Details

sample75.0ms

Algorithm

intervals

Results

19.0ms	182×	body	80	valid
14.0ms	25×	body	1280	valid
13.0ms	29×	body	640	valid
11.0ms	256×	pre	80	true
4.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
18	2002
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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite143.0ms

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:

34.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
105.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series134.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
80.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	2000
3	2000
2	1126
1	328
0	126

prune317.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.5b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `insert-posit16` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 141

Calls

4 calls:

1.0s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
22.0ms	(/ beta (+ (+ alpha beta) 2.0))
36.0ms	(/ alpha (+ (+ alpha beta) 2.0))
140.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series375.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
64.0ms	(/ beta (+ (+ alpha beta) 2.0))
86.0ms	(/ alpha (+ (+ alpha beta) 2.0))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

153 → 153

Iterations

Iter	Nodes
done	2004
3	2004
2	1887
1	567
0	242

prune783.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.7b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
24×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `insert-posit16` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 114

Calls

4 calls:

29.0ms	(/ beta (+ (+ alpha beta) 2.0))
22.0ms	(/ alpha (+ (+ alpha beta) 2.0))
305.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
152.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series373.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ beta (+ (+ alpha beta) 2.0))
85.0ms	(/ alpha (+ (+ alpha beta) 2.0))
106.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	2035
3	2035
2	1141
1	400
0	186

prune693.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

localize83.0ms

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

rewrite246.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `times-frac` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

20.0ms	(cbrt (+ (+ alpha beta) 2.0))
21.0ms	(cbrt (+ (+ alpha beta) 2.0))
12.0ms	(cbrt (+ (+ alpha beta) 2.0))
192.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series455.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (+ (+ alpha beta) 2.0))
115.0ms	(cbrt (+ (+ alpha beta) 2.0))
120.0ms	(cbrt (+ (+ alpha beta) 2.0))
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify952.0ms

Counts

76 → 76

Iterations

Iter	Nodes
done	2016
3	2016
2	751
1	284
0	122

prune460.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.8b

regimes349.0ms

Accuracy

98.5% (0.2b remaining)

Error of 3.0b against oracle of 2.8b and baseline of 15.3b

bsearch2.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample2.3s

Algorithm

intervals

Results

600.0ms	5904×	body	80	valid
529.0ms	390×	body	320	valid
433.0ms	844×	body	1280	valid
263.0ms	8000×	pre	80	true
221.0ms	656×	body	640	valid
58.0ms	206×	body	160	valid