Details

analyze455.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample46.0ms

Algorithm

intervals

Results

9.0ms	161×	body	80	valid
8.0ms	27×	body	2560	valid
8.0ms	31×	body	1280	valid
4.0ms	22×	body	640	valid
2.0ms	3×	body	160	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	18×	body	80	nan
1.0ms	11×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

prune7.0ms

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: 36.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 69

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify34.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5129	1264

prune162.0ms

Filtered

62 candidates to 81 candidates (-30.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	10	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	10	82

Merged error: 7.3b

Counts

82 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.7b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.6b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `sqrt-prod` `add-log-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `distribute-rgt-neg-in` `flip--`
4×	`div-inv`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

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

series131.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
59.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5041	2615

prune189.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Merged error: 7.2b

Counts

141 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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) (* 4.0 (* a c))))))
5.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ c (- (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))))

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4942	1771
1	4942	1771

prune155.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 7.2b

Counts

109 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (* c (* (/ 4.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)))
6.6b	(sqrt (* c (* (/ 4.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
8×	`add-sqr-sqrt` `sqrt-pow1` `sqrt-prod`
6×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div` `pow-prod-down`
4×	`add-exp-log` `pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `associate-r/` `associate-l/` `flip--`

Counts

4 → 56

Calls

4 calls:

13.0ms	(sqrt (* c (* (/ 4.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)))
13.0ms	(sqrt (* c (* (/ 4.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (* c (* (/ 4.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)))
71.0ms	(sqrt (* c (* (/ 4.0 (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) a)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5455	978

prune146.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	67	11	78

Merged error: 7.1b

Counts

78 → 11

regimes305.0ms

Accuracy

92.6% (1.8b remaining)

Error of 7.1b against oracle of 5.3b and baseline of 29.5b

bsearch534.0ms

Steps

Iters	Range		Point
7	1.7708775382058754e+36	1.3639375438100629e+38	1.3430984366882957e+38
10	-1.827838511064216e-303	3.8584104484824506e-299	-2.902356368962004e-306
3	-9.3022547310091e+44	-6.850425518396183e+44	-9.131152096149943e+44

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	64
1	45	64

end0.0ms

analyze454.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample1.3s

Algorithm

intervals

Results

319.0ms	1047×	body	2560	valid
278.0ms	5184×	body	80	valid
224.0ms	889×	body	1280	valid
85.0ms	427×	body	640	valid
36.0ms	97×	body	5120	valid
33.0ms	224×	body	320	valid
32.0ms	638×	body	80	nan
23.0ms	429×	body	80	invalid
13.0ms	132×	body	160	valid

Details

analyze455.0ms

sample46.0ms

simplify3.0ms

prune7.0ms

localize12.0ms

rewrite27.0ms

series63.0ms

simplify34.0ms

prune162.0ms

localize13.0ms

rewrite47.0ms

series131.0ms

simplify50.0ms

prune189.0ms

localize13.0ms

rewrite29.0ms

series85.0ms

simplify61.0ms

prune155.0ms

localize19.0ms

rewrite34.0ms

series169.0ms

simplify38.0ms

prune146.0ms

regimes305.0ms

bsearch534.0ms

simplify1.0ms

end0.0ms

analyze454.0ms

sample1.3s

Profiling