Details

sample38.0ms

Algorithm

intervals

Results

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

simplify1.3s

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
4.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

192.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
473.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
790.0ms	(/ (/ (/ (+ (+ (+ 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))
394.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
462.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
176.0ms	(/ (/ (/ (+ (+ (+ 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))
86.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify987.0ms

Counts: 477 → 477

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
0.1b	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
4.6b	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
4.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

1659×	`times-frac`
1185×	`*-un-lft-identity`
689×	`add-sqr-sqrt` `add-cube-cbrt`
672×	`cbrt-prod`
306×	`unpow-prod-down` `cube-prod`
248×	`distribute-lft-out`
145×	`associate-/l*`
82×	`associate-/r/`
42×	`flip3-+` `flip-+`
41×	`div-inv`
17×	`cube-mult` `unpow3` `sqr-pow`
14×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-div` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 869

Calls

4 calls:

226.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
958.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
208.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
409.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series712.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
183.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
88.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))
115.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Counts: 881 → 881

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(* (/ 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)))
4.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

297×	`times-frac`
277×	`*-un-lft-identity`
168×	`add-sqr-sqrt`
138×	`add-cube-cbrt`
78×	`associate-r`
68×	`distribute-lft-out`
54×	`add-exp-log`
34×	`add-cbrt-cube`
28×	`associate-/r/`
25×	`associate-/l*`
24×	`div-exp`
15×	`flip3-+` `associate-l` `flip-+`
14×	`cbrt-undiv` `div-inv`
12×	`prod-exp`
10×	`associate-/r*`
9×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 311

Calls

4 calls:

36.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
615.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.1s	(* (/ 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)))
416.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series658.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
166.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
288.0ms	(* (/ 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)))
137.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify777.0ms

Counts: 323 → 323

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (/ (+ (+ (+ 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) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
4.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.8b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite8.6s

Algorithm

rewrite-expression-head

Rules

79305×	`times-frac`
44568×	`*-un-lft-identity`
31140×	`sqrt-prod`
27018×	`add-sqr-sqrt` `add-cube-cbrt`
8775×	`distribute-lft-out`
4222×	`associate-/r/`
2144×	`div-inv`
2081×	`flip3-+` `flip-+`
326×	`associate-/r*`
75×	`associate-/l*`
66×	`sqrt-div`
15×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 16931

Calls

4 calls:

1.4s	(/ (sqrt (/ (/ (+ (+ (+ 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) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
678.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
389.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
492.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series846.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
386.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
120.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
123.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify49.1s

Counts: 16943 → 16943

prune1.4m

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 1.3b

regimes142.0ms

Accuracy

50.5% (1.5b remaining)

Error of 2.7b against oracle of 1.3b and baseline of 4.2b

bsearch98.0ms

Steps

Iters	Range		Point
9	2.2640296726345306e+185	3.9406620462617037e+192	9.316239619114071e+188

simplify467.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

776.0ms	8000×	body	80	valid
244.0ms	8000×	pre	80	true