Details

sample72.0ms

Algorithm

intervals

Results

46.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify644.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2244
3	434
2	100
1	33
0	15

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite650.0ms

Algorithm

rewrite-expression-head

Rules

4332×	`*-un-lft-identity`
2696×	`times-frac`
2173×	`distribute-lft-out`
778×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1217

Calls

4 calls:

62.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
160.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
229.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
134.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
178.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
175.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
95.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.3s

Counts

1229 → 1229

Iterations

Iter	Nodes
2	4287
1	1424
0	601

prune13.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
0.1b	(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.1b	(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

14577×	`*-un-lft-identity`
11720×	`times-frac`
6745×	`distribute-lft-out`
3526×	`add-sqr-sqrt` `add-cube-cbrt`
422×	`associate-/l*`
300×	`associate-/r/`
172×	`associate-/r*`
167×	`div-inv`
135×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`clear-num` `frac-2neg` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 3694

Calls

4 calls:

165.0ms	(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
124.0ms	(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
305.0ms	(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0))
135.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
223.0ms	(/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
252.0ms	(/ (/ 1 (/ (+ 2 (+ beta alpha)) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ (+ 2 (+ beta alpha)) 1.0))
95.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify34.4s

Counts

3706 → 3706

Iterations

Iter	Nodes
1	4283
0	1589

prune48.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 2 (+ beta alpha)))
0.0b	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
0.1b	(/ (/ 1 (+ 2 (+ beta alpha))) (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

15542×	`*-un-lft-identity`
12214×	`times-frac`
7448×	`distribute-lft-out`
3494×	`add-sqr-sqrt` `add-cube-cbrt`
630×	`associate-/r/`
327×	`div-inv`
305×	`flip3-+` `flip-+`
197×	`associate-/r*`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube` `associate-/l*`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 3884

Calls

4 calls:

31.0ms	(/ 1 (+ 2 (+ beta alpha)))
331.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
214.0ms	(/ (/ 1 (+ 2 (+ beta alpha))) (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
158.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series595.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1 (+ 2 (+ beta alpha)))
186.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
207.0ms	(/ (/ 1 (+ 2 (+ beta alpha))) (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
148.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify31.2s

Counts

3896 → 3896

Iterations

Iter	Nodes
1	5999
0	1651

prune49.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))))
0.3b	(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1))
3.6b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.6b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

19826×	`times-frac`
19081×	`*-un-lft-identity`
7284×	`distribute-lft-out`
6508×	`add-sqr-sqrt`
6506×	`add-cube-cbrt`
5220×	`sqrt-prod`
391×	`div-inv`
306×	`associate-/r/`
135×	`associate-/l*`
134×	`flip3-+` `flip-+`
66×	`associate-/r*`
39×	`add-exp-log`
30×	`add-cbrt-cube`
27×	`div-exp`
18×	`cbrt-undiv`
6×	`pow1`
4×	`sqrt-div` `add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 5732

Calls

4 calls:

347.0ms	(/ (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))))
98.0ms	(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1))
64.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
64.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series736.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (+ 2 (+ beta alpha))))
368.0ms	(/ (+ 2 (+ beta alpha)) (/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) 1))
57.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
95.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify39.6s

Counts

5744 → 5744

Iterations

Iter	Nodes
1	8878
0	2508

prune1.2m

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes91.0ms

Accuracy

68.2% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.3b

bsearch66.0ms

Steps

Iters	Range		Point
9	6.19458565197337e+159	4.2871002840354243e+164	6.2498429104423194e+159

simplify4.0ms

Iterations

Iter	Nodes
2	31
1	31
0	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

756.0ms	8000×	body	80	valid
230.0ms	8000×	pre	80	true