Details

sample41.0ms

Algorithm

intervals

Results

14.0ms	201×	body	80	valid
6.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	19×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify78.0ms

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	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: 12.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite129.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
100.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune211.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite492.0ms

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:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
305.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify136.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (68.0ms)

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

prune747.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.2b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite611.0ms

Algorithm

rewrite-expression-head

Rules

1202×	`*-un-lft-identity`
1020×	`times-frac`
895×	`add-sqr-sqrt`
566×	`add-cube-cbrt`
498×	`prod-diff`
300×	`distribute-lft-out`
131×	`difference-of-squares`
83×	`fma-neg`
69×	`distribute-lft-out--`
65×	`associate--r+`
43×	`div-inv`
22×	`associate-/r*` `associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube` `add-log-exp`
8×	`flip3-+` `div-exp` `flip-+` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `frac-sub` `associate-/l/`
1×	`pow-flip` `inv-pow` `associate--r-`

Counts

4 → 768

Calls

4 calls:

358.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
34.0ms	(/ (+ (+ alpha beta) 2.0) beta)
22.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series260.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(- (/ 1 (/ (+ (+ alpha beta) 2.0) beta)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
26.0ms	(/ (+ (+ alpha beta) 2.0) beta)
56.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify181.0ms

Algorithm

egg-herbie

Counts

780 → 780

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1499	20817
1	5001	14368

prune901.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))))
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)))
1.3b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite402.0ms

Algorithm

rewrite-expression-head

Rules

846×	`*-un-lft-identity`
576×	`prod-diff`
462×	`add-sqr-sqrt`
456×	`unpow-prod-down` `cube-prod`
431×	`times-frac`
416×	`add-cube-cbrt`
252×	`distribute-lft-out`
72×	`sqr-pow`
62×	`cube-mult` `unpow3`
58×	`associate-/r/`
48×	`fma-neg`
29×	`flip3-+` `flip-+` `div-inv`
24×	`difference-of-squares`
12×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-/l*`
2×	`associate-*r/` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `fma-udef`

Counts

4 → 767

Calls

4 calls:

0.0ms	(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)))))
22.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
11.0ms	(/ (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)))
301.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series781.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(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)))))
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)))
118.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify276.0ms

Algorithm

egg-herbie

Counts

779 → 779

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	1199	13906
1	4611	9920
2	5001	9872

prune657.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

regimes142.0ms

Accuracy

70.5% (3.9b remaining)

Error of 7.0b against oracle of 3.1b and baseline of 16.2b

bsearch84.0ms

Steps

Iters	Range		Point
9	3.721228267677956e+48	9.335976331147918e+57	3.988530834094386e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	56
1	59	56
2	63	56
3	63	56

end0.0ms

sample1.2s

Algorithm

intervals

Results

407.0ms	5774×	body	80	valid
245.0ms	878×	body	1280	valid
177.0ms	754×	body	640	valid
153.0ms	8000×	pre	80	true
68.0ms	377×	body	320	valid
27.0ms	217×	body	160	valid