Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	188×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	24×	body	1280	valid
2.0ms	20×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	10×	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: 15.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite40.0ms

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

series107.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune218.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
3.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite102.0ms

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:

8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
36.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
19.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series229.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify134.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (68.0ms)

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

prune760.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.1b

localize13.0ms

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))))
3.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.4b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite98.0ms

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:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
31.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
32.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ beta (+ (+ alpha beta) 2.0))
65.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
75.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
134.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (50.0ms)

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

prune429.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3))
0.6b	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
3.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.4b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite68.0ms

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`
28×	`cbrt-prod`
21×	`fma-neg`
17×	`exp-prod`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod` `associate-/r/`
7×	`log-prod` `add-log-exp`
5×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`cube-mult` `unpow3` `frac-sub` `sqr-pow`
1×	`sub-neg` `pow1/3` `diff-log` `rem-log-exp` `rem-cbrt-cube` `rem-exp-log`

Counts

4 → 175

Calls

4 calls:

2.0ms	(cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3))
5.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
32.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3))
63.0ms	(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)
124.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	618	2423
1	2144	1939
2	5001	1902

prune417.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.1b

regimes138.0ms

Accuracy

78% (2.8b remaining)

Error of 5.8b against oracle of 3.0b and baseline of 15.8b

bsearch65.0ms

Steps

Iters	Range		Point
9	326.37052880660207	1446799629.2404633	522468654.9348684

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	46
1	42	46

end0.0ms

sample611.0ms

Algorithm

intervals

Results

151.0ms	5844×	body	80	valid
109.0ms	829×	body	1280	valid
97.0ms	8000×	pre	80	true
71.0ms	701×	body	640	valid
30.0ms	407×	body	320	valid
11.0ms	219×	body	160	valid