Details

sample17.0ms

Algorithm

intervals

Results

6.0ms	256×	body	80	valid
2.0ms	90×	body	80	nan

simplify13.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
16.0ms	(+ 1.0 (sqrt (+ x 1.0)))
40.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(sqrt (+ x 1.0))
45.0ms	(+ 1.0 (sqrt (+ x 1.0)))
172.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify582.0ms

Counts: 70 → 70

prune178.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ x 1.0)))
0.0b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

16.0ms	(sqrt (sqrt (+ x 1.0)))
14.0ms	(sqrt (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
67.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt (sqrt (+ x 1.0)))
112.0ms	(sqrt (sqrt (+ x 1.0)))
152.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
32.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify1.2s

Counts: 173 → 173

prune528.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
3.8b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
8.7b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
62×	`sqrt-div`
43×	`add-sqr-sqrt`
34×	`sqrt-prod`
32×	`flip3-+` `flip-+`
31×	`add-cube-cbrt`
28×	`associate-*r/` `distribute-lft-out`
27×	`times-frac`
23×	`unpow-prod-down` `cube-prod`
21×	`pow1`
16×	`frac-sub`
12×	`frac-times`
11×	`swap-sqr`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `associate-/r*` `add-cbrt-cube`
8×	`associate-*l/`
7×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`pow-prod-up`
4×	`sum-cubes` `sub-div` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 184

Calls

4 calls:

71.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
17.0ms	(pow (sqrt (+ x 1.0)) 3)
40.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
153.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
77.0ms	(pow (sqrt (+ x 1.0)) 3)
71.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
285.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify2.4s

Counts: 196 → 196

prune527.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (- (* 1.0 1.0) x) 1.0) (- 1.0 (sqrt (+ x 1.0))))
0.2b	(/ x (/ (- (- (* 1.0 1.0) x) 1.0) (- 1.0 (sqrt (+ x 1.0)))))
3.7b	(- (- (* 1.0 1.0) x) 1.0)
3.8b	(- 1.0 (sqrt (+ x 1.0)))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

274×	`add-sqr-sqrt`
258×	`times-frac`
220×	`*-un-lft-identity`
102×	`add-cube-cbrt`
86×	`difference-of-squares`
59×	`distribute-lft-out--`
42×	`associate-/r*`
27×	`sqrt-prod`
11×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
8×	`flip3--` `flip--` `associate-/l*`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `diff-log` `div-exp`
3×	`sub-neg`
2×	`frac-2neg` `associate--l+` `clear-num` `associate-/l/`
1×	`associate--l-` `div-sub`

Counts

4 → 253

Calls

4 calls:

164.0ms	(/ (- (- (* 1.0 1.0) x) 1.0) (- 1.0 (sqrt (+ x 1.0))))
94.0ms	(/ x (/ (- (- (* 1.0 1.0) x) 1.0) (- 1.0 (sqrt (+ x 1.0)))))
78.0ms	(- (- (* 1.0 1.0) x) 1.0)
37.0ms	(- 1.0 (sqrt (+ x 1.0)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(/ (- (- (* 1.0 1.0) x) 1.0) (- 1.0 (sqrt (+ x 1.0))))
89.0ms	(/ x (/ (- (- (* 1.0 1.0) x) 1.0) (- 1.0 (sqrt (+ x 1.0)))))
22.0ms	(- (- (* 1.0 1.0) x) 1.0)
67.0ms	(- 1.0 (sqrt (+ x 1.0)))

simplify1.6s

Counts: 265 → 265

prune690.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify13.0ms

end0.0ms

sample676.0ms

Algorithm

intervals

Results

374.0ms	7995×	body	80	valid
71.0ms	2602×	body	80	nan
1.0ms	5×	body	1280	valid