Details

sample147.0ms

Algorithm

intervals

Results

62.0ms	273×	body	160	nan
41.0ms	593×	body	80	nan
22.0ms	256×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
8	2237
7	713
6	239
5	97
4	60
3	35
2	19
1	16
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) 1)
0.0b	(+ x (sqrt (- (* x x) 1)))
26.4b	(sqrt (- (* x x) 1))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-log-exp`
6×	`sqrt-prod`
4×	`pow1` `add-cube-cbrt` `difference-of-squares`
3×	`add-cbrt-cube` `add-exp-log` `insert-posit16`
2×	`flip3--` `sqrt-div` `difference-of-sqr-1` `flip--`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+` `distribute-lft-out`

Counts

3 → 48

Calls

3 calls:

14.0ms	(- (* x x) 1)
23.0ms	(+ x (sqrt (- (* x x) 1)))
16.0ms	(sqrt (- (* x x) 1))

series219.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(- (* x x) 1)
73.0ms	(+ x (sqrt (- (* x x) 1)))
75.0ms	(sqrt (- (* x x) 1))

simplify1.7s

Counts

57 → 57

Iterations

Iter	Nodes
4	4096
3	1327
2	504
1	228
0	101

prune497.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`sqrt-prod`
15×	`*-un-lft-identity`
14×	`sqrt-div`
10×	`associate-r`
8×	`pow1` `add-cube-cbrt`
7×	`associate-l`
5×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `insert-posit16` `flip--`
2×	`associate-l/` `associate-r/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 73

Calls

3 calls:

4.0ms	(sqrt (+ x 1))
5.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
37.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series232.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(sqrt (+ x 1))
102.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
88.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify3.8s

Counts

82 → 82

Iterations

Iter	Nodes
4	5834
3	1930
2	718
1	312
0	142

prune768.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sqrt (+ x 1)))
0.5b	(cbrt (sqrt (+ x 1)))
0.5b	(* (* (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt (- x 1)))
0.5b	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

232×	`sqrt-div`
178×	`cbrt-div`
140×	`frac-times`
89×	`flip3-+` `flip-+`
70×	`associate-*l/`
62×	`cbrt-prod`
48×	`add-sqr-sqrt`
43×	`*-un-lft-identity` `sqrt-prod`
28×	`associate-*r/`
27×	`flip3--` `flip--`
22×	`add-cube-cbrt`
20×	`pow1` `associate-r`
15×	`add-exp-log`
14×	`swap-sqr`
11×	`associate-l`
9×	`add-cbrt-cube` `unswap-sqr`
8×	`pow1/3` `pow-prod-down` `distribute-lft-out`
7×	`prod-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `difference-of-squares`
1×	`pow2` `pow-plus` `difference-of-sqr-1` `distribute-lft-out--`

Counts

4 → 215

Calls

4 calls:

3.0ms	(cbrt (sqrt (+ x 1)))
3.0ms	(cbrt (sqrt (+ x 1)))
167.0ms	(* (* (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt (- x 1)))
30.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(cbrt (sqrt (+ x 1)))
39.0ms	(cbrt (sqrt (+ x 1)))
98.0ms	(* (* (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))) (cbrt (sqrt (+ x 1)))) (sqrt (- x 1)))
41.0ms	(* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))

simplify925.0ms

Counts

227 → 227

Iterations

Iter	Nodes
2	2362
1	933
0	362

prune3.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	14
1	14
0	9

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.7s	16393×	body	80	nan
1.5s	7679×	body	160	nan
698.0ms	8000×	body	80	valid