Details

sample43.0ms

Algorithm

intervals

Results

12.0ms	48×	body	640	valid
8.0ms	248×	body	80	nan
7.0ms	49×	body	1280	valid
4.0ms	132×	body	80	valid
2.0ms	20×	body	320	valid
0.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1))
1.9b	(- (sqrt (+ x 1)) (sqrt x))

rewrite92.0ms

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:

13.0ms	(sqrt (+ x 1))
77.0ms	(- (sqrt (+ x 1)) (sqrt x))

series401.0ms

Counts

2 → 6

Calls

2 calls:

332.0ms	(sqrt (+ x 1))
69.0ms	(- (sqrt (+ x 1)) (sqrt x))

simplify1.8s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
4	2095
3	848
2	350
1	165
0	81

prune165.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (+ x 1)) (sqrt x))
0.0b	(sqrt (+ x 1))
0.1b	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

rewrite124.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`insert-posit16`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

3 → 83

Calls

3 calls:

37.0ms	(+ (sqrt (+ x 1)) (sqrt x))
6.0ms	(sqrt (+ x 1))
76.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

series196.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+ (sqrt (+ x 1)) (sqrt x))
31.0ms	(sqrt (+ x 1))
108.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))

simplify2.5s

Counts

92 → 92

Iterations

Iter	Nodes
done	5004
4	4239
3	1697
2	688
1	274
0	133

prune298.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
0.1b	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
0.2b	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 320

Calls

4 calls:

45.0ms	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
53.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
91.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
313.0ms	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x))))
100.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
93.0ms	(/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))
108.0ms	(* (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ (+ 1 0) (+ (sqrt (+ x 1)) (sqrt x)))))

simplify2.4s

Counts

332 → 332

Iterations

Iter	Nodes
done	5000
3	2376
2	961
1	467
0	236

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

702×	`sqrt-prod`
655×	`*-un-lft-identity`
461×	`times-frac`
264×	`distribute-lft-out`
197×	`add-sqr-sqrt`
192×	`add-cube-cbrt`
30×	`associate-/l*`
26×	`associate-/r/`
15×	`associate-/r*`
14×	`flip3-+` `flip-+`
13×	`div-inv`
10×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
6×	`sqrt-div`
4×	`rem-sqrt-square` `sqrt-pow1` `insert-posit16` `add-log-exp`
3×	`div-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/2` `pow-flip` `inv-pow`
1×	`rec-exp` `sqrt-undiv` `1-exp` `associate-/l/`

Counts

4 → 401

Calls

4 calls:

49.0ms	(sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
47.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
82.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
123.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

series566.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x))))
150.0ms	(sqrt (+ (sqrt (+ x 1)) (sqrt x)))
122.0ms	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
102.0ms	(/ (sqrt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

simplify2.0s

Counts

413 → 413

Iterations

Iter	Nodes
done	5007
3	2932
2	1184
1	609
0	365

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes76.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample2.2s

Algorithm

intervals

Results

931.0ms	1671×	body	1280	valid
408.0ms	8127×	body	80	nan
346.0ms	1227×	body	640	valid
192.0ms	4169×	body	80	valid
83.0ms	618×	body	320	valid
27.0ms	315×	body	160	valid