Details

sample57.0ms

Algorithm

intervals

Results

14.0ms	189×	body	80	valid
8.0ms	256×	pre	80	true
8.0ms	22×	body	1280	valid
8.0ms	25×	body	640	valid
3.0ms	13×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
17	1985
16	1722
15	1474
14	1236
13	995
12	795
11	669
10	582
9	467
8	348
7	290
6	209
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: 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)

rewrite183.0ms

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-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 102

Calls

2 calls:

58.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
123.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series168.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify783.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2016
2	1170
1	342
0	130

prune390.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.9b

localize35.0ms

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)

rewrite753.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 417

Calls

4 calls:

400.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
41.0ms	(/ beta (+ (+ alpha beta) 2.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
257.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series339.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
62.0ms	(/ beta (+ (+ alpha beta) 2.0))
67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify924.0ms

Counts

429 → 429

Iterations

Iter	Nodes
done	2002
1	995
0	406

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.6b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity`
131×	`times-frac`
89×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r/`
11×	`pow1`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 214

Calls

4 calls:

37.0ms	(/ alpha (+ (+ alpha beta) 2.0))
252.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
130.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
66.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series449.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ alpha (+ (+ alpha beta) 2.0))
192.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
100.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
98.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify737.0ms

Counts

226 → 226

Iterations

Iter	Nodes
done	2000
1	855
0	269

prune967.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt alpha)
0.7b	(cbrt alpha)
0.7b	(cbrt alpha)
1.6b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt alpha)
1.0ms	(cbrt alpha)
1.0ms	(cbrt alpha)
46.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series853.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt alpha)
285.0ms	(cbrt alpha)
234.0ms	(cbrt alpha)
105.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify823.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	2000
3	1839
2	567
1	200
0	84

prune434.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

regimes115.0ms

Accuracy

74.6% (3.2b remaining)

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

bsearch76.0ms

Steps

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

simplify11.0ms

Iterations

Iter	Nodes
done	42
1	42
0	36

end0.0ms

sample1.9s

Algorithm

intervals

Results

564.0ms	5840×	body	80	valid
389.0ms	882×	body	1280	valid
277.0ms	8000×	pre	80	true
268.0ms	691×	body	640	valid
156.0ms	379×	body	320	valid
33.0ms	208×	body	160	valid