Details

sample75.0ms

Algorithm

intervals

Results

17.0ms	138×	body	80	valid
15.0ms	264×	body	80	nan
14.0ms	44×	body	1280	valid
10.0ms	43×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	28
2	28
1	23
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
3.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite59.0ms

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-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `distribute-lft-out`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `flip--`

Counts

2 → 37

Calls

2 calls:

17.0ms	(sqrt (+ x 1))
41.0ms	(- (sqrt (+ x 1)) (sqrt x))

series115.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(sqrt (+ x 1))
79.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.3s

Counts

43 → 43

Iterations

Iter	Nodes
5	3357
4	1632
3	918
2	511
1	301
0	81

prune271.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.1b	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
7×	`add-exp-log`
6×	`associate-/r*`
5×	`pow1` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `insert-posit16` `associate-/l*`
2×	`sqrt-div` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

3 → 78

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
24.0ms	(+ (sqrt (+ x 1)) (sqrt x))
34.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1))
71.0ms	(+ (sqrt (+ x 1)) (sqrt x))
81.0ms	(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.0s

Counts

87 → 87

Iterations

Iter	Nodes
4	2263
3	1357
2	780
1	435
0	120

prune716.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.2b	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`pow1` `sqrt-div`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l` `add-exp-log`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`pow2` `cbrt-undiv` `rec-exp` `clear-num` `rem-square-sqrt` `frac-2neg` `pow-plus` `sqrt-unprod` `1-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 169

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x 1)))
10.0ms	(sqrt (sqrt (+ x 1)))
33.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
40.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(sqrt (sqrt (+ x 1)))
61.0ms	(sqrt (sqrt (+ x 1)))
103.0ms	(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
42.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.5s

Counts

181 → 181

Iterations

Iter	Nodes
3	2803
2	1446
1	774
0	211

prune1.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cbrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 124

Calls

4 calls:

7.0ms	(cbrt (sqrt (+ x 1)))
6.0ms	(cbrt (sqrt (+ x 1)))
6.0ms	(cbrt (sqrt (+ x 1)))
32.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt (sqrt (+ x 1)))
42.0ms	(cbrt (sqrt (+ x 1)))
62.0ms	(cbrt (sqrt (+ x 1)))
70.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

simplify1.5s

Counts

136 → 136

Iterations

Iter	Nodes
4	3713
3	1917
2	1022
1	580
0	149

prune1.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	11
1	11
0	7

end0.0ms

sample2.1s

Algorithm

intervals

Results

766.0ms	1749×	body	1280	valid
430.0ms	8045×	body	80	nan
321.0ms	1226×	body	640	valid
192.0ms	4078×	body	80	valid
108.0ms	639×	body	320	valid
52.0ms	308×	body	160	valid