Details

sample61.0ms

Algorithm

intervals

Results

35.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify731.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize31.0ms

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))
2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite849.0ms

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` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1221

Calls

4 calls:

62.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
224.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
351.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
144.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
181.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
200.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
106.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.4s

Counts

1233 → 1233

Iterations

Iter	Nodes
2	4172
1	1424
0	605

prune13.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
2.5b	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

rewrite531.0ms

Algorithm

rewrite-expression-head

Rules

222×	`*-un-lft-identity`
123×	`times-frac`
115×	`distribute-lft-out`
50×	`add-exp-log`
49×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
32×	`add-cbrt-cube`
22×	`div-exp`
21×	`associate-r`
20×	`associate-/r/`
15×	`flip3-+` `flip-+`
13×	`cbrt-undiv` `add-log-exp`
12×	`prod-exp` `associate-/l*`
11×	`associate-/r*`
10×	`div-inv`
7×	`associate-/l/`
6×	`pow1` `sum-log` `cbrt-unprod`
4×	`frac-times` `associate-l` `associate-*l/` `insert-posit16`
3×	`rec-exp` `1-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-*r/` `un-div-inv`
1×	`+-commutative` `associate-+l+` `pow-prod-down` `*-commutative`

Counts

4 → 213

Calls

4 calls:

109.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
67.0ms	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
181.0ms	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
166.0ms	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

series570.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
163.0ms	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
251.0ms	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
138.0ms	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

simplify1.6s

Counts

225 → 225

Iterations

Iter	Nodes
2	3405
1	843
0	293

prune2.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ 2 (+ beta alpha)))
0.0b	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ (+ beta alpha) 1.0)))
2.5b	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

rewrite516.0ms

Algorithm

rewrite-expression-head

Rules

243×	`*-un-lft-identity`
138×	`times-frac`
121×	`distribute-lft-out`
59×	`add-sqr-sqrt`
54×	`add-exp-log`
52×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
22×	`associate-/r/`
21×	`associate-r`
16×	`associate-/r*`
15×	`flip3-+` `flip-+` `associate-/l*`
14×	`cbrt-undiv`
12×	`prod-exp`
11×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 237

Calls

4 calls:

37.0ms	(/ 1 (+ 2 (+ beta alpha)))
89.0ms	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
131.0ms	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ (+ beta alpha) 1.0)))
251.0ms	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1 (+ 2 (+ beta alpha)))
218.0ms	(/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha)))
239.0ms	(/ (/ (* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha)))) (+ 2 (+ beta alpha))) (+ 2 (+ (+ beta alpha) 1.0)))
141.0ms	(* (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (/ 1 (+ 2 (+ beta alpha))))

simplify2.3s

Counts

249 → 249

Iterations

Iter	Nodes
2	3873
1	849
0	290

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 2 (+ beta alpha)) (+ 2 (+ (+ beta alpha) 1.0)))
0.0b	(* (+ alpha beta) (+ alpha beta))
0.8b	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ alpha (+ 2 beta))) (- 4 (* (+ alpha beta) (+ alpha beta))))
2.4b	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ alpha (+ 2 beta)))

rewrite696.0ms

Algorithm

rewrite-expression-head

Rules

409×	`*-un-lft-identity`
260×	`times-frac`
161×	`distribute-lft-out`
153×	`add-sqr-sqrt`
110×	`add-cube-cbrt`
36×	`associate-/l*`
34×	`difference-of-squares`
16×	`associate-/r/`
15×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+` `distribute-lft-out--`
11×	`pow1`
8×	`div-inv`
6×	`swap-sqr`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`frac-times` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`flip3--` `associate-l/` `associate-r/` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `div-sub` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 305

Calls

4 calls:

139.0ms	(/ (- 2 (+ beta alpha)) (+ 2 (+ (+ beta alpha) 1.0)))
37.0ms	(* (+ alpha beta) (+ alpha beta))
321.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ alpha (+ 2 beta))) (- 4 (* (+ alpha beta) (+ alpha beta))))
188.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ alpha (+ 2 beta)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- 2 (+ beta alpha)) (+ 2 (+ (+ beta alpha) 1.0)))
25.0ms	(* (+ alpha beta) (+ alpha beta))
241.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ alpha (+ 2 beta))) (- 4 (* (+ alpha beta) (+ alpha beta))))
98.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ alpha (+ 2 beta)))

simplify2.1s

Counts

317 → 317

Iterations

Iter	Nodes
2	4331
1	1153
0	407

prune4.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes122.0ms

Accuracy

52.9% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.5b

bsearch132.0ms

Steps

Iters	Range		Point
10	3.3838621513037655e+153	2.0577599465650627e+167	1.8207254528844126e+167

simplify6.0ms

Iterations

Iter	Nodes
2	41
1	41
0	31

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
359.0ms	8000×	pre	80	true