Details

sample29.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	6
1	6
0	5

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize17.0ms

Local error

Found 1 expressions with local error:

15.3b

(/ x (+ (* x x) 1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
3×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `insert-posit16` `div-inv` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

24.0ms

(/ x (+ (* x x) 1))

series80.0ms

Counts

1 → 3

Calls

1 calls:

80.0ms

(/ x (+ (* x x) 1))

simplify1.1s

Counts

33 → 33

Iterations

Iter	Nodes
4	2810
3	858
2	333
1	147
0	69

prune305.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
15.2b	(sqrt (+ (* x x) 1))
15.2b	(sqrt (+ (* x x) 1))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 266

Calls

4 calls:

19.0ms	(/ x (sqrt (+ (* x x) 1)))
59.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
13.0ms	(sqrt (+ (* x x) 1))
13.0ms	(sqrt (+ (* x x) 1))

series271.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ x (sqrt (+ (* x x) 1)))
74.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
54.0ms	(sqrt (+ (* x x) 1))
46.0ms	(sqrt (+ (* x x) 1))

simplify3.2s

Counts

278 → 278

Iterations

Iter	Nodes
3	5489
2	1574
1	712
0	321

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
1.1b	(/ x (+ (* (* (* x x) x) (* (* x x) x)) 1))
13.0b	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
25.2b	(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

117×	`pow1`
36×	`pow-prod-up`
25×	`add-sqr-sqrt`
24×	`pow-prod-down`
23×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`pow-plus`
16×	`associate-l`
13×	`pow2`
10×	`prod-exp` `cbrt-unprod`
9×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-r` `associate-/r/` `insert-posit16`
3×	`associate-/r` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `associate-+r+` `sum-log` `div-exp` `associate-r/` `-commutative` `div-inv`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `associate-+r-` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `swap-sqr` `associate-*l/`

Counts

4 → 151

Calls

4 calls:

24.0ms	(* (* x x) (* x x))
191.0ms	(/ x (+ (* (* (* x x) x) (* (* x x) x)) 1))
99.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
701.0ms	(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* x x) (* x x))
281.0ms	(/ x (+ (* (* (* x x) x) (* (* x x) x)) 1))
58.0ms	(+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1)))
161.0ms	(* (/ x (+ (* (* (* x x) x) (* (* x x) x)) 1)) (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

simplify884.0ms

Counts

163 → 163

Iterations

Iter	Nodes
2	2271
1	609
0	197

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(/ (/ 1 x) (* x x))
0.2b	(/ 1 (* (* (* x x) x) (* x x)))
18.2b	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (* (* (* x x) x) (* x x))))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

160×	`pow1`
104×	`add-exp-log`
77×	`pow-prod-up`
52×	`prod-exp`
50×	`add-cbrt-cube`
47×	`pow-flip`
41×	`pow-plus`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`div-exp`
22×	`add-sqr-sqrt`
21×	`pow2` `pow-sqr` `add-cube-cbrt`
20×	`cbrt-unprod`
18×	`pow-prod-down`
16×	`associate-/l*`
13×	`cbrt-undiv`
9×	`rec-exp` `1-exp` `div-inv` `add-log-exp`
8×	`pow-div`
6×	`distribute-lft-out`
5×	`pow3` `inv-pow`
4×	`insert-posit16` `distribute-lft-out--`
3×	`associate-r` `frac-add`
2×	`associate-+l+` `clear-num` `associate-/r*` `sum-log` `frac-2neg`
1×	`+-commutative` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-l` `*-commutative` `frac-sub` `associate-+l-` `flip-+` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 203

Calls

4 calls:

17.0ms	(* (* x x) x)
11.0ms	(/ (/ 1 x) (* x x))
145.0ms	(/ 1 (* (* (* x x) x) (* x x)))
178.0ms	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (* (* (* x x) x) (* x x))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* x x) x)
56.0ms	(/ (/ 1 x) (* x x))
69.0ms	(/ 1 (* (* (* x x) x) (* x x)))
40.0ms	(+ (- (/ 1 x) (/ (/ 1 x) (* x x))) (/ 1 (* (* (* x x) x) (* x x))))

simplify1.1s

Counts

215 → 215

Iterations

Iter	Nodes
2	2116
1	705
0	269

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes42.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch105.0ms

Steps

Iters	Range		Point
7	15.597049771107491	3862.7483140020904	465.1323802232794
10	-1231591086050.0088	-0.0006858147917088189	-236646845.7820609

simplify6.0ms

Iterations

Iter	Nodes
2	36
1	36
0	25

end0.0ms

sample701.0ms

Algorithm

intervals

Results

549.0ms

8000×

body

valid