Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	186×	body	80	valid
3.0ms	29×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	4×	body	160	valid

simplify72.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite37.0ms

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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
23.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune160.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 16.0b

Counts

72 → 11

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite59.0ms

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:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series237.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (38.0ms)

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

prune242.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	117	6	123
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 2.7b

Counts

134 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.8b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`exp-prod` `distribute-lft-out`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

14.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
14.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series282.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
79.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify143.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	325	652
1	1064	606
2	4504	591
3	5001	591

prune229.0ms

Filtered

103 candidates to 73 candidates (70.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	103	6	109

Merged error: 2.7b

Counts

109 → 6

localize17.0ms

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))
1.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series382.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(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)

simplify70.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512

prune229.0ms

Filtered

72 candidates to 56 candidates (77.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	71	7	78

Merged error: 2.7b

Counts

78 → 7

regimes102.0ms

Accuracy

73.2% (3.4b remaining)

Error of 6.5b against oracle of 3.1b and baseline of 15.7b

bsearch92.0ms

Steps

Iters	Range		Point
4	8.85312560244671e+136	1.6661249883901243e+137	8.982165201665328e+136
8	3.1357525583305223e+117	2.3462675926281506e+120	4.535383575684779e+119
0	1596871.5183753124	1650110.102945949	1623490.8106606307

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	70
1	54	70

end0.0ms

sample597.0ms

Algorithm

intervals

Results

148.0ms	5837×	body	80	valid
103.0ms	856×	body	1280	valid
95.0ms	8000×	pre	80	true
73.0ms	712×	body	640	valid
27.0ms	377×	body	320	valid
11.0ms	218×	body	160	valid