Details

analyze503.0ms

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

sample47.0ms

Algorithm

intervals

Results

12.0ms	32×	body	2560	valid
9.0ms	166×	body	80	valid
5.0ms	21×	body	1280	valid
4.0ms	19×	body	640	valid
3.0ms	7×	body	5120	valid
1.0ms	20×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	invalid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune4.0ms

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: 31.6b

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))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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 → 70

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune161.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 6.1b

Counts

83 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* 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))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	525	1585
1	2550	1372
2	5001	1305

prune151.0ms

Filtered

72 candidates to 126 candidates (-75.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	3	6
Picked	0	1	1
Done	1	0	1
Total	127	7	134

Merged error: 6.0b

Counts

134 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.2b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

14.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	453	918
1	2083	801
2	5002	799

prune132.0ms

Filtered

66 candidates to 96 candidates (-45.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Merged error: 6.0b

Counts

103 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify110.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	211	596
1	802	556
2	3351	536
3	5001	532

prune145.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 6.0b

Counts

79 → 7

regimes296.0ms

Accuracy

88.7% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 33.9b

bsearch628.0ms

Steps

Iters	Range	Point
8	6.029001116355918e+25	1.6676262361556963e+28	1.0861034364166031e+28
7	1.7100919896914193e-235	3.9743121543390314e-234	1.903249263771736e-235
6	-9.30457335168013e+120	-6.183477667694778e+119	-1.2770854895858139e+120

Iters

Range

Point

6.029001116355918e+25

1.6676262361556963e+28

1.0861034364166031e+28

1.7100919896914193e-235

3.9743121543390314e-234

1.903249263771736e-235

-9.30457335168013e+120

-6.183477667694778e+119

-1.2770854895858139e+120

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	32
1	48	32

end0.0ms

analyze467.0ms

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

329.0ms	1059×	body	2560	valid
296.0ms	5140×	body	80	valid
216.0ms	862×	body	1280	valid
101.0ms	485×	body	640	valid
45.0ms	119×	body	5120	valid
34.0ms	227×	body	320	valid
31.0ms	603×	body	80	nan
22.0ms	415×	body	80	invalid
11.0ms	108×	body	160	valid

Details

analyze503.0ms

sample47.0ms

simplify11.0ms

prune4.0ms

localize12.0ms

rewrite29.0ms

series70.0ms

simplify47.0ms

prune161.0ms

localize13.0ms

rewrite33.0ms

series78.0ms

simplify71.0ms

prune151.0ms

localize12.0ms

rewrite33.0ms

series77.0ms

simplify56.0ms

prune132.0ms

localize15.0ms

rewrite26.0ms

series60.0ms

simplify110.0ms

prune145.0ms

regimes296.0ms

bsearch628.0ms

simplify2.0ms

end0.0ms

analyze467.0ms

sample1.3s

Profiling