Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	53×	body	1280	valid
5.0ms	217×	body	80	nan
3.0ms	139×	body	80	valid
3.0ms	33×	body	640	valid
1.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify14.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

14.0ms	(sqrt (+ x 1.0))
98.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series152.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(sqrt (+ x 1.0))
121.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts: 41 → 41

prune129.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 80

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
37.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
85.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1.0))
92.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
152.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify814.0ms

Counts: 89 → 89

prune296.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
29×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
12×	`times-frac` `distribute-lft-out`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
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 → 167

Calls

4 calls:

8.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(sqrt (sqrt (+ x 1.0)))
88.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
74.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (sqrt (+ x 1.0)))
131.0ms	(sqrt (sqrt (+ x 1.0)))
187.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
50.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify1.6s

Counts: 179 → 179

prune573.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))
0.3b	(cbrt (+ x 1.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

59.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series586.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
133.0ms	(cbrt (+ x 1.0))
154.0ms	(cbrt (+ x 1.0))
122.0ms	(cbrt (+ x 1.0))

simplify2.0s

Counts: 107 → 107

prune669.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes61.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.8s

end0.0ms

sample1.8s

Algorithm

intervals

Results

663.0ms	1735×	body	1280	valid
270.0ms	7899×	body	80	nan
217.0ms	4028×	body	80	valid
180.0ms	1259×	body	640	valid
140.0ms	648×	body	320	valid
19.0ms	330×	body	160	valid