Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	190×	body	80	valid
5.0ms	256×	pre	80	true
3.0ms	21×	body	1280	valid
3.0ms	21×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	9×	body	160	valid

simplify77.0ms

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: 15.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.4b	(+ (/ (- 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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
101.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify36.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune221.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.4b

localize13.0ms

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	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

514×	`*-un-lft-identity`
350×	`add-sqr-sqrt`
273×	`times-frac`
252×	`prod-diff`
215×	`add-cube-cbrt`
138×	`distribute-lft-out`
65×	`associate--r+`
54×	`difference-of-squares`
42×	`fma-neg`
37×	`distribute-lft-out--`
30×	`associate-/r/`
16×	`div-inv`
15×	`flip3-+` `flip-+`
11×	`add-log-exp`
10×	`associate-/l*`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `diff-log` `frac-sub` `log1p-expm1-u` `associate-/l/`
3×	`sub-neg`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`div-sub` `associate--r-`

Counts

4 → 424

Calls

4 calls:

674.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
304.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series260.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify152.0ms

Algorithm

egg-herbie

Counts

436 → 436

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1108	8978
1	3663	6785
2	5001	6782

prune840.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite154.0ms

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:

9.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series384.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
101.0ms	(cbrt (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (36.0ms)

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

prune436.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.7b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite494.0ms

Algorithm

rewrite-expression-head

Rules

206×	`*-un-lft-identity`
129×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
63×	`prod-diff`
50×	`log-prod`
48×	`distribute-lft-out`
25×	`exp-sum`
21×	`fma-neg`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log`
7×	`div-inv`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `exp-diff` `diff-log` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 218

Calls

4 calls:

20.0ms	(/ beta (+ (+ alpha beta) 2.0))
171.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
172.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series329.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
69.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
134.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	743	2916
1	2269	2402
2	5001	2352

prune479.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

regimes121.0ms

Accuracy

77% (2.9b remaining)

Error of 6.1b against oracle of 3.1b and baseline of 15.8b

bsearch50.0ms

Steps

Iters	Range		Point
7	432360580204.07007	20661599466384.8	2780207232289.987

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	25
1	39	25

end0.0ms

sample888.0ms

Algorithm

intervals

Results

283.0ms	5840×	body	80	valid
150.0ms	8000×	pre	80	true
136.0ms	833×	body	1280	valid
104.0ms	740×	body	640	valid
39.0ms	375×	body	320	valid
16.0ms	212×	body	160	valid