Details

sample28.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify22.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize16.0ms

Local error

Found 1 expressions with local error:

14.3b

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

rewrite18.0ms

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:

Slowest

17.0ms

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

series60.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

60.0ms

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

simplify651.0ms

Counts: 43 → 33

prune191.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (+ (* x x) 1))
14.3b	(sqrt (+ (* x x) 1))
0.0b	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
0.0b	(/ x (sqrt (+ (* x x) 1)))

rewrite59.0ms

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:

Slowest

29.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
12.0ms	(/ x (sqrt (+ (* x x) 1)))
7.0ms	(sqrt (+ (* x x) 1))
6.0ms	(sqrt (+ (* x x) 1))

series230.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

71.0ms	(/ x (sqrt (+ (* x x) 1)))
66.0ms	(/ (/ x (sqrt (+ (* x x) 1))) (sqrt (+ (* x x) 1)))
49.0ms	(sqrt (+ (* x x) 1))
43.0ms	(sqrt (+ (* x x) 1))

simplify448.0ms

Counts: 448 → 278

prune2.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

20.4b	(* (/ x (- (* (* x x) (* x x)) 1)) (- (* x x) 1))
1.6b	(/ x (- (* (* x x) (* x x)) 1))
0.1b	(* (* x x) (* x x))
0.0b	(- (* x x) 1)

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

Slowest

165.0ms	(* (/ x (- (* (* x x) (* x x)) 1)) (- (* x x) 1))
70.0ms	(/ x (- (* (* x x) (* x x)) 1))
43.0ms	(* (* x x) (* x x))
11.0ms	(- (* x x) 1)

series376.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(/ x (- (* (* x x) (* x x)) 1))
118.0ms	(* (/ x (- (* (* x x) (* x x)) 1)) (- (* x x) 1))
69.0ms	(* (* x x) (* x x))
68.0ms	(- (* x x) 1)

simplify882.0ms

Counts: 220 → 189

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

21.0b	(- (/ (/ 1 x) (* x x)) (/ 1 (* (* x (* x x)) (* x x))))
0.3b	(/ 1 (* (* x (* x x)) (* x x)))
0.1b	(/ (/ 1 x) (* x x))
0.1b	(* x (* x x))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
104×	`add-exp-log`
52×	`prod-exp` `pow-prod-up`
50×	`add-cbrt-cube`
40×	`times-frac`
31×	`add-sqr-sqrt` `pow-flip`
26×	`*-un-lft-identity` `div-exp`
21×	`add-cube-cbrt`
20×	`cbrt-unprod`
18×	`pow-prod-down`
16×	`associate-/l*`
13×	`cbrt-undiv`
12×	`pow2` `pow-plus` `pow-sqr`
9×	`rec-exp` `1-exp`
8×	`pow-div`
6×	`div-inv` `add-log-exp`
5×	`cube-unmult` `inv-pow`
4×	`insert-posit16` `difference-of-squares`
3×	`associate-l`
2×	`clear-num` `associate-/r*` `frac-2neg` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `diff-log` `associate-r` `*-commutative` `frac-sub` `flip--` `unswap-sqr` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

Slowest

120.0ms	(/ 1 (* (* x (* x x)) (* x x)))
82.0ms	(- (/ (/ 1 x) (* x x)) (/ 1 (* (* x (* x x)) (* x x))))
26.0ms	(* x (* x x))
19.0ms	(/ (/ 1 x) (* x x))

series331.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

170.0ms	(- (/ (/ 1 x) (* x x)) (/ 1 (* (* x (* x x)) (* x x))))
59.0ms	(/ 1 (* (* x (* x x)) (* x x)))
59.0ms	(/ (/ 1 x) (* x x))
42.0ms	(* x (* x x))

simplify698.0ms

Counts: 214 → 191

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.7b

bsearch94.0ms

end0.0ms

sample601.0ms

Algorithm

intervals

Results

482.0ms

8000×

body

valid