Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	550	35
4	4087	35
done	5000	35

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

1.9b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

542.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

720.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

386.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series583.0ms

Counts

3 → 9

Calls

3 calls:

203.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

237.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

141.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.7s

Counts

459 → 459

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	580	25719
1	1395	24955
2	4628	24032
done	5000	23292

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.9s

Algorithm

rewrite-expression-head

Rules

18109×	`times-frac`
9724×	`*-un-lft-identity`
6724×	`add-sqr-sqrt` `add-cube-cbrt`
1500×	`distribute-lft-out`
792×	`associate-/l*`
684×	`div-inv`
572×	`associate-/r/`
245×	`flip3-+` `flip-+`
154×	`add-exp-log`
134×	`div-exp`
84×	`associate-/r*`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
30×	`1-exp`
12×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4911

Calls

4 calls:

297.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
316.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
753.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
490.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
206.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
214.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.7s

Counts

4923 → 4923

Iterations

Useful iterations: 0 (778.0ms)

Iter	Nodes	Cost
0	5274	351082
done	5274	351082

prune23.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt 1) (sqrt 1)) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))))
0.1b	(/ (* (/ (/ (sqrt 1) (sqrt 1)) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))) (/ (/ (sqrt 1) (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (- (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))
15.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

10256×	`times-frac`
4955×	`*-un-lft-identity`
3925×	`add-sqr-sqrt` `add-cube-cbrt`
2592×	`sqrt-prod`
564×	`add-exp-log`
515×	`distribute-lft-out`
513×	`difference-of-squares`
414×	`div-exp`
301×	`associate-/r/`
270×	`add-cbrt-cube`
244×	`div-inv`
186×	`cbrt-undiv`
128×	`flip3--` `flip--`
101×	`associate-/r*`
75×	`prod-exp`
48×	`associate-/l*`
35×	`cbrt-unprod`
26×	`rec-exp` `1-exp`
6×	`associate-/l/`
5×	`pow1`
4×	`frac-2neg` `clear-num` `add-log-exp`
2×	`flip3-+` `flip-+`
1×	`frac-times` `pow-flip` `associate-r/` `associate-l/` `inv-pow`

Counts

4 → 3271

Calls

4 calls:

336.0ms	(/ (/ (sqrt 1) (sqrt 1)) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))))
526.0ms	(/ (* (/ (/ (sqrt 1) (sqrt 1)) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))) (/ (/ (sqrt 1) (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (- (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
255.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))
408.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series783.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (/ (sqrt 1) (sqrt 1)) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))))
330.0ms	(/ (* (/ (/ (sqrt 1) (sqrt 1)) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))) (/ (/ (sqrt 1) (sqrt 1)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (- (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
143.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))
169.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify3.1s

Counts

3283 → 3283

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	3273	226951
done	5000	203665

prune14.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.1b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.8b	(/ (/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite5.0s

Algorithm

rewrite-expression-head

Rules

58048×	`times-frac`
25033×	`*-un-lft-identity`
20963×	`add-sqr-sqrt` `add-cube-cbrt`
3098×	`associate-/r/`
2633×	`div-inv`
2035×	`distribute-lft-out`
1403×	`flip3-+` `flip-+`
675×	`div-exp`
666×	`add-exp-log`
258×	`associate-/l*`
193×	`1-exp`
121×	`rec-exp`
92×	`add-cbrt-cube`
87×	`associate-/r*`
66×	`cbrt-undiv`
8×	`pow1`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
2×	`pow-flip` `inv-pow` `pow-div`

Counts

4 → 12841

Calls

4 calls:

236.0ms	(/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
203.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
198.0ms	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
822.0ms	(/ (/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
44.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
45.0ms	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
269.0ms	(/ (/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

simplify8.8s

Counts

12853 → 12853

Iterations

Useful iterations: 0 (2.3s)

Iter	Nodes	Cost
0	15259	959853
done	15259	959853

prune1.3m

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes105.0ms

Accuracy

66.2% (1.5b remaining)

Error of 1.5b against oracle of 0.1b and baseline of 4.4b

bsearch122.0ms

Steps

Iters	Range		Point
10	3.787217848124224e+152	3.104754081890425e+165	2.4580673707165206e+153

simplify8.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	36	92
1	48	82
done	48	82

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
337.0ms	8000×	pre	80	true