Details

sample50.0ms

Algorithm

intervals

Results

11.0ms	189×	body	80	valid
11.0ms	13×	body	320	valid
7.0ms	256×	pre	80	true
6.0ms	22×	body	1280	valid
5.0ms	25×	body	640	valid
1.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
17	1763
16	1558
15	1364
14	1138
13	931
12	742
11	607
10	526
9	431
8	318
7	267
6	197
5	124
4	69
3	50
2	33
1	20
0	10

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite154.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `insert-posit16` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 67

Calls

2 calls:

39.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
114.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series151.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify652.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2000
2	1126
1	328
0	126

prune263.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.0b

localize34.0ms

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))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite483.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 115

Calls

4 calls:

246.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
25.0ms	(/ beta (+ (+ alpha beta) 2.0))
40.0ms	(/ alpha (+ (+ alpha beta) 2.0))
171.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series312.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
65.0ms	(/ beta (+ (+ alpha beta) 2.0))
67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
91.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify931.0ms

Counts

127 → 127

Iterations

Iter	Nodes
done	2008
2	1554
1	467
0	197

prune604.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.4b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
148×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
60×	`distribute-lft-out`
27×	`associate-/r*`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
7×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg` `associate-/r/`
2×	`rec-exp` `flip3-+` `1-exp` `flip-+` `difference-of-squares` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 193

Calls

4 calls:

23.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(/ (+ (+ alpha beta) 2.0) beta)
36.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
132.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series259.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ alpha (+ (+ alpha beta) 2.0))
27.0ms	(/ (+ (+ alpha beta) 2.0) beta)
72.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
106.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify993.0ms

Counts

205 → 205

Iterations

Iter	Nodes
done	2006
2	1982
1	646
0	263

prune869.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
120×	`times-frac`
75×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
36×	`distribute-lft-out`
19×	`associate-/r*`
15×	`add-exp-log`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`div-exp`
6×	`difference-of-squares`
5×	`pow1` `div-inv`
4×	`insert-posit16`
3×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*` `distribute-lft-out--`
2×	`rec-exp` `1-exp`
1×	`clear-num` `frac-2neg` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 149

Calls

4 calls:

28.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
179.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
146.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
180.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series422.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
106.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
110.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify780.0ms

Counts

161 → 161

Iterations

Iter	Nodes
done	2004
2	1325
1	494
0	202

prune746.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

regimes240.0ms

Accuracy

74.5% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 15.7b

bsearch90.0ms

Steps

Iters	Range		Point
8	6.100049870521302e+20	3.2635646560629e+25	9.338107713205004e+21

simplify28.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	5840×	body	80	valid
511.0ms	882×	body	1280	valid
333.0ms	8000×	pre	80	true
319.0ms	691×	body	640	valid
107.0ms	379×	body	320	valid
39.0ms	208×	body	160	valid