Details

sample27.0ms

Algorithm

intervals

Results

11.0ms	255×	body	80	valid
2.0ms	75×	body	80	nan
0.0ms	1×	body	1280	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
12×	`times-frac`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`associate-/r*` `distribute-lft-out`
3×	`add-exp-log` `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 → 33

Calls

1 calls:

39.0ms

(/ x (+ 1.0 (sqrt (+ x 1.0))))

series198.0ms

Counts

1 → 3

Calls

1 calls:

198.0ms

(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify102.0ms

Counts: 36 → 36

prune99.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0b	(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
0.0b	(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
9.0b	(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

rewrite668.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-exp-log`
31×	`prod-exp`
24×	`div-exp`
22×	`associate-*r/`
20×	`frac-add`
18×	`add-cbrt-cube` `add-log-exp`
16×	`times-frac`
14×	`add-sqr-sqrt` `pow-to-exp` `*-un-lft-identity` `pow-exp`
12×	`add-cube-cbrt` `associate-r` `frac-sub`
9×	`unpow-prod-down`
8×	`associate-/l*`
6×	`pow1` `flip3-+` `sum-log` `flip-+`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `frac-times` `flip3--` `associate-*l/` `flip--`
3×	`diff-log` `associate-l` `unpow2` `sqr-pow`
2×	`sub-neg` `associate-+r+` `div-inv`
1×	`+-commutative` `associate-+r-` `associate-+l+` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

35.0ms	(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
489.0ms	(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
86.0ms	(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
49.0ms	(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
551.0ms	(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
213.0ms	(* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))
1.0s	(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

simplify185.0ms

Counts: 144 → 144

prune820.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
2.7b	(- (- (* 1.0 1.0) x) 1.0)
3.0b	(- 1.0 (sqrt (+ x 1.0)))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`associate-l`
16×	`times-frac`
13×	`add-cube-cbrt`
10×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`associate-r` `distribute-lft-out--`
5×	`pow1` `sub-neg` `flip3--` `flip--`
4×	`diff-log`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-*r/` `prod-exp` `associate--l+` `sqrt-prod` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

3 → 84

Calls

3 calls:

235.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
81.0ms	(- (- (* 1.0 1.0) x) 1.0)
17.0ms	(- 1.0 (sqrt (+ x 1.0)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
23.0ms	(- (- (* 1.0 1.0) x) 1.0)
60.0ms	(- 1.0 (sqrt (+ x 1.0)))

simplify39.0ms

Counts: 93 → 93

prune266.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample620.0ms

Algorithm

intervals

Results

281.0ms	7997×	body	80	valid
127.0ms	2651×	body	80	nan
0.0ms	3×	body	1280	valid