Details

sample46.0ms

Algorithm

intervals

Results

9.0ms	13×	body	320	valid
8.0ms	192×	body	80	valid
6.0ms	32×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	16×	body	640	valid
0.0ms	3×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4691
8	1531
7	665
6	318
5	164
4	74
3	53
2	34
1	20
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite327.0ms

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` `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 → 100

Calls

2 calls:

64.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
259.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series188.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
100.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	1431
1	340
0	128

prune489.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.5b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
91×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 179

Calls

3 calls:

54.0ms	(/ beta (+ (+ alpha beta) 2.0))
28.0ms	(/ alpha (+ (+ alpha beta) 2.0))
191.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series271.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ beta (+ (+ alpha beta) 2.0))
62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
145.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

188 → 188

Iterations

Iter	Nodes
done	5001
2	1881
1	514
0	221

prune704.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite585.0ms

Algorithm

rewrite-expression-head

Rules

263×	`*-un-lft-identity`
179×	`times-frac`
176×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
81×	`sqrt-prod`
78×	`distribute-lft-out`
63×	`prod-diff`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
21×	`fma-neg`
20×	`add-cbrt-cube`
16×	`associate-/r*` `associate-/r/`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `flip3-+` `sqrt-div` `prod-exp` `flip-+` `div-inv`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 310

Calls

4 calls:

203.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
32.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
38.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
278.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series439.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
124.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
111.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

322 → 322

Iterations

Iter	Nodes
done	5000
1	990
0	374

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.0b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

144×	`*-un-lft-identity`
118×	`times-frac`
114×	`add-sqr-sqrt`
81×	`sqrt-prod`
68×	`add-cube-cbrt`
42×	`distribute-lft-out`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `inv-pow` `difference-of-squares`

Counts

4 → 226

Calls

4 calls:

261.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
49.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
34.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
54.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series476.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
134.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
94.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
143.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify2.8s

Counts

238 → 238

Iterations

Iter	Nodes
done	5000
2	4590
1	837
0	296

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

regimes216.0ms

Accuracy

75.1% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.6b

bsearch84.0ms

Steps

Iters	Range		Point
8	1541639454070.677	19367525498197844.0	10272132967178968.0

simplify7.0ms

Iterations

Iter	Nodes
done	39
1	39
0	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

423.0ms	5862×	body	80	valid
242.0ms	841×	body	1280	valid
204.0ms	8000×	pre	80	true
133.0ms	694×	body	640	valid
101.0ms	410×	body	320	valid
21.0ms	193×	body	160	valid