Details

sample34.0ms

Algorithm

intervals

Results

6.0ms	25×	body	640	valid
6.0ms	188×	body	80	valid
5.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify78.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite35.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
20.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series105.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

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

prune192.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	12	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 15.2b

Counts

107 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

41.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	714	2537
1	2533	2035
2	5001	2004

prune392.0ms

Filtered

241 candidates to 137 candidates (56.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	233	8	241
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	243	10	253

Merged error: 3.6b

Counts

253 → 10

localize25.0ms

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)))) (* (* 2.0 (+ (+ alpha beta) 2.0)) (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
2.1b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

1026×	`*-un-lft-identity`
576×	`prod-diff`
531×	`times-frac`
522×	`add-sqr-sqrt`
464×	`add-cube-cbrt`
456×	`unpow-prod-down` `cube-prod`
324×	`distribute-lft-out`
99×	`associate-*r/`
89×	`flip3-+` `flip-+`
72×	`sqr-pow`
66×	`associate-/r/` `associate-/l/`
64×	`frac-sub`
62×	`cube-mult` `unpow3`
49×	`frac-times`
48×	`fma-neg` `frac-add`
39×	`swap-sqr`
35×	`associate-*l/`
33×	`div-inv`
28×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
21×	`associate-r` `associate-l`
12×	`pow1`
8×	`cbrt-undiv` `div-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 937

Calls

4 calls:

24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
46.0ms	(/ (- (* 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)))) (* (* 2.0 (+ (+ alpha beta) 2.0)) (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
56.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series675.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
419.0ms	(/ (- (* 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)))) (* (* 2.0 (+ (+ alpha beta) 2.0)) (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
118.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify241.0ms

Algorithm

egg-herbie

Counts

949 → 949

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2264	17916
1	5001	15106

prune1.6s

Filtered

949 candidates to 235 candidates (24.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	946	3	949
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	947	12	959

Merged error: 3.6b

Counts

959 → 12

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt alpha)
0.6b	(cbrt alpha)
0.6b	(cbrt alpha)
2.1b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

798×	`*-un-lft-identity`
576×	`prod-diff`
444×	`add-sqr-sqrt`
435×	`unpow-prod-down` `cube-prod`
398×	`add-cube-cbrt` `times-frac`
234×	`distribute-lft-out`
71×	`sqr-pow`
61×	`cube-mult` `unpow3`
52×	`associate-/r/`
48×	`fma-neg`
26×	`flip3-+` `flip-+` `div-inv`
24×	`difference-of-squares`
9×	`cbrt-prod`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 707

Calls

4 calls:

1.0ms	(cbrt alpha)
2.0ms	(cbrt alpha)
1.0ms	(cbrt alpha)
56.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series652.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt alpha)
187.0ms	(cbrt alpha)
177.0ms	(cbrt alpha)
111.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify238.0ms

Algorithm

egg-herbie

Counts

719 → 719

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	1001	11937
1	3235	8328
2	5001	8310

prune692.0ms

Filtered

719 candidates to 101 candidates (14.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	719	0	719
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	719	12	731

Merged error: 3.6b

Counts

731 → 12

regimes151.0ms

Accuracy

73.8% (3.2b remaining)

Error of 6.4b against oracle of 3.1b and baseline of 15.5b

bsearch46.0ms

Steps

Iters	Range		Point
7	20637641668174496.0	1.196592586218352e+18	6.909964380351935e+16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample733.0ms

Algorithm

intervals

Results

182.0ms	5872×	body	80	valid
132.0ms	839×	body	1280	valid
129.0ms	8000×	pre	80	true
92.0ms	714×	body	640	valid
35.0ms	367×	body	320	valid
13.0ms	208×	body	160	valid