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

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	184	6
6	250	6
7	287	6
8	349	6
9	437	6
10	574	6
11	654	6
12	712	6
13	785	6
14	1075	6
15	1150	6
16	1193	6
17	1213	6
18	1221	6
19	1221	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)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
101.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	335	555
1	1087	529
2	5002	525

prune224.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.8b

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

rewrite490.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

302.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series234.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify132.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	977	8429
1	3143	6259
2	5002	6131

prune761.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 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))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
1.7b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

876×	`*-un-lft-identity`
576×	`prod-diff`
472×	`add-sqr-sqrt`
456×	`unpow-prod-down` `cube-prod`
446×	`times-frac`
426×	`add-cube-cbrt`
264×	`distribute-lft-out`
72×	`sqr-pow`
62×	`cube-mult` `unpow3`
60×	`associate-/r/`
48×	`fma-neg`
30×	`flip3-+` `flip-+` `div-inv`
24×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`pow-unpow`
2×	`frac-2neg` `associate-*r/` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `prod-exp` `flip--` `cbrt-unprod`

Counts

4 → 796

Calls

4 calls:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
21.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
14.0ms	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 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))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
295.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series650.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
414.0ms	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 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))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
116.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify319.0ms

Algorithm

egg-herbie

Counts

808 → 808

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1213	13807
1	4802	9873
2	5001	9873

prune792.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.2b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1590×	`*-un-lft-identity`
1152×	`prod-diff`
882×	`add-sqr-sqrt`
870×	`unpow-prod-down` `cube-prod`
799×	`times-frac`
790×	`add-cube-cbrt`
581×	`log-prod`
578×	`exp-sum`
468×	`distribute-lft-out`
142×	`sqr-pow`
122×	`cube-mult` `unpow3`
106×	`associate-/r/`
53×	`flip3-+` `flip-+` `div-inv`
48×	`fma-neg` `difference-of-squares`
34×	`log-pow`
33×	`exp-prod`
12×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out--`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/l*`
2×	`difference-cubes` `sub-neg` `associate-*r/` `pow-exp` `rem-cube-cbrt`
1×	`cube-div` `pow-to-exp` `log-div` `flip3--` `pow-pow` `frac-2neg` `exp-diff` `diff-log` `rem-log-exp` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod`

Counts

4 → 1383

Calls

4 calls:

20.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
13.0ms	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 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))))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
290.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
591.0ms	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
414.0ms	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 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))))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
108.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
118.0ms	(log (exp (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))

simplify307.0ms

Algorithm

egg-herbie

Counts

1395 → 1395

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1651	25153
1	5001	18824

prune936.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.1b

regimes71.0ms

Accuracy

75.8% (3.1b remaining)

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

bsearch31.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	45
1	50	45

end0.0ms

sample1.1s

Algorithm

intervals

Results

323.0ms	5802×	body	80	valid
228.0ms	849×	body	1280	valid
155.0ms	699×	body	640	valid
133.0ms	8000×	pre	80	true
69.0ms	421×	body	320	valid
25.0ms	229×	body	160	valid