Details

analyze738.0ms

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

sample42.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	27×	body	80	nan
2.0ms	20×	body	80	invalid

simplify443.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	57	38
1	57	38

prune11.0ms

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: 19.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

4.0ms	(- (* 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)))
5.0ms	(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)))

simplify36.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4963	913
1	4963	913

prune184.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 5.6b

Counts

69 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
2.1b	(* c (/ a b))
3.6b	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
23.2b	(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))
6.0ms	(* c (/ a b))
13.0ms	(/ (- (* 2.0 (* c (/ a b))) (+ b b)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify41.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4971	1082
1	4971	1082

prune198.0ms

Filtered

73 candidates to 96 candidates (-31.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	94	9	103

Merged error: 5.5b

Counts

103 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.5b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.2b	(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-/r*`
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-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

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

series89.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (* 2.0 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4959	1384
1	4959	1384

prune180.0ms

Filtered

67 candidates to 86 candidates (-28.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 5.5b

Counts

95 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 c) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

15.0ms	(* (* 2.0 c) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(- (* b b) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* 2.0 c) (/ 1 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4994	1621
1	4994	1621

prune138.0ms

Filtered

69 candidates to 107 candidates (-55.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	106	10	116

Merged error: 5.5b

Counts

116 → 10

regimes336.0ms

Accuracy

92.8% (1.1b remaining)

Error of 6.5b against oracle of 5.4b and baseline of 20.5b

bsearch680.0ms

Steps

Iters	Range	Point
8	5.577324776364052e+100	1.6720001984542291e+103	1.3541818436210891e+101
10	-4.850209077949418e-236	-2.648215819544756e-246	-2.68629153848681e-246
5	-6.112864252289094e+90	-2.534970147017114e+90	-6.032911191180909e+90

Iters

Range

Point

5.577324776364052e+100

1.6720001984542291e+103

1.3541818436210891e+101

-4.850209077949418e-236

-2.648215819544756e-246

-2.68629153848681e-246

-6.112864252289094e+90

-2.534970147017114e+90

-6.032911191180909e+90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	126
1	67	126

end0.0ms

analyze512.0ms

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

sample1.0s

Algorithm

intervals

Results

721.0ms	8000×	body	80	valid
59.0ms	678×	body	80	nan
36.0ms	401×	body	80	invalid

Details

analyze738.0ms

sample42.0ms

simplify443.0ms

prune11.0ms

localize25.0ms

rewrite34.0ms

series60.0ms

simplify36.0ms

prune184.0ms

localize26.0ms

rewrite29.0ms

series44.0ms

simplify41.0ms

prune198.0ms

localize23.0ms

rewrite27.0ms

series89.0ms

simplify62.0ms

prune180.0ms

localize24.0ms

rewrite34.0ms

series85.0ms

simplify47.0ms

prune138.0ms

regimes336.0ms

bsearch680.0ms

simplify2.0ms

end0.0ms

analyze512.0ms

sample1.0s

Profiling