Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	181×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	23×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	8×	body	160	valid

simplify82.0ms

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: 17.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite38.0ms

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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series113.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (32.0ms)

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

prune232.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.6b

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))
2.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite90.0ms

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:

44.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series245.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (58.0ms)

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

prune489.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
2.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

6.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series376.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	460	1755
1	1302	1290
2	5001	1240

prune447.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3)
2.0b	(- 1.0 (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
2.7b	(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

850×	`*-un-lft-identity`
384×	`times-frac`
326×	`add-sqr-sqrt`
266×	`distribute-lft-out`
175×	`add-cube-cbrt`
93×	`prod-diff`
90×	`distribute-lft-out--`
83×	`swap-sqr`
69×	`difference-of-squares`
68×	`fma-def`
66×	`unpow-prod-down` `cube-prod`
31×	`associate-r` `associate-l`
22×	`associate-/r/`
19×	`add-exp-log` `add-cbrt-cube`
12×	`pow1` `flip3-+` `flip-+`
11×	`div-inv`
8×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `fma-neg`
2×	`cube-mult` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `cube-div` `pow2` `frac-times` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `pow-sqr` `sum-cubes` `*-commutative` `pow-prod-up` `flip--` `associate--r-`

Counts

4 → 460

Calls

4 calls:

39.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
17.0ms	(pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3)
21.0ms	(- 1.0 (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
62.0ms	(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series512.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) 2.0)) (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
80.0ms	(pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3)
101.0ms	(- 1.0 (/ (- beta alpha) (+ (+ alpha beta) 2.0)))
264.0ms	(+ (pow (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1366	6783
1	5001	5185

prune857.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

regimes172.0ms

Accuracy

98.8% (0.2b remaining)

Error of 3.3b against oracle of 3.1b and baseline of 16.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	56
1	49	56

end0.0ms

sample608.0ms

Algorithm

intervals

Results

150.0ms	5870×	body	80	valid
106.0ms	861×	body	1280	valid
98.0ms	8000×	pre	80	true
69.0ms	690×	body	640	valid
29.0ms	401×	body	320	valid
9.0ms	178×	body	160	valid