Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify13.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize7.0ms

Local error

Found 1 expressions with local error:

16.6b

(/ x (+ (* x x) 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

30.0ms

(/ x (+ (* x x) 1.0))

series101.0ms

Counts

1 → 3

Calls

1 calls:

101.0ms

(/ x (+ (* x x) 1.0))

simplify927.0ms

Counts: 32 → 32

prune97.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* x x) 1.0)))
0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
16.5b	(sqrt (+ (* x x) 1.0))
16.5b	(sqrt (+ (* x x) 1.0))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 262

Calls

4 calls:

25.0ms	(/ x (sqrt (+ (* x x) 1.0)))
65.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
15.0ms	(sqrt (+ (* x x) 1.0))
10.0ms	(sqrt (+ (* x x) 1.0))

series425.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ x (sqrt (+ (* x x) 1.0)))
109.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
67.0ms	(sqrt (+ (* x x) 1.0))
64.0ms	(sqrt (+ (* x x) 1.0))

simplify1.1s

Counts: 274 → 274

prune764.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
0.2b	(/ 1 (pow x 5))
0.4b	(/ 1 (pow x 3))
17.2b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-sqr-sqrt`
173×	`times-frac`
112×	`*-un-lft-identity`
63×	`difference-of-squares`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
40×	`sqr-pow`
26×	`cube-prod`
22×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
8×	`add-cbrt-cube` `add-log-exp`
7×	`distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv` `associate-/l*`
4×	`pow1` `cube-mult` `associate-+l+` `unpow3`
3×	`sub-neg` `associate-*r/` `frac-add`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `frac-sub` `flip--` `inv-pow`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 227

Calls

4 calls:

121.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
9.0ms	(/ 1 (pow x 5))
11.0ms	(/ 1 (pow x 3))
131.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
85.0ms	(/ 1 (pow x 5))
72.0ms	(/ 1 (pow x 3))
153.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify1.4s

Counts: 239 → 239

prune656.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes61.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 15.3b

bsearch2.0ms

simplify756.0ms

end0.0ms

sample585.0ms

Algorithm

intervals

Results

372.0ms

8000×

body

valid