Details

sample32.0ms

Algorithm

intervals

Results

6.0ms	183×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	27×	body	1280	valid
4.0ms	27×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	418	13
1	418	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: 17.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 65

Calls

2 calls:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
23.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series21.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
13.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5295	998

prune126.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 16.2b

Counts

72 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
2.5b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite64.0ms

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` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
28.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
8.0ms	(/ alpha (+ beta (+ alpha 2.0)))
16.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series43.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
7.0ms	(/ alpha (+ beta (+ alpha 2.0)))
13.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify25.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5211	1698

prune205.0ms

Filtered

88 candidates to 123 candidates (-39.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	127	6	133

Merged error: 3.2b

Counts

133 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 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)))))
2.5b	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
57×	`times-frac`
39×	`unpow-prod-down` `cube-prod`
35×	`add-cube-cbrt`
28×	`distribute-lft-out`
25×	`flip3-+` `flip-+`
24×	`associate-*r/` `difference-of-squares`
21×	`associate-l`
18×	`associate-/l/`
17×	`add-exp-log` `add-cbrt-cube`
16×	`frac-sub`
14×	`frac-times` `associate-/r/`
11×	`sqr-pow`
8×	`flip3--` `flip--`
7×	`pow1` `associate-*l/`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
3×	`pow-unpow` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt` `unswap-sqr`
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`

Counts

4 → 199

Calls

4 calls:

28.0ms	(* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))
10.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
22.0ms	(/ (- (* 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)))))
38.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

series155.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (/ alpha (+ alpha (+ beta 2.0))) (+ (/ alpha (+ alpha (+ beta 2.0))) 1.0))
13.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
102.0ms	(/ (- (* 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)))))
22.0ms	(- (pow (/ alpha (+ alpha (+ beta 2.0))) 3) (pow 1.0 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5142	6406

prune1.0s

Filtered

133 candidates to 211 candidates (-58.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	212	5	217

Merged error: 3.1b

Counts

217 → 5

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)))))
0.8b	(log (exp (pow (/ alpha (+ alpha (+ beta 2.0))) 3)))
2.5b	(- (log (exp (pow (/ alpha (+ alpha (+ beta 2.0))) 3))) (pow 1.0 3))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
63×	`times-frac`
53×	`add-sqr-sqrt`
50×	`log-pow`
48×	`exp-prod`
46×	`add-cube-cbrt`
43×	`unpow-prod-down` `cube-prod`
36×	`distribute-lft-out`
24×	`flip3-+` `flip-+`
22×	`associate-*r/`
18×	`associate-/l/`
16×	`associate-/r/` `frac-sub`
12×	`add-exp-log` `frac-times` `add-cbrt-cube`
8×	`flip3--` `flip--`
7×	`pow1`
6×	`log-prod` `associate-*l/`
5×	`div-inv` `add-log-exp`
4×	`difference-of-squares`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate--l+` `associate-/l*` `sqr-pow`
2×	`cube-mult` `unpow3` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt`
1×	`cube-div` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `rem-log-exp` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod`

Counts

4 → 191

Calls

4 calls:

11.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
22.0ms	(/ (- (* 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)))))
17.0ms	(log (exp (pow (/ alpha (+ alpha (+ beta 2.0))) 3)))
49.0ms	(- (log (exp (pow (/ alpha (+ alpha (+ beta 2.0))) 3))) (pow 1.0 3))

series155.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow (/ alpha (+ alpha (+ beta 2.0))) 3)
102.0ms	(/ (- (* 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)))))
13.0ms	(log (exp (pow (/ alpha (+ alpha (+ beta 2.0))) 3)))
27.0ms	(- (log (exp (pow (/ alpha (+ alpha (+ beta 2.0))) 3))) (pow 1.0 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5025	5318

prune873.0ms

Filtered

121 candidates to 203 candidates (-67.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	202	6	208

Merged error: 3.1b

Counts

208 → 6

regimes129.0ms

Accuracy

77.6% (2.8b remaining)

Error of 5.9b against oracle of 3.1b and baseline of 15.8b

bsearch16.0ms

Steps

Iters	Range		Point
6	7170427078.972401	99835565477.3547	18187930964.32793

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	118
1	54	118

end0.0ms

sample882.0ms

Algorithm

intervals

Results

205.0ms	5836×	body	80	valid
141.0ms	854×	body	1280	valid
135.0ms	8000×	pre	80	true
92.0ms	702×	body	640	valid
37.0ms	376×	body	320	valid
15.0ms	232×	body	160	valid

Details

sample32.0ms

simplify12.0ms

prune5.0ms

localize8.0ms

rewrite37.0ms

series21.0ms

simplify39.0ms

prune126.0ms

localize11.0ms

rewrite64.0ms

series43.0ms

simplify25.0ms

prune205.0ms

localize23.0ms

rewrite110.0ms

series155.0ms

simplify53.0ms

prune1.0s

localize24.0ms

rewrite110.0ms

series155.0ms

simplify47.0ms

prune873.0ms

regimes129.0ms

bsearch16.0ms

simplify1.0ms

end0.0ms

sample882.0ms

Profiling