Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	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
1.0ms	10×	body	160	valid

simplify71.0ms

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	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	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)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series111.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
65.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune159.0ms

Pruning

12 alts after pruning (12 fresh and 0 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)

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
30.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series388.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
207.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune285.0ms

Pruning

7 alts after pruning (7 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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
14×	`log-prod`
12×	`distribute-lft-out`
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--` `associate-/r*` `flip--`
4×	`exp-prod` `exp-diff` `frac-sub`
3×	`associate-/l*`
2×	`associate-/r/` `log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 95

Calls

4 calls:

8.0ms	(/ beta (+ (+ alpha beta) 2.0))
26.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
26.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ beta (+ (+ alpha beta) 2.0))
64.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	467	1121
1	1528	1058
2	5001	1029

prune282.0ms

Pruning

8 alts after pruning (8 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)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`exp-prod`
12×	`add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
7×	`log-prod` `add-log-exp`
5×	`add-exp-log` `log-pow`
4×	`log-div` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`cube-mult` `times-frac` `unpow3` `frac-sub` `sqr-pow`
1×	`sub-neg` `pow1/3` `diff-log` `rem-log-exp` `rem-cbrt-cube` `rem-exp-log`

Counts

4 → 83

Calls

4 calls:

3.0ms	(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)))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
25.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(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)))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	387	1188
1	1259	1140
2	5002	1127

prune246.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.1b

regimes124.0ms

Accuracy

78% (2.8b remaining)

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

bsearch61.0ms

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	46	47
1	46	47

end0.0ms

sample587.0ms

Algorithm

intervals

Results

142.0ms	5844×	body	80	valid
109.0ms	829×	body	1280	valid
91.0ms	8000×	pre	80	true
65.0ms	701×	body	640	valid
29.0ms	407×	body	320	valid
13.0ms	219×	body	160	valid