Details

sample57.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize24.0ms

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:

514.0ms

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

647.0ms

(/ (/ (/ (+ (+ (+ 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))

455.0ms

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

series629.0ms

Counts

3 → 9

Calls

3 calls:

240.0ms

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

275.0ms

(/ (/ (/ (+ (+ (+ 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))

113.0ms

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

simplify2.6s

Counts

459 → 459

Iterations

Useful iterations: done (2.6s)

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

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

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)))

rewrite3.3s

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:

360.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
246.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
855.0ms	(/ (/ (/ 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))
485.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
205.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
205.0ms	(/ (/ (/ 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))
110.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.6s

Counts

4923 → 4923

Iterations

Useful iterations: 0 (704.0ms)

Iter	Nodes	Cost
0	5274	351082
done	5274	351082

prune23.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

4500×	`add-exp-log`
4225×	`div-exp`
3317×	`times-frac`
1661×	`*-un-lft-identity`
1286×	`1-exp`
1279×	`add-sqr-sqrt` `add-cube-cbrt`
750×	`prod-exp`
650×	`rec-exp`
270×	`add-cbrt-cube`
191×	`distribute-lft-out`
189×	`difference-of-squares`
186×	`cbrt-undiv`
136×	`div-inv`
112×	`associate-/r/`
101×	`associate-/r*`
47×	`flip3--` `flip--`
35×	`cbrt-unprod`
21×	`associate-/l*`
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 → 2037

Calls

4 calls:

247.0ms	(/ (/ 1 1) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))))
495.0ms	(/ (* (/ (/ 1 1) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))) (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (- (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
265.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))
429.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series862.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (/ 1 1) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))))
339.0ms	(/ (* (/ (/ 1 1) (/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))) (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (- (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
155.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))))
159.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify7.4s

Counts

2049 → 2049

Iterations

Useful iterations: done (7.3s)

Iter	Nodes	Cost
0	3239	130630
done	5000	112042

prune4.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize21.0ms

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:

208.0ms	(/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
194.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
186.0ms	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
882.0ms	(/ (/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ 1 1) (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
44.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
61.0ms	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
245.0ms	(/ (/ (/ 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 (2.2s)

Iter	Nodes	Cost
0	15259	959853
done	15259	959853

prune1.3m

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

66.2% (1.5b remaining)

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

bsearch155.0ms

Steps

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

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	35	108
1	48	100
done	48	100

end0.0ms

sample1.3s

Algorithm

intervals

Results

802.0ms	8000×	body	80	valid
193.0ms	8000×	pre	80	true