Details

analyze2.0ms

Algorithm: search

sample25.0ms

Algorithm

intervals

Results

6.0ms	192×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	23×	body	1280	valid
2.0ms	19×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	6×	body	160	valid

simplify66.0ms

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

prune3.0ms

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: 15.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

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:

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

series22.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
14.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify34.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (26.0ms)

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

prune118.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 14.5b

Counts

72 → 11

localize9.0ms

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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite60.0ms

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:

29.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series35.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
12.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (34.0ms)

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

prune188.0ms

Filtered

84 candidates to 123 candidates (-46.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	7	123
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Merged error: 2.0b

Counts

134 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.2b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
24×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 110

Calls

4 calls:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
16.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series34.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ alpha (+ (+ alpha beta) 2.0))
6.0ms	(/ beta (+ (+ alpha beta) 2.0))
11.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
11.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	368	741
1	1178	696
2	5001	683

prune197.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 2.0b

Counts

130 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
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)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
2.2b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite156.0ms

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:

25.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
57.0ms	(/ (- (* 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)))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
40.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series138.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
90.0ms	(/ (- (* 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)))
11.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
27.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify119.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2085	7822
1	5003	7442

prune3.1s

Filtered

212 candidates to 339 candidates (-59.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	342	5	347

Merged error: 2.0b

Counts

347 → 5

regimes122.0ms

Accuracy

75.2% (3.1b remaining)

Error of 6.0b against oracle of 2.9b and baseline of 15.4b

bsearch46.0ms

Steps

Iters	Range		Point
9	1197679.8349820138	64466408205262.34	17606717392792.64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	72
1	66	72

end0.0ms

analyze2.0ms

Algorithm: search

sample722.0ms

Algorithm

intervals

Results

194.0ms	5890×	body	80	valid
134.0ms	831×	body	1280	valid
127.0ms	8000×	pre	80	true
89.0ms	695×	body	640	valid
36.0ms	376×	body	320	valid
13.0ms	208×	body	160	valid

Details

analyze2.0ms

sample25.0ms

simplify66.0ms

prune3.0ms

localize8.0ms

rewrite30.0ms

series22.0ms

simplify34.0ms

prune118.0ms

localize9.0ms

rewrite60.0ms

series35.0ms

simplify46.0ms

prune188.0ms

localize13.0ms

rewrite47.0ms

series34.0ms

simplify37.0ms

prune197.0ms

localize25.0ms

rewrite156.0ms

series138.0ms

simplify119.0ms

prune3.1s

regimes122.0ms

bsearch46.0ms

simplify2.0ms

end0.0ms

analyze2.0ms

sample722.0ms

Profiling