Details

sample86.0ms

Algorithm

intervals

Results

30.0ms	238×	body	160	nan
26.0ms	565×	body	80	nan
14.0ms	256×	body	80	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	1825
6	472
5	156
4	60
3	35
2	19
1	16
0	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) 1)
0.0b	(+ x (sqrt (- (* x x) 1)))
31.2b	(sqrt (- (* x x) 1))

rewrite51.0ms

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:

16.0ms	(- (* x x) 1)
20.0ms	(+ x (sqrt (- (* x x) 1)))
14.0ms	(sqrt (- (* x x) 1))

series214.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(- (* x x) 1)
88.0ms	(+ x (sqrt (- (* x x) 1)))
69.0ms	(sqrt (- (* x x) 1))

simplify1.7s

Counts

57 → 57

Iterations

Iter	Nodes
done	5003
3	1879
2	582
1	231
0	101

prune172.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.4b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 56

Calls

2 calls:

5.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
25.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series161.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
84.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify2.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	2248
2	738
1	304
0	132

prune246.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	14
1	14
0	9

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	16814×	body	80	nan
1.2s	7741×	body	160	nan
695.0ms	8000×	body	80	valid