Details

analyze778.0ms

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

sample45.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	14×	body	80	invalid

simplify613.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune33.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.1b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* c (* 4.0 a)))
1.4b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
21.7b	(sqrt (- (* b b) (* c (* 4.0 a))))
21.7b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`*-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--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (* b b) (* c (* 4.0 a)))
8.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
6.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* c (* 4.0 a)))
19.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
23.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify43.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4994	921
1	4994	921

prune175.0ms

Filtered

53 candidates to 67 candidates (-26.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	6	68

Merged error: 5.5b

Counts

68 → 6

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* c (* 4.0 a)))
2.3b	(* c (/ a b))
4.5b	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
21.7b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite27.0ms

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

Counts

4 → 81

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* c (* 4.0 a)))
4.0ms	(* c (/ a b))
15.0ms	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify38.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4966	1089
1	4966	1089

prune189.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	91	8	99

Merged error: 5.4b

Counts

99 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* c (* 4.0 a))))))
0.4b	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
1.2b	(- (* b b) (* c (* 4.0 a)))
21.7b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* c (* 4.0 a))))))
9.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
4.0ms	(- (* b b) (* c (* 4.0 a)))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* c (* 4.0 a))))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* c (* 4.0 a)))))
9.0ms	(- (* b b) (* c (* 4.0 a)))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify56.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4970	1768
1	4970	1768

prune201.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	97	11	108

Merged error: 5.4b

Counts

108 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* c (/ -1 (+ b (sqrt (- (* b b) (* c (* 4.0 a)))))))
0.4b	(+ b (sqrt (- (* b b) (* c (* 4.0 a)))))
1.2b	(- (* b b) (* c (* 4.0 a)))
21.7b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`distribute-lft-out`
3×	`associate-l` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

13.0ms	(* c (/ -1 (+ b (sqrt (- (* b b) (* c (* 4.0 a)))))))
6.0ms	(+ b (sqrt (- (* b b) (* c (* 4.0 a)))))
4.0ms	(- (* b b) (* c (* 4.0 a)))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* c (/ -1 (+ b (sqrt (- (* b b) (* c (* 4.0 a)))))))
14.0ms	(+ b (sqrt (- (* b b) (* c (* 4.0 a)))))
8.0ms	(- (* b b) (* c (* 4.0 a)))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5212	1238

prune147.0ms

Filtered

67 candidates to 87 candidates (-29.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	88	10	98

Merged error: 5.4b

Counts

98 → 10

regimes310.0ms

Accuracy

93.2% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 20.8b

bsearch99.0ms

Steps

Iters	Range	Point
6	1.5064367927023083e+49	1.4581755772385306e+50	1.4342762859357804e+50
8	-2.7309312649220104e-307	8.040189689418536e-306	3.2284907585376e-310
11	-7.089589185984279e+158	-1.1108893609621617e+138	-6.57239956873832e+148

Iters

Range

Point

1.5064367927023083e+49

1.4581755772385306e+50

1.4342762859357804e+50

-2.7309312649220104e-307

8.040189689418536e-306

3.2284907585376e-310

-7.089589185984279e+158

-1.1108893609621617e+138

-6.57239956873832e+148

simplify19.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	975	130
1	975	130

end0.0ms

sample1.0s

Algorithm

intervals

Results

746.0ms	8000×	body	80	valid
64.0ms	663×	body	80	nan
37.0ms	416×	body	80	invalid

Details

analyze778.0ms

sample45.0ms

simplify613.0ms

prune33.0ms

localize24.0ms

rewrite25.0ms

series64.0ms

simplify43.0ms

prune175.0ms

localize31.0ms

rewrite27.0ms

series42.0ms

simplify38.0ms

prune189.0ms

localize26.0ms

rewrite30.0ms

series86.0ms

simplify56.0ms

prune201.0ms

localize23.0ms

rewrite30.0ms

series82.0ms

simplify51.0ms

prune147.0ms

regimes310.0ms

bsearch99.0ms

simplify19.0ms

end0.0ms

sample1.0s

Profiling