Details

sample40.0ms

Algorithm

intervals

Results

8.0ms	38×	body	1280	valid
7.0ms	170×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	29×	body	640	valid
2.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	53	13
4	74	13
5	163	13
6	314	13
7	647	13
8	1463	13
9	4388	13
done	5001	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite380.0ms

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

Counts

2 → 100

Calls

2 calls:

86.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
286.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series148.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
95.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify964.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	128	1178
1	341	1110
2	1440	1056
done	5000	1056

prune325.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.4b

localize11.0ms

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))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.2s

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

Counts

4 → 413

Calls

4 calls:

727.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
42.0ms	(/ beta (+ (+ alpha beta) 2.0))
59.0ms	(/ alpha (+ (+ alpha beta) 2.0))
348.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series342.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
83.0ms	(/ beta (+ (+ alpha beta) 2.0))
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
102.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

425 → 425

Iterations

Useful iterations: 2 (850.0ms)

Iter	Nodes	Cost
0	402	16706
1	993	13424
2	3869	11385
done	5000	11385

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.8b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

166×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
78×	`times-frac`
74×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
14×	`log-prod`
10×	`associate-/r/`
8×	`log-div`
7×	`add-exp-log` `exp-sum` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`flip3--` `flip3-+` `associate-/r*` `flip--` `flip-+` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 187

Calls

4 calls:

45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
446.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
314.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
619.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ alpha (+ (+ alpha beta) 2.0))
121.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
202.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.9s

Counts

199 → 199

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	279	4746
1	654	3957
2	2503	3535
done	5000	3378

prune610.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3))
0.8b	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
1.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
13.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

136×	`*-un-lft-identity`
79×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
63×	`prod-diff`
62×	`times-frac`
36×	`distribute-lft-out`
28×	`cbrt-prod`
21×	`fma-neg`
17×	`exp-prod`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod` `associate-/r/`
7×	`log-prod` `add-log-exp`
5×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`cube-mult` `unpow3` `frac-sub` `sqr-pow`
1×	`sub-neg` `pow1/3` `diff-log` `rem-log-exp` `rem-cbrt-cube` `rem-exp-log`

Counts

4 → 175

Calls

4 calls:

3.0ms	(cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3))
13.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
721.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
651.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3))
86.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
137.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
163.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.8s

Counts

187 → 187

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	275	4991
1	654	4042
2	2581	3498
done	5001	3340

prune573.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

regimes261.0ms

Accuracy

76.8% (3.0b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 15.8b

bsearch74.0ms

Steps

Iters	Range		Point
10	0.002308426731173248	209018734.74226573	94141546.97903764

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	51
1	34	51
2	36	51
done	36	51

end0.0ms

sample1.5s

Algorithm

intervals

Results

336.0ms	8000×	pre	80	true
295.0ms	5886×	body	80	valid
209.0ms	848×	body	1280	valid
207.0ms	690×	body	640	valid
89.0ms	387×	body	320	valid
18.0ms	189×	body	160	valid