`
2×	`distribute-rgt-neg-in` `frac-2neg` `flip3-+` `clear-num` `associate-/r/` `*-commutative` `frac-sub` `flip-+` `unswap-sqr`
1×	`flip3--` `div-sub` `associate-*l/` `flip--`

Counts

4 → 106

Calls

4 calls:

13.0ms	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
6.0ms	(* c (/ a b))
6.0ms	(* c (* (/ a b) 2.0))
12.0ms	(/ (* 2.0 c) (+ (neg b) (- (* c (* (/ a b) 2.0)) b)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
4.0ms	(* c (/ a b))
5.0ms	(* c (* (/ a b) 2.0))
22.0ms	(/ (* 2.0 c) (+ (neg b) (- (* c (* (/ a b) 2.0)) b)))

simplify31.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4994	1323
1	4994	1323

prune204.0ms

Filtered

80 candidates to 118 candidates (-47.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	115	15	130

Merged error: 7.0b

Counts

130 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (neg b) (- (* c (* (/ a b) 2.0)) b))
0.0b	(- (/ c b) (/ b a))
3.2b	(* c (* (/ a b) 2.0))
3.5b	(/ (* 2.0 c) (+ (neg b) (- (* c (* (/ a b) 2.0)) b)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

9.0ms	(+ (neg b) (- (* c (* (/ a b) 2.0)) b))
14.0ms	(- (/ c b) (/ b a))
6.0ms	(* c (* (/ a b) 2.0))
12.0ms	(/ (* 2.0 c) (+ (neg b) (- (* c (* (/ a b) 2.0)) b)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (neg b) (- (* c (* (/ a b) 2.0)) b))
6.0ms	(- (/ c b) (/ b a))
5.0ms	(* c (* (/ a b) 2.0))
22.0ms	(/ (* 2.0 c) (+ (neg b) (- (* c (* (/ a b) 2.0)) b)))

simplify34.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5199	1252

prune108.0ms

Filtered

65 candidates to 97 candidates (-49.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	99	13	112

Merged error: 7.0b

Counts

112 → 13

regimes352.0ms

Accuracy

93% (1.2b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 22.5b

bsearch666.0ms

Steps

Iters	Range		Point
10	1.8474890661223862e+68	1.5619980041658235e+86	2.3540792276628007e+82
8	-2.3254693171194322e+87	-2.27925317029843e+84	-1.7107578880942487e+87

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	132
1	74	132

end0.0ms

analyze536.0ms

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample1.0s

Algorithm

intervals

Results

736.0ms	8000×	body	80	valid
57.0ms	660×	body	80	nan
37.0ms	418×	body	80	invalid

Details

analyze536.0ms

sample40.0ms

simplify3.0ms

prune13.0ms

localize21.0ms

rewrite26.0ms

series60.0ms

simplify49.0ms

prune176.0ms

localize24.0ms

rewrite29.0ms

series44.0ms

simplify39.0ms

prune205.0ms

localize25.0ms

rewrite41.0ms

series51.0ms

simplify31.0ms

prune204.0ms

localize20.0ms

rewrite44.0ms

series42.0ms

simplify34.0ms

prune108.0ms

regimes352.0ms

bsearch666.0ms

simplify2.0ms

end0.0ms

analyze536.0ms

sample1.0s

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