Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	191×	body	80	valid
5.0ms	25×	body	640	valid
5.0ms	18×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	17×	body	320	valid
1.0ms	5×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite106.0ms

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:

22.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
81.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune153.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite337.0ms

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:

208.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
91.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune287.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
1.7b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite486.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
131×	`add-sqr-sqrt`
123×	`associate-*r/`
90×	`distribute-lft-out`
83×	`flip3-+` `flip-+`
73×	`add-cube-cbrt`
71×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
47×	`associate-*l/`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
38×	`associate-/r/`
26×	`flip3--` `flip--`
24×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
21×	`associate-r` `associate-l`
12×	`pow1`
11×	`sqr-pow`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 327

Calls

4 calls:

80.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
20.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
138.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
220.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series634.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
388.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
109.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify117.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2085	7822
1	5002	7442

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
1.7b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.7b	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

rewrite867.0ms

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`
46×	`associate-*r/`
39×	`flip3-+` `flip-+`
34×	`associate-*l/` `log-pow`
33×	`exp-prod`
30×	`frac-add` `associate-/r/`
27×	`add-cube-cbrt`
26×	`frac-times`
21×	`sqr-pow`
18×	`associate-/l/` `distribute-lft-out`
16×	`frac-sub`
12×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
5×	`log-prod`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `div-inv` `associate-/l*`
2×	`difference-cubes` `sub-neg` `flip3--` `exp-sum` `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` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod`

Counts

4 → 218

Calls

4 calls:

19.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
132.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
218.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
484.0ms	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

series676.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
386.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
106.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
112.0ms	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

simplify74.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1454	5043
1	5001	4740

prune905.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

regimes69.0ms

Accuracy

75.8% (3.1b remaining)

Error of 6.3b against oracle of 3.2b and baseline of 16.0b

bsearch29.0ms

Steps

Iters	Range		Point
4	8.686824422699933e+17	1.4574795904389796e+18	9.096060146374545e+17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	37
1	44	37

end0.0ms

sample1.1s

Algorithm

intervals

Results

327.0ms	5802×	body	80	valid
231.0ms	849×	body	1280	valid
151.0ms	699×	body	640	valid
135.0ms	8000×	pre	80	true
70.0ms	421×	body	320	valid
25.0ms	229×	body	160	valid