Details

sample54.0ms

Algorithm

intervals

Results

16.0ms	62×	body	640	valid
9.0ms	127×	body	80	valid
6.0ms	19×	body	1280	valid
5.0ms	26×	body	320	valid
3.0ms	24×	body	160	valid

simplify139.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite551.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1.0 (- x 1.0))
17.0ms	(/ 1.0 (+ x 1.0))
101.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
415.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1.0 (- x 1.0))
37.0ms	(/ 1.0 (+ x 1.0))
71.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
323.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify790.0ms

Counts: 126 → 126

prune426.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.3b	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.4b	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
14.5b	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

340×	`*-un-lft-identity`
225×	`times-frac`
176×	`add-sqr-sqrt`
150×	`frac-sub`
101×	`distribute-lft-out--`
94×	`frac-times`
65×	`add-cube-cbrt`
64×	`flip3--` `flip--`
52×	`associate-r/` `associate-l/`
51×	`difference-of-squares`
47×	`associate-/l/`
41×	`swap-sqr`
31×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`pow1`
16×	`distribute-lft-out`
13×	`associate-/r/`
11×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `sub-neg` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`distribute-rgt-in` `distribute-lft-in` `associate--l+` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 352

Calls

4 calls:

85.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
426.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
269.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
1.1s	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
91.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
354.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
1.0s	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify999.0ms

Counts: 364 → 364

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
0.0b	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.5b	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite583.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity`
47×	`times-frac`
43×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`distribute-lft-out--`
13×	`distribute-lft-out`
11×	`add-log-exp`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`flip3--` `frac-add` `flip--`
2×	`cbrt-undiv` `sub-neg` `associate-+l+` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `div-inv`
1×	`+-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

12.0ms	(/ 1.0 (- x 1.0))
19.0ms	(/ 1.0 (+ x 1.0))
84.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
464.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (- x 1.0))
43.0ms	(/ 1.0 (+ x 1.0))
61.0ms	(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
315.0ms	(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify705.0ms

Counts: 126 → 126

prune408.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.4b	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
14.9b	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0)) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) 1.0)))
16.5b	(* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

363×	`frac-sub`
284×	`associate-*l/`
253×	`frac-times`
135×	`associate-*r/`
119×	`flip3--` `flip--`
111×	`associate-/r/`
89×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
52×	`times-frac`
47×	`associate-/l/`
39×	`frac-add`
35×	`flip3-+` `flip-+`
23×	`difference-of-squares`
19×	`add-cube-cbrt` `distribute-lft-out--`
15×	`associate-r`
14×	`swap-sqr` `associate-l`
13×	`pow1`
10×	`add-exp-log` `add-cbrt-cube`
7×	`sub-neg`
6×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out` `add-log-exp`
4×	`associate--l+` `associate-/l*` `sub-div`
3×	`associate-/r*`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv`

Counts

4 → 381

Calls

4 calls:

448.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
273.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
559.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0)) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) 1.0)))
143.0ms	(* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

504.0ms	(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
300.0ms	(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
622.0ms	(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0)) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) 1.0)))
82.0ms	(* (- (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))) (* (/ 2.0 x) (/ 2.0 x))) (- x 1.0))

simplify1.7s

Counts: 393 → 393

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

regimes132.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 10.1b

bsearch3.0ms

simplify1.5s

end0.0ms

sample1.4s

Algorithm

intervals

Results

444.0ms	1855×	body	640	valid
351.0ms	4161×	body	80	valid
201.0ms	945×	body	320	valid
143.0ms	556×	body	1280	valid
88.0ms	489×	body	160	valid