Details

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample27.0ms

Algorithm

intervals

Results

7.0ms	188×	body	80	valid
5.0ms	29×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	23×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	7×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	85	13
1	85	13

prune5.0ms

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: 15.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ alpha beta) 2.0)
0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
25×	`times-frac`
22×	`distribute-lft-out`
15×	`add-cube-cbrt`
10×	`add-log-exp`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`sum-log`
3×	`pow1` `flip3-+` `flip-+`
2×	`+-commutative` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate-+l-` `associate-+l+` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

3 → 80

Calls

3 calls:

6.0ms	(+ (+ alpha beta) 2.0)
10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
18.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series26.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+ (+ alpha beta) 2.0)
8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
15.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5117	1126

prune135.0ms

Filtered

61 candidates to 89 candidates (-45.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	11	90

Merged error: 14.9b

Counts

90 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
1.3b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv`
1×	`associate--r+` `associate--r-`

Counts

4 → 108

Calls

4 calls:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series41.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(/ alpha (+ beta (+ alpha 2.0)))
16.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5838	1671

prune190.0ms

Filtered

88 candidates to 120 candidates (-36.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Merged error: 2.0b

Counts

131 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
0.1b	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
0.1b	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
1.2b	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
41×	`times-frac`
39×	`unpow-prod-down` `cube-prod`
28×	`flip3-+` `flip-+`
27×	`add-cube-cbrt`
24×	`associate-*r/` `difference-of-squares`
21×	`distribute-lft-out`
18×	`associate-/l/`
16×	`frac-times` `frac-sub`
14×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`sqr-pow`
8×	`flip3--` `associate-*l/` `flip--`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-l` `distribute-lft-out--`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-r` `div-inv` `associate-/l*`
2×	`pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `unswap-sqr`

Counts

4 → 181

Calls

4 calls:

10.0ms	(* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
9.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
21.0ms	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
41.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

series155.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))))
13.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
94.0ms	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
21.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4981	6589
1	4981	6589

prune886.0ms

Filtered

124 candidates to 193 candidates (-55.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	193	8	201

Merged error: 2.0b

Counts

201 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
0.1b	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (log (exp (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
1.2b	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))
1.3b	(log (exp (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

119×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
57×	`unpow-prod-down` `cube-prod`
49×	`times-frac`
48×	`difference-of-squares`
34×	`log-pow`
33×	`exp-prod`
27×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`distribute-lft-out`
12×	`add-exp-log` `flip3-+` `associate-/r/` `add-cbrt-cube` `flip-+`
10×	`distribute-lft-out--`
6×	`pow1` `associate-r/` `associate-l/` `associate-/l/` `add-log-exp`
4×	`frac-times` `log-prod` `frac-sub`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `div-inv` `associate-/l*`
2×	`difference-cubes` `sub-neg` `flip3--` `pow-exp` `flip--` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `log-div` `pow-pow` `frac-2neg` `exp-diff` `diff-log` `unpow3` `div-sub` `rem-log-exp` `exp-sum` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod`

Counts

4 → 186

Calls

4 calls:

10.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
17.0ms	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (log (exp (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
41.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))
43.0ms	(log (exp (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
92.0ms	(/ (- (* beta (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))) (* (+ alpha (+ beta 2.0)) (log (exp (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3)))))) (* (+ alpha (+ beta 2.0)) (+ (* 1.0 1.0) (* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0)))))
24.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))
21.0ms	(log (exp (- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))))

simplify83.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5025	4911

prune670.0ms

Filtered

110 candidates to 198 candidates (-80.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	198	8	206

Merged error: 1.9b

Counts

206 → 8

regimes137.0ms

Accuracy

76.3% (3.0b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 15.8b

bsearch46.0ms

Steps

Iters	Range		Point
9	5172.658301258955	3774536581.476637	1550527369.5997407

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	122
1	57	122

end0.0ms

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample737.0ms

Algorithm

intervals

Results

192.0ms	5828×	body	80	valid
139.0ms	861×	body	1280	valid
127.0ms	8000×	pre	80	true
94.0ms	726×	body	640	valid
40.0ms	390×	body	320	valid
15.0ms	195×	body	160	valid

Details

analyze7.0ms

sample27.0ms

simplify4.0ms

prune5.0ms

localize8.0ms

rewrite37.0ms

series26.0ms

simplify46.0ms

prune135.0ms

localize14.0ms

rewrite58.0ms

series41.0ms

simplify46.0ms

prune190.0ms

localize21.0ms

rewrite90.0ms

series155.0ms

simplify83.0ms

prune886.0ms

localize24.0ms

rewrite122.0ms

series148.0ms

simplify83.0ms

prune670.0ms

regimes137.0ms

bsearch46.0ms

simplify1.0ms

end0.0ms

analyze2.0ms

sample737.0ms

Profiling