Details

sample22.0ms

Algorithm

intervals

Results

5.0ms	203×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	21×	body	1280	valid
1.0ms	15×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid

simplify83.0ms

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: 12.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite133.0ms

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:

27.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
102.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series113.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune222.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 179

Calls

3 calls:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
122.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series177.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	493	1766
1	1623	1302
2	5002	1263

prune349.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.6b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

904×	`*-un-lft-identity`
576×	`prod-diff`
480×	`add-sqr-sqrt`
458×	`times-frac`
456×	`unpow-prod-down` `cube-prod`
434×	`add-cube-cbrt`
276×	`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`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `flip--`

Counts

4 → 810

Calls

4 calls:

21.0ms	(/ alpha (+ (+ alpha beta) 2.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
23.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
304.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series295.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
75.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
116.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify256.0ms

Algorithm

egg-herbie

Counts

822 → 822

Iterations

Useful iterations: 2 (129.0ms)

Iter	Nodes	Cost
0	1161	12710
1	4145	9010
2	5001	8865

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.6b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.6b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.6b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

2426×	`*-un-lft-identity`
1728×	`prod-diff`
1334×	`add-sqr-sqrt`
1326×	`unpow-prod-down` `cube-prod`
1224×	`times-frac`
1196×	`add-cube-cbrt`
720×	`distribute-lft-out`
214×	`sqr-pow`
184×	`cube-mult` `unpow3`
160×	`associate-/r/`
144×	`fma-neg`
80×	`flip3-+` `flip-+` `div-inv`
72×	`difference-of-squares`
15×	`distribute-lft-out--`
10×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`difference-cubes` `sub-neg` `pow-unpow` `flip3--` `diff-log` `flip--`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `pow-to-exp` `pow-pow` `div-exp`

Counts

4 → 2068

Calls

4 calls:

21.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
300.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
298.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
299.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series428.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
111.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
112.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
127.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify493.0ms

Algorithm

egg-herbie

Counts

2080 → 2080

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	1018	35797
1	3474	24874
2	5001	24400

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

regimes105.0ms

Accuracy

76.5% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.7b

bsearch50.0ms

Steps

Iters	Range		Point
8	24737842517792.957	13792859963305502.0	1188863810682620.8

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	24
1	33	24

end0.0ms

sample625.0ms

Algorithm

intervals

Results

158.0ms	5853×	body	80	valid
100.0ms	824×	body	1280	valid
97.0ms	8000×	pre	80	true
78.0ms	709×	body	640	valid
30.0ms	416×	body	320	valid
10.0ms	198×	body	160	valid