Details

sample35.0ms

Algorithm

intervals

Results

6.0ms	185×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	20×	body	320	valid
2.0ms	13×	body	640	valid
0.0ms	7×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite418.0ms

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:

90.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
323.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.1s

Counts

106 → 106

Iterations

Useful iterations: 2 (252.0ms)

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

prune496.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.8b

localize20.0ms

Local error

Found 3 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))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

481×	`*-un-lft-identity`
317×	`add-sqr-sqrt`
252×	`prod-diff`
248×	`times-frac`
202×	`add-cube-cbrt`
138×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
30×	`associate-/r/`
25×	`distribute-lft-out--`
15×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`diff-log`
3×	`pow1` `expm1-log1p-u` `sub-neg` `flip3--` `flip--` `log1p-expm1-u` `associate-/l*`
2×	`frac-sub`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate--r-`

Counts

3 → 374

Calls

3 calls:

862.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
649.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series289.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
76.0ms	(/ beta (+ (+ alpha beta) 2.0))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Counts

383 → 383

Iterations

Useful iterations: 2 (852.0ms)

Iter	Nodes	Cost
0	385	16218
1	958	12979
2	3649	10954
done	5000	10954

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.8b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.5s

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:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
492.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
335.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
615.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ beta (+ (+ alpha beta) 2.0))
111.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
100.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
157.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify2.0s

Counts

199 → 199

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	299	4746
1	687	3959
2	2551	3535
done	5000	3378

prune908.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(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)))
2.2b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.7b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.0s

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`
21×	`fma-neg`
17×	`exp-prod`
14×	`cbrt-prod`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod` `associate-/r/`
7×	`log-prod` `add-log-exp`
6×	`add-exp-log`
5×	`log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-div` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `distribute-lft-out--` `difference-of-squares`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `unpow3` `frac-sub` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 177

Calls

4 calls:

5.0ms	(pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)
12.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
337.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
680.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series829.0ms

Counts

4 → 12

Calls

4 calls:

432.0ms	(pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)
89.0ms	(exp (cbrt (pow (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) 3)))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
190.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify2.1s

Counts

189 → 189

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	305	4944
1	783	4074
2	3104	3522
done	5001	3383

prune891.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

regimes596.0ms

Accuracy

99% (0.1b remaining)

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

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	58
1	33	58
done	33	58

end0.0ms

sample1.4s

Algorithm

intervals

Results

303.0ms	855×	body	1280	valid
267.0ms	5893×	body	80	valid
234.0ms	8000×	pre	80	true
159.0ms	667×	body	640	valid
86.0ms	384×	body	320	valid
18.0ms	201×	body	160	valid