Details

sample113.0ms

Algorithm

intervals

Results

27.0ms	64×	body	640	valid
22.0ms	243×	body	80	nan
22.0ms	40×	body	1280	valid
13.0ms	123×	body	80	valid
10.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	15
2	15
1	11
0	8

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.2b	(/ 1 (sqrt (+ x 1)))
0.3b	(/ 1 (sqrt x))
2.4b	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `times-frac`
64×	`sqrt-prod`
42×	`add-cube-cbrt`
25×	`difference-of-squares`
13×	`associate-/r*` `distribute-lft-out--`
12×	`add-exp-log`
9×	`pow1`
8×	`add-cbrt-cube` `distribute-lft-out`
6×	`div-inv` `pow-flip` `associate-/l*` `add-log-exp`
4×	`sqrt-div` `div-exp` `insert-posit16`
3×	`sqrt-pow1` `pow1/2`
2×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `associate-/r/` `flip-+` `inv-pow`
1×	`rem-sqrt-square` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

4 → 167

Calls

4 calls:

9.0ms	(sqrt (+ x 1))
17.0ms	(/ 1 (sqrt (+ x 1)))
10.0ms	(/ 1 (sqrt x))
60.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(sqrt (+ x 1))
36.0ms	(/ 1 (sqrt (+ x 1)))
44.0ms	(/ 1 (sqrt x))
91.0ms	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

simplify7.5s

Counts

179 → 179

Iterations

Iter	Nodes
3	2042
2	940
1	393
0	208

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1))
0.1b	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
2.4b	(- (sqrt (+ x 1)) (sqrt x))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`sqrt-prod`
36×	`*-un-lft-identity`
12×	`difference-of-squares`
11×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`times-frac` `associate-/l*`
9×	`pow1` `distribute-lft-out--`
7×	`associate-r`
6×	`sqrt-div` `associate-l` `add-log-exp`
5×	`distribute-lft-out`
4×	`associate-*r/` `insert-posit16` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-unprod` `diff-log` `div-sub` `-commutative` `div-inv`

Counts

4 → 112

Calls

4 calls:

4.0ms	(sqrt (+ x 1))
61.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
30.0ms	(* (sqrt x) (sqrt (+ x 1)))
56.0ms	(- (sqrt (+ x 1)) (sqrt x))

series361.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ x 1))
213.0ms	(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
58.0ms	(* (sqrt x) (sqrt (+ x 1)))
60.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify3.3s

Counts

124 → 124

Iterations

Iter	Nodes
3	4682
2	1250
1	397
0	164

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.3b	(* (sqrt x) (sqrt (+ x 1)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
78×	`times-frac`
55×	`sqrt-prod`
47×	`add-sqr-sqrt`
45×	`distribute-lft-out`
39×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
14×	`div-exp`
9×	`pow1`
8×	`associate-/r/`
7×	`cbrt-undiv` `associate-/r` `associate-r*`
6×	`flip3-+` `associate-l` `flip-+` `add-log-exp`
5×	`prod-exp`
4×	`sqrt-div` `associate-*r/` `insert-posit16` `div-inv` `unswap-sqr`
3×	`rec-exp` `1-exp` `pow-prod-down` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `sum-log` `sqrt-unprod` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

25.0ms	(+ (sqrt (+ x 1)) (sqrt x))
50.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
71.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
36.0ms	(* (sqrt x) (sqrt (+ x 1)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (sqrt (+ x 1)) (sqrt x))
90.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
240.0ms	(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
78.0ms	(* (sqrt x) (sqrt (+ x 1)))

simplify1.0m

Counts

182 → 182

Iterations

Iter	Nodes
3	7329
2	1659
1	541
0	226

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.3b	(* (sqrt x) (sqrt (+ x 1)))
0.3b	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

2754×	`times-frac`
2239×	`sqrt-prod`
2068×	`*-un-lft-identity`
765×	`distribute-lft-out`
737×	`add-sqr-sqrt`
729×	`add-cube-cbrt`
155×	`associate-/r/`
92×	`div-inv`
64×	`flip3-+` `flip-+`
44×	`associate-/r*`
33×	`associate-/l*`
31×	`sqrt-div`
23×	`add-exp-log`
19×	`add-cbrt-cube`
10×	`pow1`
9×	`div-exp`
7×	`cbrt-undiv` `associate-r`
6×	`associate-l`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `pow-prod-down`
2×	`rec-exp` `sqrt-undiv` `sqrt-pow1` `pow1/2` `sqrt-unprod` `1-exp` `prod-exp` `associate-*r/` `cbrt-unprod` `pow-flip` `inv-pow`
1×	`*-commutative` `associate-/l/`

Counts

4 → 1069

Calls

4 calls:

26.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms	(* (sqrt x) (sqrt (+ x 1)))
72.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
66.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
54.0ms	(* (sqrt x) (sqrt (+ x 1)))
188.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))

simplify1.2s

Counts

1081 → 1081

Iterations

Iter	Nodes
1	2532
0	1000

prune8.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes48.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

763.0ms	7976×	body	80	nan
477.0ms	1901×	body	640	valid
364.0ms	1148×	body	1280	valid
294.0ms	4067×	body	80	valid
138.0ms	581×	body	320	valid
54.0ms	303×	body	160	valid