Details

sample51.0ms

Algorithm

intervals

Results

15.0ms	171×	body	80	valid
12.0ms	43×	body	1280	valid
6.0ms	26×	body	640	valid
5.0ms	256×	pre	80	true
2.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify79.0ms

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: 20.3b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite124.0ms

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:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
94.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series114.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
61.0ms	(+ (/ (- 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

prune229.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite464.0ms

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:

288.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series250.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify137.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (71.0ms)

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

prune763.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.8b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.9b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite515.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 187

Calls

4 calls:

19.0ms	(/ beta (+ (+ alpha beta) 2.0))
161.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
110.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
216.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ beta (+ (+ alpha beta) 2.0))
211.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
130.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	666	2336
1	2236	1838
2	5002	1790

prune438.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)
0.8b	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
1.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.9b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite346.0ms

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
79×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
63×	`prod-diff`
62×	`times-frac`
36×	`distribute-lft-out`
21×	`fma-neg`
17×	`exp-prod`
14×	`cbrt-prod`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod` `associate-/r/`
7×	`log-prod` `add-log-exp`
6×	`add-exp-log`
5×	`log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-div` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `unpow3` `frac-sub` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 177

Calls

4 calls:

2.0ms	(pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)
7.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
215.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)
64.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
125.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	707	2439
1	2580	1894
2	5001	1852

prune419.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

regimes183.0ms

Accuracy

97.6% (0.3b remaining)

Error of 3.5b against oracle of 3.2b and baseline of 16.8b

bsearch5.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	36
1	37	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

415.0ms	5754×	body	80	valid
244.0ms	880×	body	1280	valid
160.0ms	721×	body	640	valid
147.0ms	8000×	pre	80	true
67.0ms	396×	body	320	valid
30.0ms	249×	body	160	valid