Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	176×	body	80	valid
4.0ms	33×	body	1280	valid
3.0ms	256×	pre	80	true
3.0ms	27×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	7×	body	160	valid

simplify75.0ms

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: 19.1b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite113.0ms

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:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune148.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.2b

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

rewrite357.0ms

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:

219.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
80.0ms	(- (/ 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

prune277.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.8b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite582.0ms

Algorithm

rewrite-expression-head

Rules

376×	`*-un-lft-identity`
211×	`times-frac`
172×	`add-sqr-sqrt`
144×	`distribute-lft-out`
124×	`associate-*r/`
102×	`add-cube-cbrt`
85×	`flip3-+` `flip-+`
78×	`swap-sqr`
72×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
48×	`associate-*l/`
42×	`associate-r` `associate-l` `associate-/r/`
33×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
18×	`pow1` `unpow-prod-down` `cube-prod`
10×	`cbrt-undiv` `div-exp` `sqr-pow`
9×	`prod-exp` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
6×	`add-log-exp`
5×	`distribute-lft-out--`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`difference-cubes` `sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*`

Counts

4 → 374

Calls

4 calls:

83.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
83.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
147.0ms	(/ (- (* 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)))
232.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series645.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
66.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
402.0ms	(/ (- (* 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)))
111.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify120.0ms

Algorithm

egg-herbie

Counts

386 → 386

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	1906	8492
1	5002	8140

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite507.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

182.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
209.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
78.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify148.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	652
1	1066	606
2	4506	591
3	5002	591

prune249.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.7b

regimes100.0ms

Accuracy

74.7% (3.2b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 15.6b

bsearch62.0ms

Steps

Iters	Range		Point
8	55.701487215568164	44831.15638062826	44214.99850275348

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	62
1	63	62

end0.0ms

sample583.0ms

Algorithm

intervals

Results

141.0ms	5858×	body	80	valid
106.0ms	870×	body	1280	valid
95.0ms	8000×	pre	80	true
62.0ms	671×	body	640	valid
31.0ms	375×	body	320	valid
10.0ms	226×	body	160	valid