Details

sample104.0ms

Algorithm

intervals

Results

34.0ms	52×	body	640	valid
18.0ms	36×	body	1280	valid
17.0ms	209×	body	80	nan
14.0ms	137×	body	80	valid
6.0ms	20×	body	320	valid
2.0ms	11×	body	160	valid

simplify31.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize32.0ms

Local error

Found 3 expressions with local error:

2.9b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b	(/ 1 (sqrt x))
0.1b	(/ 1 (sqrt (+ x 1)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
97×	`times-frac`
93×	`*-un-lft-identity`
60×	`sqrt-prod`
40×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
11×	`add-exp-log`
7×	`pow1` `add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*`
5×	`add-log-exp`
4×	`div-exp`
3×	`insert-posit16`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `1-exp` `associate-/r/` `inv-pow`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `flip-+` `flip--`

Counts

3 → 150

Calls

3 calls:

Slowest

49.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms	(/ 1 (sqrt (+ x 1)))
5.0ms	(/ 1 (sqrt x))

series156.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

87.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
36.0ms	(/ 1 (sqrt (+ x 1)))
34.0ms	(/ 1 (sqrt x))

simplify389.0ms

Counts: 226 → 159

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.8b

localize28.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.5b	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.3b	(/ 1 (sqrt x))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

296×	`times-frac`
274×	`*-un-lft-identity`
209×	`add-sqr-sqrt`
134×	`sqrt-prod`
127×	`add-cube-cbrt`
80×	`distribute-lft-out`
50×	`add-exp-log`
32×	`frac-sub`
30×	`swap-sqr`
29×	`pow1`
28×	`div-inv`
27×	`pow-flip`
25×	`unswap-sqr`
22×	`associate-/r` `associate-r` `associate-l*`
20×	`add-cbrt-cube`
19×	`div-exp`
18×	`difference-of-squares` `associate-/l/`
17×	`frac-times` `associate-l/` `associate-r/` `un-div-inv`
16×	`prod-exp`
9×	`rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-up` `inv-pow`
7×	`associate-/l*`
6×	`cbrt-undiv` `add-log-exp`
5×	`pow-prod-down` `pow-sqr`
4×	`cbrt-unprod` `insert-posit16`
3×	`associate-/r/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`pow2` `sub-neg` `flip3-+` `pow-plus` `diff-log` `div-sub` `frac-add` `*-commutative` `flip-+`

Counts

4 → 348

Calls

4 calls:

Slowest

102.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
22.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
21.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
8.0ms	(/ 1 (sqrt x))

series277.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
55.0ms	(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
38.0ms	(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
37.0ms	(/ 1 (sqrt x))

simplify802.0ms

Counts: 516 → 360

prune3.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.6b

localize54.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
2.4b	(- (* (* 1 1) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* 1 1)))
0.6b	(* (sqrt x) (sqrt x))
0.6b	(* (sqrt x) (sqrt x))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow1` `*-un-lft-identity`
51×	`add-sqr-sqrt`
48×	`sqrt-div` `associate-*r/` `sqrt-prod`
40×	`frac-times`
33×	`flip3-+` `flip-+`
28×	`associate-l`
27×	`add-cube-cbrt`
26×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
18×	`times-frac`
16×	`sqrt-pow1` `pow1/2` `swap-sqr` `distribute-lft-out`
15×	`prod-exp` `cbrt-unprod`
13×	`associate-r`
11×	`associate-*l/`
10×	`pow-prod-up`
9×	`frac-add`
8×	`unswap-sqr`
6×	`pow-sqr` `add-log-exp`
4×	`insert-posit16` `div-inv`
3×	`*-commutative`
2×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 189

Calls

4 calls:

Slowest

319.0ms	(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
86.0ms	(- (* (* 1 1) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* 1 1)))
18.0ms	(* (sqrt x) (sqrt x))
18.0ms	(* (sqrt x) (sqrt x))

series246.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
22.0ms	(* (sqrt x) (sqrt x))
21.0ms	(* (sqrt x) (sqrt x))
20.0ms	(- (* (* 1 1) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* 1 1)))

simplify332.0ms

Counts: 244 → 201

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
0.6b	(* (sqrt x) (sqrt x))
0.5b	(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
0.3b	(* (sqrt (+ x 1)) (sqrt (+ x 1)))

rewrite707.0ms

Algorithm

rewrite-expression-head

Rules

108×	`sqrt-div`
98×	`associate-*r/`
89×	`add-exp-log`
84×	`frac-times`
72×	`flip3-+` `flip-+`
71×	`pow1`
68×	`*-un-lft-identity`
56×	`sqrt-prod`
54×	`prod-exp`
53×	`add-sqr-sqrt`
51×	`add-cbrt-cube`
35×	`associate-/r/`
32×	`pow-prod-down`
29×	`associate-l` `add-cube-cbrt`
28×	`cbrt-unprod`
24×	`associate-*l/`
22×	`distribute-lft-out`
21×	`times-frac`
19×	`swap-sqr`
18×	`frac-add`
16×	`sqrt-pow1` `pow1/2`
14×	`associate-r`
12×	`div-exp`
10×	`pow-prod-up`
8×	`unswap-sqr`
6×	`cbrt-undiv` `rec-exp` `1-exp` `pow-sqr` `pow-flip`
5×	`div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod`
1×	`clear-num` `associate-/r*` `frac-2neg` `inv-pow`

Counts

4 → 273

Calls

4 calls:

Slowest

378.0ms	(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
289.0ms	(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
24.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
9.0ms	(* (sqrt x) (sqrt x))

series407.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

210.0ms	(/ 1 (* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1))))))
157.0ms	(* (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (* (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt (+ x 1)))))
19.0ms	(* (sqrt (+ x 1)) (sqrt (+ x 1)))
19.0ms	(* (sqrt x) (sqrt x))

simplify548.0ms

Counts: 336 → 285

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

regimes34.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

630.0ms	1862×	body	640	valid
609.0ms	4125×	body	80	valid
591.0ms	7809×	body	80	nan
414.0ms	1080×	body	1280	valid
216.0ms	629×	body	320	valid
92.0ms	304×	body	160	valid